INTRODUCTION
The necessity of vibration isolation
Vibration in engineering systems can lead to damage and instability in machinery and equipment, while also adversely affecting human health and work efficiency Unwanted vibrations reduce comfort for individuals operating within these systems For instance, vehicles experience vibrations from rough road surfaces and engine noise, even with suspension systems in place.
Low-frequency vibrations, particularly those below 25Hz, pose significant risks to the human spine, as highlighted by various studies Research has been conducted to assess the level of discomfort experienced by individuals exposed to these vibrations Notably, a study involving twelve participants evaluated the discomfort associated with vibrations under 5Hz, further emphasizing the potential dangers of low-frequency exposure.
To effectively reduce unwanted vibrations, it is essential to eliminate their source; however, this is not always feasible, as vibrations can occur during the operation of machinery and vehicles on rough surfaces Therefore, incorporating intelligent isolators between the vibrating source and the affected object is crucial for managing these vibrations.
Traditional linear isolators, which consist of an elastic element and a damper arranged in parallel, struggle to effectively mitigate the transmission of low-frequency vibrations to other system components Consequently, this thesis aims to develop an adaptive low-frequency vibration isolator to address this challenge.
The study on quasi-zero stiffness vibration isolation systems explores innovative methods to minimize vibrations in various applications These systems are designed to achieve near-zero stiffness, allowing for enhanced performance in environments susceptible to disturbances By focusing on the mechanics and design principles of these systems, the research aims to improve stability and reduce the impact of external vibrations The findings highlight the potential benefits of implementing quasi-zero stiffness solutions in fields such as engineering, construction, and manufacturing, ultimately leading to increased efficiency and longevity of sensitive equipment.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
The aim of the research
This research focuses on creating an advanced quasi-zero stiffness adaptive vibration isolation model that enhances low-frequency isolation capabilities It aims to improve vibration attenuation rates compared to traditional isolators while maintaining load support and minimizing deformation.
In order to achieve the overall aim, the specific problems are considered as following:
- Studying comprehensively types of vibration isolation model including passive and active, advantage and limitation of each type
- Developing an innovated quasi-zero stiffness adaptive vibration isolation model featuring non-steel elastic element
- Studying and identifying the restoring properties of elastic elements without steel material
- Analyzing the nonlinear dynamic response comprising bifurcation as well as jump frequency phenomenon;
- Simulating, experimenting and evaluating the proposed model
The scope of this thesis is:
- Non-steel elastic element is the pneumatic spring
- Isolation region is within 32-63 (rad/s) corresponding to 5-10 (Hz)
This article explores the concept of quasi-zero stiffness vibration isolation systems, which are designed to minimize vibrations effectively These systems utilize innovative engineering principles to achieve low stiffness, allowing for enhanced stability and performance in various applications The study highlights the advantages of quasi-zero stiffness systems in improving vibration isolation, making them essential for sensitive equipment and structures By reducing the impact of external disturbances, these systems contribute significantly to the longevity and reliability of technological installations Overall, the research underscores the importance of advancing vibration isolation technologies for better operational efficiency.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
Inheritability: studying and synthesizing previous works related to vibration isolation methods to develop a vibration isolation model featuring quasi-zero stiffness characteristic
Analysis: establishing the stiffness model, dynamic equation, vibration transmissibility of the system through using thermodynamic laws, ideal gas equations, mechanism laws, etc
Simulation: from analysis results, the simulation method is realized to determine nonlinear dynamic response and isolated effectiveness of the system
Experiment: verifying and comparing the dynamic response and isolation effectiveness of the proposed model compared with that of the equivalent linear model
1.6 The contents of the thesis:
In order to achieve the objectives above, the thesis” Study on the quasi-zero stiffness vibration isolation system” will solve some problems as following:
- Studying on the demand of the vibration isolation especially under low frequency excitation
- Referring to the previous studies about the vibration isolation methods
- Presenting the necessary of the thesis, the object, scope and objectives of the thesis Moreover, the scientific contribution and application of the thesis have also showed
The fundamental principles of relative theories are essential for analyzing the dynamic response, vibration transmissibility, and stability of the proposed model Key theories utilized include thermodynamics, Normal form, Multi-scale analysis, and Poincaré maps Additionally, models such as the Berg model and Kelvin-Voigt are employed to examine the characteristics of the suggested system.
The study focuses on quasi-zero stiffness vibration isolation systems, which are designed to minimize vibrations effectively These systems utilize innovative engineering principles to achieve low stiffness characteristics, enhancing their performance in various applications By significantly reducing vibration transmission, they offer improved stability and protection for sensitive equipment The research highlights the advantages of quasi-zero stiffness systems in maintaining operational efficiency and prolonging the lifespan of machinery Overall, the findings underscore the importance of advanced vibration isolation techniques in modern engineering solutions.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
Quasi-zero stiffness adaptive vibration isolation model using a rubber air spring:
- An innovated quasi-zero stiffness adaptive vibration isolation system using rubber air spring is introduced
- The force models of which such as compressed air, frictional and viscoelastic forces are analyzed
- An experimental model is set up to identify the restoring characteristic of a rubber air spring
- The stiffness model and dynamic equation is established and the complex dynamic analysis of the system was conducted
- The effects of configurative parameters on stiffness curve and equilibrium position are analyzed
- The vibration transmissibility and stability of the system was examined, the jump and bifurcation phenomena were considered
- An experiment to compare the isolation effectiveness between the QSAVIM and ETVIM are carried out
Quasi-zero stiffness adaptive vibration isolator using a pneumatic spring:
- Another model of the isolator which is modified by replacing the air spring by a pneumatic cylinder
- The stiffness of a pneumatic cylinder is analyzed and the frictional model is investigated by using virtual prototyping technology
- The stiffness of the modified model is found The stiffness of each mechanism and the equilibrium position of the modified model are also analyzed
- The effects of the configuration such as the auxiliary tank volume as well as the wedge angle on the system stiffness are considered
This article examines the relationship between frequency and amplitude, as well as the stability of the steady-state solution It also compares the amplitude-frequency curves derived from the Multi-scale method with those obtained using the fourth-order Runge-Kutta algorithm.
The study focuses on quasi-zero stiffness vibration isolation systems, which are designed to effectively reduce vibrations These systems utilize innovative engineering principles to achieve minimal stiffness, allowing for superior vibration absorption By examining their performance, the research aims to enhance the understanding of their applications in various fields, including engineering and construction The findings highlight the potential benefits of implementing quasi-zero stiffness systems in environments where vibration control is critical Overall, this study contributes valuable insights into the development and optimization of advanced vibration isolation technologies.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
Research scope and object
The scope of this thesis is:
- Non-steel elastic element is the pneumatic spring
- Isolation region is within 32-63 (rad/s) corresponding to 5-10 (Hz)
The study focuses on quasi-zero stiffness vibration isolation systems, which are designed to minimize vibrations effectively These systems utilize innovative engineering principles to achieve near-zero stiffness, allowing for enhanced performance in various applications By reducing the transmission of vibrations, they provide significant benefits in maintaining stability and protecting sensitive equipment The research highlights the importance of these systems in fields requiring high precision and reliability, showcasing their potential to revolutionize vibration control technologies.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
Research approach
Inheritability: studying and synthesizing previous works related to vibration isolation methods to develop a vibration isolation model featuring quasi-zero stiffness characteristic
Analysis: establishing the stiffness model, dynamic equation, vibration transmissibility of the system through using thermodynamic laws, ideal gas equations, mechanism laws, etc
Simulation: from analysis results, the simulation method is realized to determine nonlinear dynamic response and isolated effectiveness of the system
Experiment: verifying and comparing the dynamic response and isolation effectiveness of the proposed model compared with that of the equivalent linear model
1.6 The contents of the thesis:
In order to achieve the objectives above, the thesis” Study on the quasi-zero stiffness vibration isolation system” will solve some problems as following:
- Studying on the demand of the vibration isolation especially under low frequency excitation
- Referring to the previous studies about the vibration isolation methods
- Presenting the necessary of the thesis, the object, scope and objectives of the thesis Moreover, the scientific contribution and application of the thesis have also showed
To analyze the dynamic response, vibration transmissibility, and stability of the proposed model, various relative theories are utilized, including thermodynamics, Normal form, Multi-scale analysis, and Poincaré maps Additionally, models such as the Berg model and Kelvin-Voigt model are employed to evaluate the characteristics of the suggested system.
The study focuses on the development and analysis of quasi-zero stiffness vibration isolation systems, which are designed to minimize vibrations effectively These systems utilize innovative engineering principles to achieve low stiffness characteristics, enhancing their ability to absorb and isolate vibrations By examining the performance and applications of these systems, the research aims to provide insights into their potential benefits in various fields, including engineering and construction The findings highlight the importance of quasi-zero stiffness technology in improving stability and comfort in environments susceptible to vibrations.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
Quasi-zero stiffness adaptive vibration isolation model using a rubber air spring:
- An innovated quasi-zero stiffness adaptive vibration isolation system using rubber air spring is introduced
- The force models of which such as compressed air, frictional and viscoelastic forces are analyzed
- An experimental model is set up to identify the restoring characteristic of a rubber air spring
- The stiffness model and dynamic equation is established and the complex dynamic analysis of the system was conducted
- The effects of configurative parameters on stiffness curve and equilibrium position are analyzed
- The vibration transmissibility and stability of the system was examined, the jump and bifurcation phenomena were considered
- An experiment to compare the isolation effectiveness between the QSAVIM and ETVIM are carried out
Quasi-zero stiffness adaptive vibration isolator using a pneumatic spring:
- Another model of the isolator which is modified by replacing the air spring by a pneumatic cylinder
- The stiffness of a pneumatic cylinder is analyzed and the frictional model is investigated by using virtual prototyping technology
- The stiffness of the modified model is found The stiffness of each mechanism and the equilibrium position of the modified model are also analyzed
- The effects of the configuration such as the auxiliary tank volume as well as the wedge angle on the system stiffness are considered
This study investigates the relationship between frequency and amplitude, along with the stability of the steady-state solution Additionally, it compares the amplitude-frequency curves derived from the Multi-scale method and the fourth-order Runge-Kutta algorithm.
The study focuses on quasi-zero stiffness vibration isolation systems, which are designed to effectively reduce vibrations in various applications These systems utilize innovative engineering principles to achieve minimal stiffness, allowing for enhanced performance in isolating vibrations By analyzing the characteristics and benefits of quasi-zero stiffness designs, the research highlights their potential in improving stability and comfort in sensitive environments The findings suggest that these systems can significantly enhance vibration control, making them a valuable solution for industries requiring precision and reliability.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
Organization of thesis
Chapter 1 Introduction Chapter 2 Literature review Chapter 3 Fundamental of relative theories Chapter 4 Quasi-zero stiffness adaptive vibration isolator using rubber air spring Chapter 5: Quasi-zero stiffness adaptive vibration isolator using pneumatic cylinder Chapter 6 Conclusions and Future works
The obtained results
- The physical models of the quasi-zero stiffness adaptive vibration isolation system using rubber air spring and pneumatic cylinder are described
- The mathematical model of the proposed system is defined
- The vibration transmissibility equation is found out and analyzed
- The effects of the configuration on the system stiffness are investigated
- The test - rig to identify the characteristics of a rubber air spring as well as pneumatic cylinder is set up
- An experiment to compare the isolation effectiveness between the QSAVIM and ETVIM are carried out
- A novel QSAVIM design procedure is suggested
The study focuses on quasi-zero stiffness vibration isolation systems, which are designed to effectively minimize vibrations in various applications These systems utilize innovative engineering principles to achieve a near-zero stiffness response, allowing for superior vibration absorption and enhanced stability By analyzing their performance characteristics, the research aims to optimize the design and implementation of these systems in real-world scenarios, thereby improving the overall effectiveness of vibration isolation solutions.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
LITERATURE REVIEWS
Vibration Isolation
Fig 2.1 A conventional vibration isolation system [4]
Fig 2.1 illustrates a conventional linear vibration isolation system comprising a spring (K) connected in parallel with a damper (C) to bear a load mass (M) The vibration transmissibility is given in [4] as below:
The study focuses on quasi-zero stiffness vibration isolation systems, which are designed to effectively reduce vibrations in various applications These systems utilize innovative engineering principles to achieve minimal stiffness, allowing for enhanced performance in vibration mitigation By analyzing the dynamics and behavior of these systems, the research aims to improve their efficiency and reliability in real-world scenarios The findings highlight the potential benefits of implementing quasi-zero stiffness designs in engineering solutions, contributing to advancements in vibration control technology.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM z is the displacement of the mass in mm z e is the excitation in mm
is the excited frequency in rad/s n K M /
is the natural frequency in rad/s
Fig 2.2 The transmissibility curve of the conventional vibration isolation system
When the excitation frequency is below 2ωn, the mass experiences a higher vibration level compared to the excitation In contrast, the linear isolator effectively reduces vibration transmissibility once the excitation frequency exceeds this threshold.
2 n Besides, it is worthy to see that the lower the natural frequency, the higher the isolation effectiveness is and the more the isolation region is enlarged
The study focuses on quasi-zero stiffness vibration isolation systems, which are designed to effectively minimize vibrations in various applications These systems utilize a unique mechanism that allows for minimal stiffness, thereby enhancing their ability to absorb and dampen vibrations By analyzing the performance and characteristics of these systems, the research aims to improve their efficiency and applicability in fields requiring high precision and stability The findings highlight the potential benefits of implementing quasi-zero stiffness systems in engineering and technology to achieve superior vibration control.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
FUNDAMENTAL OF RELATIVE THEORIES
Air spring
An air spring is a system that utilizes compressed air as its elastic element, typically classified into rubber bellow and pneumatic cylinder types Its load-bearing capacity is determined by the effective area and internal air pressure, offering advantages such as low static deformation, adjustable elasticity through pressure changes, and a higher energy-storage capacity compared to mechanical springs Air springs also feature lower resonance frequencies, reduced static deformation, and a more compact design than mechanical springs Additionally, they can function as dampers, contributing to their growing popularity in various applications Therefore, exploring the use of air springs in vibration isolation systems is essential for enhancing low-frequency isolation.
This article explores the concept of quasi-zero stiffness vibration isolation systems, which are designed to effectively mitigate vibrations in various applications These innovative systems offer minimal stiffness, allowing for enhanced performance in isolating vibrations compared to traditional methods By focusing on the mechanics and design principles behind quasi-zero stiffness systems, the study highlights their potential advantages, including improved stability and reduced transmission of vibrations The findings suggest that such systems can significantly benefit industries requiring precise vibration control, ultimately leading to advancements in engineering and technology.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
3.1.2 General structure of rubber bellow
Fig.3.1 Configuration of a rubber air spring: (a) Reversible sleeve, (b) Convoluted [50]
There are basic types of rubber bellow such as reversible sleeve, convoluted as shown in Fig 3.1 It comprises some following parts:
- Mounting stud (1), which is a part, is fixed on the bead plate used to connect the air spring to the suspension
- Combination stud (2) is to combine the mounting stud and the air fitting
The blind nut (3) serves as an alternative mounting system to traditional studs and is a fixed component of the bead plate Additionally, it features a tapped air fitting hole that allows for air to enter the part efficiently.
- Air fitting hole (4) is a hole allows air entrancing which is tapped
The bead plate, constructed from corrosion-resistant steel, securely seals the top end of the flexible member This component is permanently crimped to the bellows, ensuring an airtight assembly It is then attached to the vehicle structure using studs, blind nuts, brackets, or pins for reliable installation.
The study focuses on the quasi-zero stiffness vibration isolation system, which is designed to effectively reduce vibrations in various applications This innovative system utilizes minimal stiffness to achieve high levels of vibration isolation, making it particularly beneficial in sensitive environments By analyzing its performance, the research highlights the advantages of using quasi-zero stiffness technology, including improved stability and enhanced durability Overall, the findings underscore the significance of this vibration isolation system in advancing engineering solutions for noise and vibration control.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
Rubber bellows are a crucial component of air springs, designed to hold a column of compressed air They consist of multiple layers, including an inner rubber liner, a first ply of fabric-reinforced rubber with cords positioned at a specific bias angle, a second ply of fabric-reinforced rubber laid in the opposite direction of the first, and an outer cover made of rubber.
- Internal bumper (7) is an internal device to prevent damage to the air spring during times when there is no air in the system
- Piston (8) which may be made of aluminum, steel, or engineered composites
The pistons with the thread holes are used to ensure the assembly to the mounting surface
- Piston bolt which (9) attached the piston to the bellows assembly
- Girdle hoop (optional) (10) is a ring between the convolutions of the convoluted-type air spring
Fig 3.2 Structure of the rubber bellow
The study focuses on quasi-zero stiffness vibration isolation systems, which are designed to minimize vibrations in various applications These systems utilize innovative engineering principles to achieve a near-zero stiffness response, effectively isolating sensitive equipment from external disturbances The research highlights the advantages of such systems in enhancing performance and reliability, particularly in environments where traditional isolation methods fall short By examining the mechanics and applications of quasi-zero stiffness systems, this study contributes valuable insights into advanced vibration control technologies.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
Mathematical model of the compressed air
Supposing a working chamber as shown in Fig 3.3, according to the first law of thermodynamics [51], the energy balance in the working chamber volume is expressed by Eq (3.1)
The pneumatic working chamber's schematic diagram illustrates the energy dynamics involved in air flow The equation \( dE = dE_{in} - dE_{out} - dE_{ch} - dE_{ae} - Q \) represents the balance of energies, where \( dE_{in} \) and \( dE_{out} \) denote the air energies at the input and output lines, respectively Additionally, \( dE_{ch} \) signifies the energy stored in the spring, \( dE_{ae} \) accounts for the work done by air expansion, and \( Q \) represents heat exchange with the environment The energies can be quantified as follows: \( dE_{in} = C_{p} T_{in} G_{in} \), \( dE_{out} = C_{p} T_{out} G_{out} \), \( dE_{ch} = C_{v} m dT + C_{p} T dm \), and \( dE_{ae} = P dV \).
C p and C v are specific heat capacities at constant pressure and volume, respectively,
T in is the temperature of air at the inlet, m air , P, V and T are the mass, pressure, volume and temperature of the air in the pneumatic working chamber,
G in and G out are mass low rates at inlet and outlet, m; P; V; T
The study focuses on quasi-zero stiffness vibration isolation systems, which are designed to effectively minimize vibrations in various applications These systems utilize unique mechanisms that allow them to maintain low stiffness levels, thereby enhancing their ability to absorb and dissipate vibrational energy By exploring the principles and performance characteristics of quasi-zero stiffness systems, the research aims to improve vibration control technologies The findings may lead to advancements in engineering solutions for sensitive equipment and structures, ensuring greater stability and longevity in environments prone to vibrations.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM α is the heat transfer coefficient, a is the heat transfer surface area,
T is the temperature difference between the air inside working chamber and environment
In analyzing the air spring's performance, we assume that heat transfer between the air in the working chamber and the surrounding environment is negligible, treating the air as an ideal gas.
(3.3) herein: n=C p /C v is the ratio of specific heat capacity,
R air is the gas constant (R air (7J/kg.K).
Frictional model of pneumatic cylinder and rubber material
Friction arises from the relative motion between a rod and a cylinder, as explained in [52] The friction model (F f) integrates Coulomb friction, viscous friction, and static friction This model's behavior is illustrated by a Stribeck curve, which depicts the friction characteristics during both the extending and retracting strokes of a pneumatic cylinder, as shown in Fig 3.4.
The study focuses on the quasi-zero stiffness vibration isolation system, which offers innovative solutions for minimizing vibrations in various applications This system is designed to achieve low stiffness characteristics, allowing it to effectively dampen vibrations while maintaining stability By exploring the mechanics and benefits of quasi-zero stiffness systems, the research highlights their potential in enhancing performance and reliability in sensitive environments The findings contribute to the ongoing development of advanced vibration control technologies, emphasizing the importance of effective isolation solutions in engineering and industrial applications.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
The frictional force model is calculated as below:
F st is the static friction force, v s is the Stribeck velocity, v r is the relative velocity between two contacting surfaces,
is the viscous friction coefficient, n s is the exponent of the Stribeck curve
3.3.2 Frictional model of rubber material
Friction arises between filled and cord fabric, and is effectively modeled by Berg’s rubber model, which accurately represents the hysteresis loop during the compression of an inflated bellow The friction force is determined by the relationship between the displacement (x) and the reference displacement (x ref).
The study focuses on quasi-zero stiffness vibration isolation systems, which are designed to effectively mitigate vibrations in various applications These systems utilize innovative engineering principles to achieve minimal stiffness, allowing for enhanced performance in isolating vibrations By examining the mechanics and effectiveness of these systems, the research aims to provide insights into their potential applications in industries requiring high precision and stability The findings contribute to the ongoing development of advanced vibration control technologies, highlighting the importance of quasi-zero stiffness designs in improving overall system reliability and efficiency.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
max 2 max 2 for x=x for x>x 1 for xx 1 for x0.905, two positions emerge where stiffness is nearly zero: point A 2 at u ˆ = 0.381 and point A 1 at u ˆ = -0.364, particularly at à=1.2 This indicates that reducing the volume leads to these conditions.
V ac leads to the increase of the pressure ratio For instance, ˆ ac 1 21.045, 13.153
The lowest pressure ratios for achieving quasi-zero stiffness in the system are identified as 1.096, 1.379, and 1.834, corresponding to extremum points B, C, and D The stiffness curve exhibits varying slopes at points A (ûA = 0.008), B (ûB = 0.021), and C, highlighting the relationship between pressure ratios and stiffness characteristics.
The dynamic stiffness values, \( C \) (0.046) and \( D \) (0.083), approach zero at specific points, as shown in Fig 5.23(c), while other positions (A1, A2, etc.) exhibit a nonzero slope This indicates that at the extreme points of the pressure ratio curve, the dynamic stiffness can reach its minimum value within the expected working region This finding is further supported by Fig 5.24(a), which provides the values of \( \alpha \) and the line type annotations in the top-right corner of the figure.
The analysis of equilibrium position
The static equilibrium position was defined in Eq.(4.32), it can be written in dimensionless form as below:
1 ˆ , , wh ˆ s ˆ g 0 f u P F F (5.37) in which the dimensionless restoring force F ˆ s F s / A 1 P wh 1 is determined by substituting Eqs (5.25 - 5.26) into Eq (5.19), obtaining
To obtain the DSEP, the isolated load (M) is calculated as following:
N on -d im e n si o n s tif fn e ss
N on -d im e ns io n st iff n e ss
The study focuses on quasi-zero stiffness vibration isolation systems, which are designed to effectively reduce vibrations in various applications These systems utilize a unique mechanism that minimizes stiffness, allowing for enhanced performance in isolating unwanted vibrations The research highlights the advantages of quasi-zero stiffness systems, including improved stability and responsiveness By exploring their operational principles, the study aims to contribute to the development of more efficient vibration isolation solutions in engineering and technology.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
Fig 5.25 (a) Equilibrium surface in space ( , , u V ˆ ˆ ac 1 ) (b) Stability curves for equilibrium positions created by section plane P wh 1 2 bar.
(Herein V ˆ ac 1 159.01, V ˆ ac 2 0, A 1 0.0079 m , 2 A ˆ 0.01, P wh2 =3.6 bar)
The equilibrium surface in space with Eq (5.41) for V ˆ ac 1 159.01, V ˆ ac 2 0, A 1 0.0079 , m 2 ˆ 0.01 ,
In the analysis of the QSAVIM system at a pressure of P wh2 = 3.6 bar, the equilibrium points are influenced by the pressure ratio μ and the initial pressure P wh1 These points may either align on the flat plane where û = 0 or on a curved surface, suggesting the potential existence of various system states.
Stable equilibrium points Unstable equilibrium points ˆ 1
The study focuses on quasi-zero stiffness vibration isolation systems, which are designed to minimize vibrations effectively These systems utilize innovative engineering principles to achieve low stiffness, allowing for enhanced performance in vibration suppression By analyzing their characteristics and applications, the research aims to improve the understanding and implementation of these advanced isolation systems in various fields The findings highlight the potential benefits of using quasi-zero stiffness designs to enhance stability and reduce unwanted oscillations in sensitive environments.
The QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM can achieve either three or one equilibrium position To demonstrate the stability of these equilibrium points, a curve representing f(û, μ) = 0 is illustrated in the (û, μ) plane, as depicted in Fig 5.25.
(b) is created by the cutting section having P wh1 +ar In the shaded region where
When the pressure ratio μ is positive, the function f(u, μ, P) is also positive; however, outside this region, it becomes negative This indicates that both the quantity and stability of equilibrium positions can change depending on the pressure ratio μ The critical insight is that at point A, the behavior of μ reveals significant implications for the system's dynamics.
A ) is a bifurcation point of the system, at this section, the value of A =1.2 When the
When the parameter \( \mu \) is less than \( \mu_A \), the system exhibits a single stable equilibrium known as the center point at \( \hat{u} = 0 \), as the function \( f(\hat{u}, \mu, P) \) transitions from positive to negative at this point However, when \( \mu \) exceeds \( \mu_A \), the system presents three equilibrium points: two stable centers represented by the solid curve and one unstable saddle point indicated by the dashed line at \( \hat{u} = 0 \) Additionally, in this scenario, the Quasi-Stable Asymptotic Vibrational Inertia Model (QSAVIM) demonstrates quasi-zero stiffness (solid line) at \( \mu = \mu_A \), greater than zero stiffness (dashed line) for \( \mu < \mu_A \), and negative stiffness (dotted line) for higher values of \( \mu \).
Fig 5.26 Quasi-zero stiffness around the DSEP for P wh1 =2 bar and à=1.1(dashed line),
This article explores the quasi-zero stiffness vibration isolation system, emphasizing its unique capabilities in minimizing vibrations The study highlights how this innovative system effectively reduces the impact of external disturbances, making it ideal for sensitive equipment and environments By leveraging advanced engineering principles, the quasi-zero stiffness design offers enhanced stability and performance, which is crucial in various industrial applications The findings underscore the importance of such systems in improving operational efficiency and protecting valuable assets from vibrations.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
Fig 5.27 Equilibrium curve of Eq (5.41) for P wh1 =3.7 bar and V ˆ ac 1 14.21 , the same other parameters as in Fig 5.25 (b) Equilibrium curve enlarged for 8.5, 8.65
(The detailed annotation is presented in the upper-left corner of each figure)
In the case of P wh1 = 3.7 bar and V ˆ ac 1 = 14.21, with consistent parameters as shown in Fig 5.25, the equilibrium curve is illustrated in Fig 5.27 (a) The shaded region indicates where f u ˆ ˆ, (μ P wh1) > 0, while the non-shaded area represents f u ˆ ˆ, (μ P wh1) < 0 Notably, the stability curve for equilibrium points is asymmetric around the DSEP, featuring two bifurcation points at μ A = 8.59 and μ B = 8.63, as detailed in Fig 5.27 (b) An enlarged view of the equilibrium curve is provided within the dashed rectangle of Fig 5.27 (a), with line types explained in the upper-left corner If μ is less than μ A, further implications arise.
Stable equilibrium points Unstable equilibrium points ˆ u
This study focuses on the quasi-zero stiffness vibration isolation system, which is designed to effectively minimize vibrations in various applications The system's innovative approach enables it to maintain low stiffness while providing superior isolation performance By analyzing its mechanics and operational principles, the research highlights the advantages of using quasi-zero stiffness systems in engineering and design These systems are particularly beneficial in environments where vibration control is critical, offering enhanced stability and protection for sensitive equipment Overall, the findings underscore the significance of quasi-zero stiffness technology in advancing vibration isolation solutions.
The QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM demonstrates a unique stable equilibrium at u ˆ = 0 When the parameter μ is within the range of μ A and μ B, the system features two centers at u ˆ = 0 and u ˆ > 1, along with a saddle point at u ˆ > 2 Beyond μ B, the system evolves to present three equilibrium points: two centers at u ˆ > 3 and u ˆ < 4, and a saddle point at u ˆ = 0.
With = A , there are two equilibrium positions including one center at u ˆ 0 marked by the filled circle D, and a center-saddle point at u ˆ 0 expressed by the non-filled square
A Oppositely, if = B , it will have one center-saddle point at u ˆ 0 denoted by the non-filled square B and one center at u ˆ 0 marked by filled circle C
Fig 5.28 (a) Stiffness curve of Eq (5.27) for P wh1 =3.7 bar, V ˆ ac 1 14.21 and =8.50, 8.59, 8.63, 8.65 (b) Stiffness curve enlarged for u ˆ -0.05, 0.15 and K ˆ S -0.004, 0.004 (The notation of the various types of lines is presented in the upper panel)
The study focuses on the quasi-zero stiffness vibration isolation system, which is designed to effectively reduce vibrations in various applications This innovative system utilizes a unique configuration that minimizes stiffness, allowing for enhanced performance in isolating vibrations By analyzing the mechanisms and benefits of quasi-zero stiffness, the research highlights its potential for improving stability and comfort in environments sensitive to vibrations The findings suggest that implementing such systems can lead to significant advancements in vibration control technology.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
The dynamic stiffness of the QSAVIM using PC is presented in Fig 5.28(b), showing an asymmetrical stiffness curve around the DSEP At central points, such as E (μ = 8.5), D (μ = μA), C (μ = μB), F, and H (μ = 8.65), the dynamic stiffness remains positive However, at the saddle point G (μ = 8.65), the stiffness becomes negative Additionally, at bifurcation points A and B, the dynamic stiffness equals zero, indicating an unstable equilibrium since the stiffness can turn negative when the isolated object deviates from the center-saddle point.
Dynamic analysis
Consider that the absolute displacement of the isolated object (z) due to a harmonic force with the amplitude F e and frequency from the isolated object as shown in Fig
Fig 5.29 Simple model of QSAVIM using PC
The kinetic energy is given by Eq (4.38), meanwhile the potential energy (E p ) of the approximate restoring force given in Eq (5.34) can be expressed as:
The study focuses on quasi-zero stiffness vibration isolation systems, which are designed to effectively minimize vibrations while maintaining stability These systems leverage unique mechanical properties to achieve near-zero stiffness, allowing for enhanced performance in various applications By examining the underlying principles and mechanisms, the research highlights the advantages of quasi-zero stiffness systems in reducing unwanted vibrations and improving overall structural integrity This innovative approach offers significant potential for advancements in vibration control technologies.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
E F d L F L a H a i i (5.41) where the relation between the origin of the relative coordinate u and the static deformation H o is denoted in Eq (4.27), that is L H o u
The generalized force in absolute coordinate of z:
Q f e Mg (5.43) with f e is the harmonic external force
The system reaches the DSEP, allowing for the determination of the isolated object's weight as indicated by Eq (5.40) Utilizing Eq (4.43), the motion equation for the load plate is formulated accordingly.
Utilizing Eq (4.41) in which z e is removed and Eq (4.27), the dynamic equation Eq
(5.44) is rewritten according to the relative coordinate (u) in dimensionless form, we obtain:
Herein, some parameters given in this equation are defined as following:
The study focuses on the quasi-zero stiffness vibration isolation system, which is designed to effectively minimize vibrations in various applications This innovative system utilizes a unique mechanism that allows for minimal stiffness, enabling it to absorb and dissipate energy from vibrations efficiently By employing this technology, the quasi-zero stiffness vibration isolation system offers enhanced performance in maintaining stability and comfort in sensitive environments The research highlights the advantages of this system, including improved durability and reduced maintenance requirements, making it a valuable solution for industries seeking effective vibration control.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM where the number of primes denote the order of differentiation with respect to time- scaling
In order to find the solution in the neighborhood of the equilibrium position u ˆ 0 , we let u ˆ x ˆ with is a small detuning term:
By applying Multi-scale method, the approximated solution of the Eq (5.46) is obtained as following:
o o o o o o x x T T T T T x T T T T T x T T T T T x T T T T T x T T T T T O (5.48) in which T i i ( i 0,1, 2,3, 4) Substituting Eq (5.48) into Eq (5.46) and letting
=1+ 2 then equating the coefficient of o , 1 , 2 , 3 , 4 on both sides of the equation
D dT i=1,2,3,4; n is the order of the differentiation The general solution of the first equation in Eq (5.49) is expressed as below:
iT o iT o x o A T T T T e A T T T T e (5.50) with A is an unknown complex function and A is the complex conjugate of A
The quasi-zero stiffness vibration isolation system is designed to effectively minimize vibrations in various applications This innovative system utilizes a unique configuration that allows for minimal stiffness, thereby enhancing its ability to absorb shocks and vibrations By focusing on reducing stiffness, the system achieves superior isolation performance, making it ideal for sensitive equipment and structures The study emphasizes the importance of this technology in improving stability and longevity in mechanical systems Overall, the quasi-zero stiffness vibration isolation system represents a significant advancement in vibration control methodologies.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
Substituting Eq (5.50) into the second equation in Eq (5.49), we obtain as following:
D o 2 x 1 x 1 2 D Ae i 1 iT o 1 A e 2 2 iT o 2 AA A e 2 2 iT o 2 D Ae 1 iT o i (5.51)
In order to obtain the periodic solution of Eq (5.51), imaginary terms in the right side of Eq (5.51) must be zero Namely,
D A 1 0; D A 1 0 A ( , , ) T T T 2 3 4 (5.52) Hence, the solution of Eq (5.51) is:
Substituting x ˆ o and x ˆ 1 into the third equation in Eq (5.49), we obtain:
o o o o iT iT iT o iT x x D Ai A A A A e A e A e
As above, the secular terms in Eq (5.54) will be ignored if the coefficient of e iT o or iT o e are equal to zero, we have:
A ae A ae (5.56) with a and β are real, then separating the real and imaginary parts, the differential equation for amplitude and frequency of Eqs (5.52, 5.55) are expressed as below:
The study focuses on the quasi-zero stiffness vibration isolation system, which is designed to effectively reduce vibrations in various applications This innovative system minimizes stiffness while maintaining stability, making it ideal for sensitive equipment and structures By analyzing its performance, the research highlights the benefits of using quasi-zero stiffness technology for enhanced vibration control The findings demonstrate significant improvements in isolation efficiency, contributing to the advancement of vibration mitigation techniques in engineering and design.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
The solution of Eq (5.54) as following:
Next, substituting Eqs (5.50, 5.53, 5.58) into the 4 th order equation in Eq.(5.49) is rewritten as following:
The periodic solution of Eq (5.59) can be achieved by:
Eqs (5.52, 5.60) reveal that the parameter A is independent on the scale time T 1 and
T 3 The solution x 3 is expressed as following:
This study focuses on the quasi-zero stiffness vibration isolation system, which is designed to effectively reduce vibrations in various applications The system operates on the principle of minimizing stiffness to enhance isolation performance, making it particularly beneficial in environments where vibration control is critical By analyzing the mechanics and applications of this innovative system, the research aims to provide insights into its advantages and potential uses in engineering and technology fields The findings highlight the effectiveness of quasi-zero stiffness systems in improving stability and comfort while mitigating unwanted vibrations.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
Similarly, substituting Eqs (5.53, 5.58, 5.61) in the last equation in Eq (5.49), then the coefficient of e iT o is set to zero as following:
A ae versus scale time T 4 , the real and imaginary parts of Eq (5.62) are obtained as following:
In addition, the differentiation of a and β with respect to dimensionless time is presented as below:
This study focuses on quasi-zero stiffness vibration isolation systems, which are designed to effectively minimize vibrations in various applications These systems utilize innovative engineering principles to achieve low stiffness characteristics, allowing them to absorb and dampen vibrations efficiently By exploring the mechanics and performance of quasi-zero stiffness systems, the research aims to enhance their effectiveness in providing superior vibration isolation Understanding these systems is crucial for improving their application in industries where vibration control is essential for equipment longevity and operational stability.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
From Eqs (5.57, 5.60, 5.63), Eq (5.64) is rewritten as following:
Substituting Eq (5.56) into (5.50) and then, the obtained result is substituted into
Eq (5.48), the primary solution of Eq (5.46) is expressed as following: x a cos( ) ( ) (5.65)
Recalling u ˆ x ˆ , the general solution of Eq (5.45) u a ˆ u cos( ) ( ) (5.66) in which a u a
Letting T 2 , and combining Eq (5.47), Eq (5.64) is expressed with respect to a u as below:
This article explores the concept of quasi-zero stiffness vibration isolation systems, which are designed to minimize vibrations effectively These systems utilize innovative engineering principles to achieve low stiffness characteristics, allowing for enhanced performance in various applications The study highlights the advantages of quasi-zero stiffness systems, including improved stability and reduced transmission of vibrations Additionally, it discusses the potential use cases and benefits in fields such as aerospace, automotive, and structural engineering, emphasizing the importance of advanced vibration isolation techniques for optimal system performance.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
As the amplitude and phase are unchanged versus time, the steady state motion will occur, meaning that
Through sin ( ) cos ( ) 1 2 2 , the sum of two sides of Eq (5.69), the frequency- response relationship of Eq (5.45) is obtained as following:
The peak amplitude ( a ˆ up ) and frequency ( p ) are calculated as below:
The study focuses on the quasi-zero stiffness vibration isolation system, which is designed to effectively reduce vibrations in various applications This innovative system utilizes a unique mechanism that minimizes stiffness, allowing for superior vibration damping By analyzing its performance, the research highlights the advantages of this technology in enhancing stability and comfort in environments sensitive to vibrations The findings suggest that the quasi-zero stiffness approach can significantly improve the efficiency of vibration isolation systems, making it a valuable solution for industries requiring precise vibration control.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
5.7.2 Stability of the steady state solution
Considering a uo & uo along with a set of steady state solutions and its neighborhood are determined by introducing small variations a u 1 & u 1 as following:
To accomplish the stable analysis, Eq (5.67) is rewritten as
uo uo u uo u uo u uo u uo u uo u a a a
Based on Routh-Hurwitz Criterion for nonlinear system, the stability of the steady state solution depending on the eigenvalues is determined as below:
The unstable region of the steady state motion above is obtained as following
The QSAVIM case, influenced by harmonic forcing excitation represented as \( f_e = F_e \cos(\omega t) \), is analyzed using Lattice Boltzmann Method (LBM), Structural Control Method (SCM), and air damping The force transmitted to the base can be expressed in a dimensionless format, highlighting the system's dynamic response under these conditions.
This article explores the innovative concept of quasi-zero stiffness vibration isolation systems, which are designed to effectively minimize vibrations in various applications By utilizing a unique mechanical design, these systems achieve significant reductions in stiffness, allowing for enhanced performance in vibration-sensitive environments The study highlights the advantages of quasi-zero stiffness systems over traditional methods, emphasizing their potential for improved stability and durability Overall, the research provides valuable insights into the development and implementation of these advanced vibration isolation technologies.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
It reveals that the transmitted force depends on the velocity and position of the load plate given in Eq (5.66) This force may be rewritten as:
Applying Eq (4.72), Eq (5.78) can be rewritten as following:
u u u u a a a a The maximum force is transmitted to the base being:
The transmissibility for forcing excitation is defined as below:
The study focuses on the quasi-zero stiffness vibration isolation system, which is designed to effectively minimize vibrations in various applications This innovative system utilizes a unique design that allows for minimal stiffness, enabling it to absorb and dampen vibrations efficiently By examining the characteristics and performance of this system, the research aims to enhance the understanding of vibration control mechanisms and improve the effectiveness of isolation solutions in engineering practices The findings could lead to advancements in technology that require precise vibration management, ultimately contributing to safer and more reliable systems.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
CONCLUSIONS AND FUTURE WORKS
Conclusion
This thesis provides a detailed guide for designing a QZS isolator using rubber air springs or pneumatic cylinders to mitigate low-frequency vibrations (≥32 rad/s) affecting isolated objects Traditional isolation methods often struggle within this frequency range, making the proposed model particularly valuable in vibration isolation applications, especially in the low-frequency domain Its potential applications include vehicle suspensions, isolation seats for enhanced comfort and health, and mounts for machinery sensitive to vibrations, ensuring efficiency for operators and passengers in moving vehicles exposed to low excitation frequencies.
The QZS vibration isolation method offers significant advantages, leading to the development of a novel QZS vibration isolation structure that utilizes a wedge and cam mechanism Unlike previous studies on quasi-zero stiffness isolation systems, this research incorporates non-steel elastic elements, such as rubber air springs or pneumatic cylinders, instead of traditional steel or magnetic components A major benefit of this innovative model is its adjustable load-bearing stiffness and stiffness correction mechanism, which allows for optimal low stiffness values at the desired dynamic stiffness equilibrium point (DSEP) as the isolated load changes Consequently, this model effectively resolves the inherent conflict between stiffness and load-bearing capacity, ensuring that it maintains both low stiffness and adequate load-bearing ability while minimizing static deformation.
Meanwhile, it is not easy for the traditional isolation method to surmount this
The study focuses on the quasi-zero stiffness vibration isolation system, which is designed to minimize vibrations effectively This innovative system operates with minimal stiffness, allowing for enhanced performance in various applications By utilizing advanced materials and engineering techniques, the quasi-zero stiffness design significantly improves vibration isolation capabilities The research highlights the potential benefits of this system in industries where vibration control is critical, such as aerospace, automotive, and manufacturing Overall, the findings suggest that implementing quasi-zero stiffness vibration isolation can lead to superior stability and longevity of sensitive equipment.
The QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM presents a significant advancement in vibration isolation technology, particularly applicable in Vietnam This model allows for easy adjustment of stiffness in both mechanisms by controlling air pressure in the air spring Furthermore, it offers the flexibility to switch between passive and active states to achieve the desired isolation response, a feat that is challenging for traditional quasi-zero stiffness vibration isolators that rely on mechanical springs.
Specifically, the result of this study obtained as following:
1 A QZS vibration isolation model using rubber air springs
Experimental identification of the physical parameters, including effective area and volume, was conducted for a commercial rubber air spring The study derived the restoring force model and stiffness of the air spring under compressed air conditions Additionally, the hysteresis curve was experimentally determined using Berg’s model and the fractional Kelvin-Voigt model, taking into account the rubber material's properties, such as friction between reinforcing fibers and rubber, as well as viscoelasticity The findings confirmed that the model of the rubber air spring, influenced by compressed air, friction, and viscoelasticity, aligns closely with the experimental data.
The stiffness equation for the QSAVIM was derived from the rubber air spring model, leading to a numerical simulation of its stiffness curve, which resembles a symmetrical concave parabola centered around the DSEP Within the expected working range, the dynamic stiffness of the QSAVIM is found to be lower than that of the ETVIM Additionally, the pressure ratio—representing the relationship between the load-bearing mechanism and the corrected stiffness—demonstrates that the dynamic stiffness of the QSAVIM increases with an increase in the pressure ratio.
Thank to this relation, the pressure of both mechanisms can be easily adjusted so that the quasi-zero dynamics stiffness of the proposed system is always remained at the
This article explores the innovative concept of quasi-zero stiffness vibration isolation systems, which are designed to effectively minimize vibrations in various applications By utilizing advanced engineering principles, these systems achieve remarkable isolation performance while maintaining structural stability The study highlights the mechanisms behind quasi-zero stiffness, emphasizing their potential benefits in enhancing the longevity and reliability of sensitive equipment Furthermore, the findings suggest that implementing such systems can lead to significant improvements in vibration control, making them essential for industries that demand precision and safety.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
DSEP as there is a change of the isolated weight From that, a procedure for designing QSAVIM was set up
The dynamic equation of the QSAVIM under harmonic excitation from the base frame was analyzed and developed, leading to the creation of an amplitude-frequency relation through an approximate analytical method An essential metric for evaluating isolation effectiveness, known as vibration transmissibility, was defined and achieved Numerical simulations indicated that the vibration transmissibility curve and amplitude-frequency response shifted to the right, exhibiting both down and up jumps in frequency, which allowed for multiple solutions, including resonant and non-resonant cases Furthermore, increasing the pressure ratio narrowed the frequency range of these jumps while expanding the isolation range towards lower frequencies, effectively reducing the resonance peak in both frequency and amplitude.
The QSAVIM exhibits a complex dynamic response, revealing that multiple solutions can arise at various frequencies, with the initial conditions of position and velocity determining the steady-state solution The system experiences bifurcation, transitioning between period-1 and multi-period solutions based on whether the isolated weight is larger or smaller than the optimal value required for achieving the DSEP This research demonstrates that the isolated effectiveness of the QSAVIM significantly surpasses that of the ETVIM.
To evaluate the theoretical model of QSAVIM and compare its isolation effectiveness with ETVIM, prototypes of both models were fabricated, and the experimental apparatus was established for testing.
The experimental results validate the effectiveness of the stiffness-corrected mechanism in enhancing isolation response, while also confirming the analysis model of the QSAVIM, which demonstrates an expanded isolation frequency region with increased pressure ratios Furthermore, the experiment reaffirms the advantages of the QSAVIM over traditional methods.
This article explores the principles and applications of quasi-zero stiffness vibration isolation systems These systems are designed to minimize vibrations effectively by utilizing innovative mechanisms that reduce stiffness to near-zero levels The study highlights the advantages of such systems in various engineering fields, particularly in enhancing the stability and performance of sensitive equipment By examining the underlying mechanics and performance metrics, the research provides insights into the potential for improved vibration control in industrial applications.
The QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM, known as ETVIM, effectively demonstrates significant vibration attenuation from the source to the isolated object at frequencies exceeding 31.5 rad/s (5Hz).
2 A QZS vibration isolation model using pneumatic cylinders
This thesis presents a comprehensive quasi-zero stiffness vibration isolation model utilizing air springs, incorporating pneumatic cylinders linked to auxiliary tanks as elastic elements The stiffness model for the pneumatic cylinder was derived through an analytical solution based on thermodynamic equations and the ideal gas law, while also accounting for sliding friction between the piston and cylinder Rather than conducting physical experiments, the research employed advanced software technology and virtual prototyping techniques A virtual model of the pneumatic cylinder with an auxiliary tank was developed to assess the analysis model and determine the sliding frictional characteristics The results of the virtual simulation validated the accuracy of the proposed analysis model.
The stiffness model of the load-bearing mechanism (LBM) utilizing a pneumatic cylinder with an auxiliary tank was developed and analyzed Simulation results indicate that the stiffness of this mechanism varies with the position of the load plate, exhibiting a nonlinear and asymmetric curve around the DSEP Notably, increasing the volume of the auxiliary tank reduces both asymmetry and nonlinearity, leading to a minimal slope in the stiffness curve when the tank volume is sufficiently large In contrast, the stiffness model of the stiffness corrected mechanism (SCM) shows a consistently symmetric parabolic curve around the DSEP, which can be either concave or convex based on the connecting tank's volume The analysis reveals that increasing the auxiliary volume from zero to a critical value significantly influences the stiffness characteristics.
Future work
Although the proposed model can improve the isolation effectiveness in low frequency region, the isolation performance of the system is still limited Because
1 Resonance peak is still high
2 Due to passive isolation model, the isolation capacity is still lower than the desirable response
The next studies will be realized contents as following:
The study focuses on quasi-zero stiffness vibration isolation systems, which are designed to effectively reduce vibrations in various applications These systems utilize unique mechanical properties to achieve minimal stiffness, allowing for enhanced performance in vibration control By analyzing the dynamics and characteristics of these systems, the research aims to improve their efficiency and applicability in engineering fields The findings contribute to the advancement of vibration isolation technology, providing solutions for environments where minimizing vibrations is critical.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
- Studying the damping methods to reduce peak frequency
- Studying control algorithms to improve the isolation performance Published papers
1 N.Y.P Vo and T.D Le, “Adaptive pneumatic vibration isolation platform”, Mechanical Systems and Signal processing, 133,106258, 2019 (ISI, Q1, IF=6.832, H-index7) https://doi.org/10.1016/j.ymssp.2019.106258
2 Ngoc Yen Phuong Vo and Thanh Danh Le, “Static analysis of low frequency Isolation model using pneumatic cylinder with auxiliary chamber,”
International Journal of Precision Engineering and Manufacturing, 21, pp 681-
3 N Y P Vo, T D Le, “Analytical study of a pneumatic vibration isolation platform featuring adjustable stiffness”, Journal of Commun Nonlinear Sci Numer Simulat, 98, 105775, 2021 (ISI, Q1, IF=4.26, H-index3) https://doi.org/10.1016/j.cnsns.2021.105775
4 Ngoc Yen Phuong Vo and Thanh Danh Le, “Dynamic analysis of quasi-zero stiffness pneumatic vibration isolator”, Applied Science, 12, 2378, 2022, (ISI, Q2, IF=2.679, H-indexR) https://doi.org/10.3390/app12052719
5 N.Y.P Vo, M.K Nguyen and T.D Le, “Dynamic Stiffness Analysis of a Nonlinear Vibration Isolation Model with Asymmetrical and Quasi-Zero Stiffness Characteristics”, Journal of Polimesin, 19, pp 7-15, 2021 (IF=0.65) http://e-jurnal.pnl.ac.id/polimesin/article/view/1956
This study explores the quasi-zero stiffness vibration isolation system, which is designed to effectively minimize vibrations in various applications By focusing on the unique properties of quasi-zero stiffness, the research highlights its advantages in enhancing stability and performance The findings indicate that this innovative system can significantly reduce the impact of external disturbances, making it ideal for sensitive equipment and structures Overall, the study underscores the potential of quasi-zero stiffness systems in improving vibration control and ensuring operational efficiency.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
6 N Y P Vo, T D Le, “Analysis model of restoring force of a rubber air spring”
Journal of Vibroengineering, 23, pp 1138-1147, 2021 (ESCI-Scopus, IF=0.83, H-index&) https://doi.org/10.21595/jve.2021.21889 International Conference
7 N.Y.P Vo and T.D Le, “Modeling and Simulation of low frequency vibration isolation table,” Proceeding of the First Conference on Material, Machines and Methods of sustainable Development, 2018
8 N.Y.P Vo and T.D Le, “Effects of configuration parameters on the dynamic stiffness and stability of pneumatic vibration isolation model,”International Conference on Fluid Machinery and Automation System,2018
9 N.Y.P Vo, M.K Nguyen and T.D Le,“Study on Vibration Transmissibility Characteristic of a novel asymmetric nonlinear model using pneumatic spring,”IEEE International Conference on System Science and Engineering,
10 N.Y.P Vo, M.K Nguyen and T.D Le, “Identification of friction force model of a pneumatic cylinder” IEEE International Conference on System Science and Engineering, August 27-28,2021
11 N.Y.P Vo,M.K Nguyen, T.D Le, “Dynamic stiffness analysis and isolation effectiveness of vibration isolation platform using pneumatic spring with auxiliary chamber,”Journal of Technical education science, 2019
12 Vo Ngoc Yen Phuong (Principal investigator), Nguyen Minh Ky, Le Thanh Danh, “Dynamic analysis of nonlinear asymmetric vibration isolator,”The
The study focuses on quasi-zero stiffness vibration isolation systems, which are designed to effectively minimize vibrations These systems utilize innovative engineering principles to achieve low stiffness while maintaining stability, making them ideal for sensitive equipment and applications By analyzing their performance, the research aims to enhance the understanding of vibration isolation technologies, leading to improved designs and applications in various fields The findings could significantly impact industries where vibration control is critical, ensuring better protection for sensitive instruments and structures.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM project grant No: T2020-05NCS funded by Ho Chi Minh City University of Technology and Education, (Completed:2021)
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This study focuses on the quasi-zero stiffness vibration isolation system, which is designed to effectively reduce vibrations in various applications By minimizing stiffness, this system enhances performance and stability, making it ideal for sensitive equipment The research explores the mechanisms behind this innovative approach, highlighting its advantages in vibration control Overall, the quasi-zero stiffness vibration isolation system represents a significant advancement in engineering solutions for vibration mitigation.
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QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM
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The study focuses on quasi-zero stiffness vibration isolation systems, which are designed to minimize vibrations effectively These systems utilize innovative engineering principles to achieve low stiffness characteristics, enhancing their ability to isolate vibrations By examining their performance and applications, the research aims to provide insights into the advantages of quasi-zero stiffness systems in various industries The findings highlight their potential in improving stability and reducing noise, making them a valuable solution for vibration-sensitive environments.
QUASI.ZERO.STIFFNESS.VIBRATION.ISOLATION.SYSTEM