dynamics of multi degree of freedom systems
DYNAMICS of MECHANICAL SYSTEMS ppt
... masses • A degree of freedom is defined as a way in which a particle, body, or system can move The number of degrees of freedom possessed by a particle, body, or system is defined as the number of geometric ... accelerations of the members of the system Inertia is a study of the mass properties of the bodies of a system and of the system as a whole in various configurations Kinetics is a study of forces ... Forced Vibration of a Damped Linear Oscillator .449 13.7 Systems with Several Degrees of Freedom 450 13.8 Analysis and Discussion of Three-Particle Movement: Modes of Vibration ...
Ngày tải lên: 27/06/2014, 15:20
Dynamics of Mechanical Systems 2009 Part 1 ppsx
... masses • A degree of freedom is defined as a way in which a particle, body, or system can move The number of degrees of freedom possessed by a particle, body, or system is defined as the number of geometric ... accelerations of the members of the system Inertia is a study of the mass properties of the bodies of a system and of the system as a whole in various configurations Kinetics is a study of forces ... Forced Vibration of a Damped Linear Oscillator .449 13.7 Systems with Several Degrees of Freedom 450 13.8 Analysis and Discussion of Three-Particle Movement: Modes of Vibration ...
Ngày tải lên: 10/08/2014, 20:20
Dynamics of Mechanical Systems 2009 Part 2 potx
... elements of the jth column of B Specifically, n cij = ∑a b ik kj k =1 where n is the number of columns of A and the number of rows of B (2.10.5) 0593_C02_fm Page 40 Monday, May 6, 2002 1:46 PM 40 Dynamics ... number of rows of the second matrix B When this occurs, the matrices are said to be conformable If C is the product AB, then the element cij is the sum of products of the elements of the ith row of ... magnitude of F be lb 0593_C02_fm Page 52 Monday, May 6, 2002 1:46 PM 52 Dynamics of Mechanical Systems a Find a unit vector n parallel to L, in the direction of P to Q Express the results in terms of...
Ngày tải lên: 10/08/2014, 20:20
Dynamics of Mechanical Systems 2009 Part 3 pptx
... a measure of the orientation of B in R In this context, the angular velocity of B in R is a measure of the rate of change of orientation of B in R The simple angular acceleration α of B in R ... (5.2.2) The number of degrees of freedom of a mechanical system is sometimes defined as the difference between the number of coordinates needed to define the location of the particles of the system ... particles will have six degrees of freedom Thus, for a system of N freely moving particles (in three dimensions), there will be 3N degrees of freedom Suppose a system of two particles, moving...
Ngày tải lên: 10/08/2014, 20:20
Dynamics of Mechanical Systems 2009 Part 4 docx
... the analysis of forces and sets of forces (force systems) as they are applied with mechanical systems We will consider various representations of force systems, various kinds of force systems, and ... configuration and positioning of the system, the system has N degrees of freedom A chain may be considered to be a finite-segment model of a cable; hence, an analysis of the system of Figure 5.6.1 can provide ... know the location of a typical point P of B, the velocity of P, and the angular speed of B, we can locate the center C of zero velocity of B Let Q be a second typical point of B (distinct from...
Ngày tải lên: 10/08/2014, 20:20
Dynamics of Mechanical Systems 2009 Part 5 pps
... square of the distance of P from O and it also depends upon the direction of the unit vector na The form of the definition of Eq (7.2.1) is motivated by the form of the terms of the inertia torque of ... elements Iij of the inertia matrix Indeed, they may be identified as: II = sum of diagonal elements of Iij III = sum of diagonal elements of the cofactor matrix of Iij IIII = determinant of Iij 0593_C07_fm ... PM 190 Dynamics of Mechanical Systems a Determine the resultant R of this system of forces b Find the moments of the force system about points C, H, E, and G Express the results in terms of the...
Ngày tải lên: 10/08/2014, 20:20
Dynamics of Mechanical Systems 2009 Part 6 pdf
... configuration of the system; n is the number of degrees 0593_C08_fm Page 243 Monday, May 6, 2002 2:45 PM Principles of Dynamics: Newton’s Laws and d’Alembert’s Principle 243 of freedom of the system; ... the principles of dynamics we can obtain mathematical models of the behavior of mechanical systems In this chapter, and in subsequent chapters, we will explore the principles of dynamics and their ... of both rods T* Q1 Q F* G2 mg FIGURE 8.10.4 Free-body diagram of rod B2 T2 0593_C08_fm Page 260 Monday, May 6, 2002 2:45 PM 260 Dynamics of Mechanical Systems Setting moments of these force systems...
Ngày tải lên: 10/08/2014, 20:20
Dynamics of Mechanical Systems 2009 Part 7 pps
... left side of Eq (10.6.2) may be recognized as the power of F (see Eq (10.4.2)) The right side of Eq (10.6.2) may be expressed in terms of a derivative of the square of the velocity of P That ... definition of work of Eq (10.2.2) takes the form: (10.2.12) 0593_C10_fm Page 324 Monday, May 6, 2002 2:57 PM 324 Dynamics of Mechanical Systems t* ∫ W = F ⋅ v dt (10.2.13) where t* is the time of action ... action of gravity FIGURE 10.2.6 ˆ A differential arc of an arbitrary curve C It happens that Eq (10.2.18) is a valid expression for the work of the gravity force regardless of the path of descent of...
Ngày tải lên: 10/08/2014, 20:20
Dynamics of Mechanical Systems 2009 Part 8 docx
... body has six degrees of freedom, the three scalar constraint equations reduce the number of degrees of freedom to three To explore this further let (x, y, z) be the X, Y, Z coordinates of G Then, ... equations A mechanical system may have any number of constraint equations, often more than the number of degrees of freedom For example, the particle of Figure 11.2.1, restricted to move on the straight ... Cartesian reference frame The number of degrees of freedom of a mechanical system is the number of coordinates of the system if it were unrestricted minus the number of constraint equations For example,...
Ngày tải lên: 10/08/2014, 20:20
Dynamics of Mechanical Systems 2009 Part 9 potx
... Coordinates, Constraints, and Degrees of Freedom P11.2.1: Determine the number of degrees of freedom of the following systems: a Pair of eyeglasses b Pair of pliers or pair of scissors c Child’s tricycle ... 0593_C11_fm Page 390 Monday, May 6, 2002 2:59 PM 390 Dynamics of Mechanical Systems where as before, n is the number of degrees of freedom of the system (The minus sign is chosen so that P is ... 2002 2:59 PM 386 Dynamics of Mechanical Systems degrees of freedom Recall that if we introduce six parameters (say, x, y, z, θ, φ, and ψ) to define the position and orientation of D we find that...
Ngày tải lên: 10/08/2014, 20:20
Dynamics of Mechanical Systems 2009 Part 10 pot
... number of governing equations are obtained as the degrees of freedom Finally, Lagrange’s equations offer the additional advantage of using energy functions, which makes the computation of vector ... listing of the many books devoted to the subject We begin with a brief review of solutions to second-order ordinary differential equations We then consider single and multiple degree of freedom systems ... currently a major interest of vibration analysts 13.7 Systems with Several Degrees of Freedom We consider next mechanical systems where more than one body can oscillate An example of such a system might...
Ngày tải lên: 10/08/2014, 20:20
Dynamics of Mechanical Systems 2009 Part 11 pptx
... 2002 6:56 AM 510 Dynamics of Mechanical Systems 14.5 Meirovitch, L., Elements of Vibration Analysis, McGraw-Hill, New York, 1975, 329 ff 14.6 Meirovitch, L., Dynamics and Control of Structures, ... Tuesday, May 7, 2002 7:05 AM 516 Dynamics of Mechanical Systems P1 (m) FIGURE 15.3.3 Dynamic balancing of the shaft of Figure 15.3.2 Q (m) Q (m) P2 (m) ˆ where M is the mass of the body (or mechanical ... 7:05 AM 522 Dynamics of Mechanical Systems Next, consider the addition of a particle P with mass m and coordinates (x, y) as in Figure 15.5.1 The components of the inertia dyadic of P relative...
Ngày tải lên: 10/08/2014, 20:20
Dynamics of Mechanical Systems 2009 Part 12 pptx
... 548 Dynamics of Mechanical Systems ρ FIGURE 16.6.7 Offset flat surface follower of Figure 16.6.1 FIGURE 16.6.8 Offset axes circle and tangent line FIGURE 16.6.9 Base circle superposed over offset ... axis of the follower shaft intersects the axis of rotation of the cam Let the follower shaft be driven by the cam 0593_C16_fm Page 542 Tuesday, May 7, 2002 7:06 AM 542 Dynamics of Mechanical Systems ... 7:12 AM 576 Dynamics of Mechanical Systems (or circles), as in Figure 17.3.2 Consider a typical pair of contacting teeth as shown Let OA and OB be the centers of the gears (and, hence, of the rolling...
Ngày tải lên: 10/08/2014, 20:20
Dynamics of Mechanical Systems 2009 Part 13 docx
... there are three translation degrees of freedom leading to a total of 3N + degrees of freedom Following the procedures of Chapter 11, we may describe these degrees of freedom with variables (or ... to Multibody Dynamics 607 10 R FIGURE 18.2.3 A numbering and labeling of the bodies in a branch of the multibody system FIGURE 18.2.4 A numbering and labeling of the bodies of two branches of ... 17.6.4) [17.6] Path of contact — locus of points of contact of a pair of meshing spur gear teeth (see also line of action, pressure line, and line of contact) [17.6] Pinion — smaller of two gears in...
Ngày tải lên: 10/08/2014, 20:20
Dynamics of Mechanical Systems 2009 Part 15 docx
... model has n degrees of freedom, then the matrix expression of Eq (20.11.1) is equivalent to n scalar equations If the movement of the model is constrained so that m of the degrees of freedom are ... n (20.9.1) where n is the number of degrees of freedom (The gross-motion model of the foregoing sections [see, for example, Figure 20.8.1], has 54 degrees of freedom. ) By substituting from Eqs ... 9:07 AM 684 Dynamics of Mechanical Systems motion of the system Expressed another way, the robot has (n – 6) more degrees of freedom than needed to uniquely determine the movement of the system...
Ngày tải lên: 10/08/2014, 20:20
Dynamics of Mechanical Systems 2009 Part 16 ppt
... Tuesday, May 7, 2002 9:14 AM 734 Dynamics of Mechanical Systems FIGURE P20.8.2 A model of the arm P20.8.3: See Problems P20.6.4 and P20.8.2 Let the movement of the arm model be defined by the ... Equality of vectors, 15 Equivalent force systems, 170 Euler angles, 82 Euler parameters, 613, 707-709 Euler torque, 230 Exhaust stroke, 529 Extremity body, 607 Dynamics of Mechanical Systems Free-body ... Principal axis of inertia, 208, 215 Principal moment of inertia, 208, 209 Principal unit vector, 209 Principle of angular momentum, 289 Principle of linear momentum, 285 Product of inertia, 200,...
Ngày tải lên: 10/08/2014, 20:20
Time dependent quantum wave packet dynamics of 3d systems
... when treating dynamics of systems larger than a few atoms The strategy is to retain the treatment for most dimensions of freedom classical, while designating a few crucial degrees of freedom to ... motions, while the classical degrees of freedom must respond effectively to quantum transitions Among a number of standard approaches which describe the dynamics of a quantum system interacting ... theoretical study of quantum reaction dynamics [6-12], calculations of simple 3D systems became just routine applications Researchers were proceeding to higher dimensional systems in 1990s, great...
Ngày tải lên: 11/09/2015, 16:08
fluid dynamics of packed columns principles of the fluid dynamic design of columns for gasliquid and liquidliquid systems
... kowiak c Fluid Dynamics of Packed Columns Jerzy Ma´ kowiak c Fluid Dynamics of Packed Columns Principles of the Fluid Dynamic Design of Columns for Gas/Liquid and Liquid/Liquid Systems Translated ... number Froude number of liquid Froude number of liquid Froude number of liquid Reynolds number of liquid Reynolds number of liquid Reynolds number of droplet modified Reynolds number of vapour or gas ... hydraulic behaviour of packed columns for the development of a new method for the standard presentation of the fluid dynamics of columns with any type of packing design The basic principles of the method...
Ngày tải lên: 02/04/2014, 14:41
Luận văn Thạc sỹ - Đề tài Nghiên cứu hệ thống có trễ (Two - Degree - of - freedom - control) và sự kết hợp Two - Degree - of - freedom - control và STR
... gian tìm hiểu, học viên định chọn điều khiển Two -degree -of- freedom- control làm đối tượng nghiên cứu Dựa vào lý thuyết điều khiển Two -degree -of- freedom- control, học viên áp dụng để điều khiển đối ... phương pháp điều khiển hệ thống có trễ, tập trung vào phương pháp Two -degree -of- freedom- control - Kết hợp điều khiển Two -degree -of- freedom- control với điều khiển Tự chỉnh định STR - Áp dụng phương ... tốt Two -degree -of- freedom- control để tiến hành nghiên cứu phát triển, sau áp dụng vào hệ quạt gió phẳng để kiểm chứng Chương 2: Trình bày chi tiết lý thuyết điều khiển Two -degree -of- freedomcontrol...
Ngày tải lên: 26/05/2014, 00:05
Mechatronics Dynamics of Electromechanical and Piezoelectric Systems P1 pptx
... the virtual changes of configuration δqk must satisfy a set of m constraint equations of the form of Equ.(1.18): alk δqk = l = 1, m (1.59) k The number of degrees of freedom of the system is n ... absolute angles The number of degrees of freedom (d.o.f.) of a system is the minimum number of coordinates necessary to provide its full geometric description If the number of generalized coordinates ... kinetic coenergy of a rigid body is the sum of the kinetic coenergy of translation of the total mass lumped at the center of mass and the kinetic coenergy of rotation around the center of mass): ˙...
Ngày tải lên: 02/07/2014, 06:20