Ảnh hưởng của khối lượng nền lên ứng xử động của kết cấu dầm và tấm

THE UNIVERSITY OF DA NANG UNIVERSITY OF SCIENCE AND TECHNOLOGY PHAM DINH TRUNG THE INFLUENCE OF FOUNDATION MASS ON DYNAMIC RESPONSES OF BEAM AND PLATE STRUCTURES MAJOR : ENGINEERING MECHANICS CODE : 9520101 (62520101) SUMMARY OF DOCTOR OF ENGINEERING DISSERTATION Da Nang - 2018 The work was finished at University of Science and Technology – The University of Da Nang Advisors: Assoc Prof Dr HOANG PHUONG HOA Assoc Prof Dr NGUYEN TRONG PHUOC Reviewer 1st: Prof Dr Pham Duy Huu Reviewer 2nd: Assoc Prof Dr Pham Hoang Anh Reviewer 3rd: Assoc Prof Dr Dang Cong Thuat This dissertation was defended at The Doctor of Engineering Committee at University of Science and Technology-The University of Da Nang on 29th of July, 2018 For the detail of the dissertation, please contact: - Information and Library Center of University of Science and Technology - The University of Da Nang - National Library of Vietnam INTRODUCTION Motivation of study The problem model of plate and beam structures on foundation subjected to moving vehicles as transportation, runway, railway, etc, has very important meaning both in theory and practical application In almost the studies, the foundation model applied to analyze dynamic response of structures was described by various foundation models The first is the one-parameter foundation model Winkler [87] and it was developed into the parameters foundation models as Filonenko-Borodich [30], Hetényi [36], Pasternak [70], Reissner [77], Kerr [44], Vlasov [83] The common character of the foundation models used elastic spring without density to describe the behavior of foundation However, the nature of foundation has density and it does not have meaning in the problem of static analysis but it can have the influence on the problem of dynamic analysis When the above structure is vibrating under dynamic loads, the foundation mass also causes vertical inertia force as external load subjected to the structures The force depends on the value of mass and acceleration of the foundation and it completely participates in the response to the above structures It is seen that the foundation mass has an influence on the dynamic response of the structures and not consider any researches presented clearly the influence of foundation mass The dissertation studies “The influence of foundation mass on dynamic responses of beam and plate structures” to describe more exactly the problem of structures on foundation under moving load It can be seen that this idea agrees with developing tendency, it has inheritability from the last foundation models and a new problem is foundation mass, it has meaning science and more agreement with reality Purpose of study The purpose of dissertation proposes a new foundation model and establishes theory to describe characteristic parameters of the influence of foundation mass Then, the experimental model is used to determine the parameters of the influence of foundation mass on the dynamic response of the structures Object and scope of the study The subject of study: The dissertation studies the influence of foundation mass on the dynamic response of the beam and plate subjected to moving load The scope of study: The material properties of the structural model and foundation are assumed as homogeneous, continuous, isotropic and linear elastic based on small deformation theory Research content Theory research: The dissertation studies overview of the characteristics of foundation models applied to the problem of the structures on the foundation And then, the dissertation proposes a new foundation model and establishes basic theory to describe characteristic parameters of the influence of foundation in the problem of dynamic analysis response of beam and plate structures Experimental research: The dissertation establishes the experimental models to verify and establish the relation of characteristic parameters of the influence of foundation mass And then, the parameter of the influence of foundation mass is determined based on a comparison between experimental and theoretical results Computer program: The dissertation also establishes a program for the above research problems based on finite element method and dynamic structures Methodology of study With above purpose and content of research, the study methodology of the dissertation is a combination between theory research such as proposition new foundation model, numerical simulations and experimental research to determine the parameter of the influence of foundation mass on the dynamic response of the structures Dissertation layout In addition to the introduction and conclusion parts, the dissertation is organized into four chapters as: Chapter 1: Overview Chapter 2: Dynamic foundation model Chapter 3: Numerical simulations Chapter 4: Experimental research Contributions of the dissertation The dissertation proposed a new foundation and established basic theory to describe the characteristic parameters of the influence of foundation mass The experimental model is established and the characteristic parameters of the influence of foundation mass are determined The computer program of the problem of the dynamic response of the beam and plate is also established So, the dissertation “The influence of foundation mass on the dynamic response of the beam and plate” has certain contributions and practical significance in the problem of dynamic analysis response of the structures on foundation subjected to moving load The results are also meaning in the problem of structures such as road-vehicle, runway, foundation-track-train interaction Chapter OVERVIEW 1.1 Introduction The purpose of the chapter presents an overview of foundation models and the applied of the foundations in the problem of dynamic analysis response of the structures on the foundation are systematically studied 1.2 Overview of the foundation models 1.2.1 The one-parameter foundation model The Winkler foundation model is suggested in 1867 [87]; called one-parameter foundation model But, one of the most important deficiencies of the model is that it appears a displacement discontinuity between the loaded and unloaded part of the foundation surface 1.2.2 The many-parameter foundation models One of the methods to overcome the deficiencies of Winkler model adds to the upper surface of linear springs a layer without mass density, the parameter of this layer is called the second parameter of foundation models 1.3 The application of foundation models 1.3.1 The studies outside the country In many last decades, the above foundation models have been quite applied in many problems of dynamic analysis response of the structures on the foundation 1.3.2 The studies inside the country In many last years, the dynamic analysis response of structures on foundation under moving load models has been attracted many Vietnam researchers 1.4 The studies of the influence of foundation mass The previous works also considered the influence of foundation mass and the results showed that the foundation mass had a significant effect on the dynamic characteristic of the structures system This study does not propose any foundation models or parameters describing the influence of foundation mass [54-57, 6] 1.5 The problem of analysis response of structures on foundations Recently, the moving oscillator model is one of the moving load models described nearly as real nature of moving vehicles has been applied in many studies [12], [26], [43], [50], [64], [75] 1.6 Conclusion The above overview of foundation models shows that the problem of the dynamic response of structures on the foundation is always topic that attracts many attentions and researches in recent years One of the most common of almost above studies is foundation model described by parameters without mass density, as same as, it overlooks the influence of foundation mass on the dynamic response of the structures But, the true nature of foundation has mass density, so, the mass density of foundation has certainly effect on the character and dynamic response of the above structures And then, the research and promotion of a new foundation model used to analyze the influence of foundation mass on dynamic characteristic and response of the structure on the foundation are really necessary, meaningful science and relevant practice Chapter DYNAMIC FOUNDATION MODEL 2.1 Introduction This chapter proposes a new foundation model, called Dynamic foundation model, and establishes the theory to describe parameter of the influence of foundation mass on responses of the structures 2.2 The dynamic foundation model 2.2.1 The basic theory of the model The study proposes the new foundation model considering fully foundation parameters such as stiffness elastic, shear layer, viscous damping and especially consideration characteristic parameters of the influence of foundation mass, called dynamic foundation model, plotted in Fig 2.1 The pressure-deflection relationship at the time t is determined based on balance principle of shear layer, see in Fig 2.2 The pressuredeflection relationship can be expressed mathematically as follows w(x, y,t) 2w(x, y,t) q(x, y,t) = kw(x, y,t)  c m  ks2w(x, y,t) (2.1) t t Fig 2.1 The dynamic foundation model (a) (b) Fig 2.2 The mechanical model of the dynamic foundation: (a) Stress in shear layer, (b) Force acting on shear layer 2.2.2 The parameter of foundation mass The lumped mass m is determined based on the principle balance kinetic energy of the elastic spring element shown in Fig 2.3, can be expressed as m = aF F H F (2.2) where a F is a parameter of the influence of foundation mass (a) (b) Fig 2.3 The lumped mass model: (a) The elastic spring, (b) The straight rod 2.2.3 Comment The Dynamic foundation model describes nearly identical real nature of the soil, at the same time it is also overall the above foundation models in both the static and dynamic problem of the structures on the foundation 2.3 The beam on the foundation 2.3.1 The beam model Consider the Euler-Bernoulli beam element on the dynamic foundation model, plotted in Fig 2.4 Fig 2.4 The beam element on the dynamic foundation model 2.3.2 The properties matrices of the beam element The stiffness, mass and damping matrices of the beam element can be expressed as b w s K e, B =  K e, B   K e, B  K e, B (2.3) b F M e, B =  M e, B   M e, B (2.4) l F T Ce, B =   N e, B c  N w, B dx (2.5) b w s where  K e, B ,  K e, B and  K e, B are stiffness matrix of the beam b element, elastic foundation, and shear layer, respectively and  M e, B F M e, B are mass matrix of the beam element and mass matrix of the foundation, respectively 2.4 The plate on the foundation 2.4.1 The plate model Consider the Reissner-Mindlin plate element on the dynamic foundation model, shown in Fig 2.5 Fig 2.5 The plate element on the dynamic foundation model 2.4.2 The matrices of the plate element The dynamic properties matrices of the plate element can be expressed as b, s w s K e, P =  K e, P   K e, P  K e, P b F M e, P =  M e, P   M e, P F T Ce, P =   N w, P c  N w, P dAe (2.6) (2.7) (2.8) Ae b,s w s where  K e, P ,  K e, P and  K e, P are stiffness matrix of the plate 12 The influence of parameter of the foundation mass on free vibration of the beam is shown in Fig 3.1 120 60 120 (b) b=0,2 b=0,6 b=1 90 l1 b=0 b=0,4 b=0,8 90 l1 (a) 60 10 100 K1 0 10 100 K1 b=0 b=0.4 b=0.8 b=0.2 b=0.6 b=1 1000 60 (d) 90 30 1000 10000 1000 10000 120 l1 90 10000 120 l1 b=0.2 b=0.6 b=1 30 30 (c) b=0 b=0.4 b=0.8 60 b=0 b=0.4 b=0.8 b=0.2 b=0.6 b=1 10 100 K1 30 0 10 100 K1 1000 10000 Fig 3.1 The dimensionless frequencies l1 of the beam with K = ,  = 0.75 : (a) S-S, (b) C-C, (c) CF, (d) C-S The parameters of the model are given by: L = m, L / h = 50 ,  = 7860 kg/m3, E = 206.109 N/m2,  v = 0.5 and  v = 0.5 (a) 1.7 1.7 (b) 1.5 DMF DMF 1.5 1.3 b=0 b=0.25 b=0.5 b=0.75 1.1 1.3 b=0 b=0.25 b=0.5 b=0.75 1.1 0.9 0.9 20 40 60 80 Velocity (m/s) 100 20 40 60 80 Velocity (m/s) 100 Fig 3.2 The DMF of the beam with various values of elastic spring: ( K = , c = 103 ,  = 0.5 ) : (a) K1 = 75 , (b) K1 = 150 1.7 (a) 1.7 (b) 1.3 b=0 b=0.25 b=0.5 b=0.75 1.1 0.9 20 40 60 80 Velocity (m/s) 100 DMF DMF b=0 b=0.25 b=0.5 b=0.75 1.5 1.5 1.3 1.1 0.9 20 40 60 80 Velocity (m/s) 100 Fig 3.3 The DMF of the beam with various values of shear layer: ( K1 = 100 , c = 103 ,  = 0.5 ) : (a) K = , (b) K = 13 1.7 (a) 1.7 (b) 1.5 DMF DMF 1.5 1.3 b=0 b=0.25 b=0.5 b=0.75 1.1 1.3 b=0 b=0.25 b=0.5 b=0.75 1.1 0.9 0.9 20 40 60 80 Velocity (m/s) 100 20 40 60 80 Velocity (m/s) 100 Fig 3.4 The DMF of beam with various values of viscous damping: ( K1 = 100 , K = , c = 103 ,  = 0.5 ): (a) c f = 102 , (b) c f = 104 1.7 (a) 1.7 (b) 1.5 DMF DMF 1.5 1.3 b=0 b=0.25 b=0.5 b=0.75 1.1 1.3 b=0 b=0.25 b=0.5 b=0.75 1.1 0.9 0.9 20 40 60 80 Velocity (m/s) 100 20 40 60 80 Velocity (m/s) 100 Fig 3.5 The DMF of the beam with various values of  v : ( K1 = 100 , K = , c = 103 ,  = 0.5 ): (a)  = 0.25 , (b)  = 1.6 (a) 1.6 (b) 1.4 DMF DMF 1.4 1.2 1.2 b=0 b=0.25 b=0.5 b=0.75 b=0 b=0.25 b=0.5 b=0.75 0.8 0.8 20 40 60 80 Velocity (m/s) 100 20 40 60 80 Velocity (m/s) 100 Fig 3.6 The DMF of the beam with various values of  v : ( K1 = 100 , K = , c = 103 ,  = 0.5 ): (a)  v = 0.75 , (b)  v = 1.5 1.6 (a) 1.6 (b) 1.4 DMF DMF 1.4 1.2 b=0 b=0.25 b=0.5 b=0.75 1.2 b=0 b=0.25 b=0.5 b=0.75 0.8 0.8 20 40 60 80 Velocity (m/s) 100 20 40 60 80 Velocity (m/s) 100 Fig 3.7 The DMF of the beam with various values of cv : ( K1 = 100 , K = , c = 103 ,  = 0.5 ): (a)  v = 5% , (b)  v = 10% 14 3.4 The plate on the foundation 3.4.1 The parameters of the plate model k B2 wa2 kB K '1 = , K '2 = s ,  =  D D h (3.3) D 3.4.2 Free vibration of the plate The effects of characteristic parameters of the foundation on free vibration of the square plate for  = 0.5 are shown in Table 3.1 Table 3.1 The dimensionless frequencies of the plate on foundation K’1 102 50 SSSS (=0.2, h/B=0.01) CCCC (=0.2, h/B=0.01) b K’2 1 2 3 1 2 3 3.8957 7.2044 10.334 5.1522 9.3363 13.058 0.25 1.0604 1.9612 2.8134 1.4024 2.5416 3.5551 0.5 0.7641 1.4132 2.0273 1.0105 1.8314 2.5618 0.75 0.6279 1.1613 1.6660 0.8304 1.505 2.1052 3.4.3 Dynamic response of the plate The parameters of the plate on the dynamic foundation are given by B = 10 m, L = 20 m, h = 0.3 m,  = 2500 kg/m3, E = 3.1x1010 N/m2,  = 0.2 ,  v = 0.5 ,  v = 0.5 , mw = , K '1 = 50 , K '2 = , c = 102 Ns/m2 and  = 0.75 , with simple support along the short two sides (a) 1.7 b=0 b=0.25 b=0.5 b=1 b=0 (b) 1.5 b=1 DMF DMF 1.3 1.1 1.1 0.9 0.9 20 1.9 b=0 40 60 ` Velocity (m/s) b=0.25 80 b=0.5 100 (d) 1.15 40 60 Velocity (m/s) b=0.25 80 b=0.5 100 b=1 1.65 DMF 1.4 20 b=0 1.9 b=1 1.65 DMF b=0.5 1.5 1.3 (c) b=0.25 1.7 1.4 1.15 0.9 0.9 20 40 60 80 Velocity (m/s) 100 20 40 60 80 Velocity (m/s) 100 15 Fig 3.8 The DMF of the beam with various values of elastic spring: (a) K1' = 25 , (b) K1' = 50 , (c) K1' = 75 , (d) K1' = 100 (a) b=0 1.7 b=0.25 b=0.5 (b) b=1 1.5 b=0.25 b=0.5 b=1 DMF DMF 1.5 1.3 1.3 1.1 1.1 0.9 0.9 (c) b=0 1.7 20 b=0 1.7 40 60 Velocity (m/s) b=0.25 80 b=0.5 100 b=1 (d) 1.7 40 60 Velocity (m/s) b=0.25 80 b=0.5 100 b=1 DMF 1.5 DMF 1.5 20 b=0 1.3 1.3 1.1 1.1 0.9 0.9 20 40 60 Velocity (m/s) 80 100 20 40 60 Velocity (m/s) 80 100 Fig 3.9 The DMF of the beam with various values of shear layer: (a) K 2' = , (b) K 2' = , (c) K 2' = 25 , (d) K 2' = 50 (a) b=0 1.7 b=0.25 b=0.5 b=1 b=0.5 b=1 DMF 1.3 1.3 1.1 1.1 0.9 0.9 20 b=0 1.5 40 60 Velocity (m/s) b=0.25 80 b=0.5 100 b=1 (d) 20 b=0 1.5 40 60 Velocity (m/s) b=0.25 80 b=0.5 100 b=1 1.35 DMF 1.35 DMF b=0.25 1.5 DMF 1.5 (c) b=0 (b)1.7 1.2 1.05 1.2 1.05 0.9 0.9 20 40 60 80 Velocity (m/s) 100 20 40 60 80 Velocity (m/s) 100 Fig 3.10 The DMF of the beam with various values of viscous damping: (a) c = 102 , (b) c = 103 , (c) c = x103 , (d) c = 104 16 b=0 1.7 (a) b=0.25 b=0.5 b=1 b=0 (b)1.7 1.5 b=0.25 b=0.5 b=1 DMF DMF 1.5 1.3 1.3 1.1 1.1 0.9 0.9 20 b=0 (c) 1.7 40 60 Velocity (m/s) b=0.25 80 b=0.5 100 b=1 20 b=0 (d) 1.7 40 60 Velocity (m/s) b=0.25 80 b=0.5 100 b=1 1.5 DMF DMF 1.5 1.3 1.3 1.1 1.1 0.9 0.9 20 40 60 Velocity (m/s) 80 100 20 40 60 Velocity (m/s) 80 100 Fig 3.11 The DMF of the beam with various values of  v : (a)  v = 0.25 , (b)  v = 0.5 , (c)  v = , (d)  v = b=0 (a) 1.7 b=0.25 b=0.5 b=1 1.5 b=0 (b)1.7 b=0.25 b=0.5 b=1 DMF DMF 1.5 1.3 1.3 1.1 1.1 0.9 0.9 20 b=0 (c) 1.7 40 60 Velocity (m/s) b=0.25 80 b=0.5 100 b=1 20 b=0 (d)1.7 40 60 Velocity (m/s) b=0.25 80 b=0.5 100 b=1 1.5 DMF DMF 1.5 1.3 1.3 1.1 1.1 0.9 0.9 20 40 60 Velocity (m/s) 80 100 20 40 60 Velocity (m/s) 80 Fig 3.12 The DMF of the beam with various values of  v : (a)  v = 0.25 , (b)  v = 0.5 , (c)  v = , (d)  v = 100 17 b=0 (a)1.7 b=0.25 b=0.5 b=1 b=0 (b)1.7 b=0.5 b=1 DMF 1.5 DMF 1.5 b=0.25 1.3 1.3 1.1 1.1 0.9 0.9 20 b=0 (c) 1.7 40 60 Velocity (m/s) b=0.5 b=1 80 100 b=1.5 20 b=0 (d)1.7 40 60 Velocity (m/s) b=0.25 80 b=0.5 100 b=1 1.5 DMF DMF 1.5 1.3 1.3 1.1 1.1 0.9 0.9 20 40 60 Velocity (m/s) 80 100 20 40 60 Velocity (m/s) 80 100 Fig 3.13 The DMF of the beam with various values of  v (a)  v = 0.01 , (b)  v = 0.1 , (c)  v = 0.15 , (d)  v = 0.2 3.4 Conclusion This chapter realized numerical results based on basic theory and the computer program of chapter With many investigation results of input circumstance (ngữ pháp) show that the influence of foundation mass is significant than without foundation mass It almost increases the dynamic response of structures and causes more unfavorable for the above structures The results are important in the content of theory research of dissertation, it presented quantitative results of the influence of foundation mass on the dynamic response of the above structures and it is basic to establish an experimental model in the next chapter Chapter THE EXPERIMENTAL STUDY FOR DETERMINING THE INFLUENCE OF FOUNDATION MASS 18 4.1 Introduction This chapter uses the experimental model to determine characteristic parameters of the influence of the foundation mass on the dynamic response of the structures 4.2 An experimental model of single degree of freedom 4.2.1 The model The experimental model is present in Fig 4.1 Fig 4.1 An experimental model of single degree of freedom The parameter of foundation mass is determined m  mS a F = eff eff H F (4.1) where mS is mass of structure and meff is vibration mass 4.2.2 The results The efficiency stiffness of foundation is determined based on the relationship between force-displacement and the characteristic parameters of the foundation are drawn in Table 4.1 Table 4.1 The character parameters of experimental models Symbol M1 M2 M3 M4 keff (kN/mm) HF (mm) ρeff (kg/m) mS (kg) 2.558 102.675 48.503 1.939 1.140 203.500 48.872 1.968 0.758 303.475 48.923 1.989 0.586 404.775 48.714 1.938 The results of natural frequency in experimental models are the average value of many times, shown in Table 4.2 and the characteristic parameter of the influence of foundation mass is plotted in Table 4.3 19 Table 4.2 The natural frequency of experimental models The natural frequency at sensors Model M1 M2 M3 M4 Value of natural A47490 A47491 A47492 frequency wF (rad/s) 694.711 456.159 354.372 296.776 689.684 451.342 353.534 302.640 682.144 453.646 353.743 295.729 688.847 453.716 353.883 298.381 Table 4.3 The parameter of influence of foundation mass Model keff wF (kN/mm) (rad/s) mS (kg) mF (kg) meff (kg) HF (mm) aF M1 2.558 688.847 1.939 3.451 5.391 102.675 0.693 M2 M3 M4 1.140 0.758 0.586 453.716 353.883 298.381 1.968 3.569 1.989 4.064 1.938 4.644 5.538 6.053 6.582 203.500 303.475 404.775 0.359 0.274 0.260 4.2.3 Comment and estimate The analysis results are shown from Fig 4.2 to Fig 4.6 5.00 1200 4.50 1000 w F (rad/s) m F Experiment 4.00 3.50 3.00 600 400 200 50 150 250 H F (mm) 350 450 Fig.4.2 The relationship mF - H F 50 5.00 0.65 4.50 0.50 150 250 H F (mm) 350 450 Fig 4.3 The frequency results 0.80 mF aF Without foundation mass 800 4.00 3.50 0.35 3.00 0.20 50 150 250 350 H F (mm) 450 0.5 1.0 1.5 2.0 2.5 3.0 k eff (kN/mm) Fig 4.4 The relationship aF - HF Fig 4.5 The relationship mF - keff 20 0.80 aF 0.65 0.50 0.35 R = 0.9963 0.20 0.5 1.0 1.5 2.0 2.5 3.0 k eff (kN/mm) Fig 4.6 The relationship a F - keff 4.3 An experimental model of the beam on the foundation 4.3.1 The model The model of the beam on the dynamic foundation is described by a steel beam on rubber layer in the Fig 4.7 Fig 4.7 The experimental model The characteristic parameters of the beam are determined based on experiment, shown in Table 4.4 and Table 4.5 Table 4.4 The character parameters of the steel beam Model L b h ρ (kg/m3) E (N/m2) Steel beam 500.00 40.00 2.80 7691.267 1.808x1011 Table 4.5 The characteristic of the rubber layer Model HF mm) D1 105.98 D2 211.96 D3 317.75 D4 423.64 ρF (kg/m3) kS (N/m) k (N/m3) 6.367x107 1206.690 1.773x105 2.807x107 1.874x107 1.452x107 21 Table 4.6 The experimental results of natural frequency of beam Model The natural frequency at sensors Value of natural A47490 A47491 A47492 frequency wF (rad/s) D1 490.298 494.696 487.366 490.787 D2 428.723 427.885 428.094 428.234 D3 335.522 336.150 337.407 336.360 D4 313.950 314.997 314.369 314.439 Table 4.7 The parameter of influence of foundation mass Model ρF (kg/m ) k (N/m3) kS (N) HF wF (mm) (rad/s) aF 6.367x107 105.98 490.787 2.253 D1 D2 2.807x107 211.96 428.234 0.748 1206.690 1.773x105 D3 1.874x107 317.75 336.360 0.592 1.452x107 423.64 314.439 0.461 D4 4.3.2 The experimental results The results of natural frequency in experimental models of the beam are shown in Table 4.6 and the parameter of the influence of foundation mass is determined, plotted in Table 4.7 4.3.3 Comment and estimate The analysis results are shown from Fig 4.8 to Fig 4.10 2000 1.80 aF 1550 w F (rad/s) 2.40 Experiment Without foundation mass 1100 1.20 0.60 650 0.00 200 50 150 250 H F (mm) 350 450 50 150 250 350 H F (mm) 450 Fig 4.8 The frequency results Fig 4.9 The relationship a F - H F 22 2.40 aF 1.80 1.20 0.60 R = 0.9858 0.00 1.E+07 3.E+07 5.E+07 7.E+07 k (N/m ) Fig 4.10 The relationship mF - k 4.4 Conclusion This chapter realized the content of experimental study: - Choosing material, designing model and using experimental equipment agreed with the object of study in the dissertation are presented The main material is rubber having the homogeneous property quite well and ideal elastic; the beam structure uses steel material having homogeneous property quite well and characteristic mechanic clearly The simple experiment model as a single degree of freedom is described by a steel plate on rubber layer and the beam structure model on rubber layer are also designed The recorder is used to determine natural frequency based on many data and various sizes of rubber layer in an experimental model of free vibration - The experiment models are realized to determine the influence of foundation mass on the structures The results show that the parameter a F has effect significantly on the dynamic response of the structures; it causes foundation mass to participate in vibration mF and it increases the general mass of the structures At the same time, the experimental results also show that the relation between foundation mass with the depth of foundation layer and stiffness of foundation agree with judgment based on characteristic physics of the structures - The analysis of the relation between the depth of foundation H F and the parameter of the influence of foundation mass a F : with an increase of depth of foundation causes increase vibration foundation 23 mass mF , and at the same time the parameter of foundation mass a F decreases with the increase of depth of foundation; the results agree in both experimental models - The analysis of the relationship between stiffness of foundation k and the parameter of the influence of foundation mass a F : the relation is linear; with an increase of the stiffness of foundation cause increase value of the parameter of the influence of foundation mass From the above comments, it can be seen that the contents of experimental research quite agree with the dynamic foundation model in the theoretical research of chapter and of the dissertation; at the same time, the experimental results also determined relation between the parameter of the influence of foundation mass a F with depth H F and stiffness of foundation k , and especially value of a F in the above experiments CONCLUSIONS Conclusion The following conclusions are summarized as follow: The study proposed a new foundation model, called the dynamic foundation model and established basic theory to describe parameter of the influence of foundation mass on the dynamic response of beam and plate structures The process of finite element method to describe the influence of foundation mass on the dynamic response of the structures subjected to moving load is established clearly, it was described by flowchart algorithm and established the computer program The analysis results show that the foundation mass effects significantly on dynamic properties of the structures, it increases general vibration mass of the structures The study determined relationship between the parameter of 24 the influence of foundation mass and stiffness foundation is linear, and the relationship between it and depth of foundation is nonlinear; at the same time, the value of a parameter of the influence of foundation mass decreases with an increase of foundation depth The study has practical significance in the problem of dynamic analysis response of the structures on foundation, such as road-vehicles, runway, rail-train-foundation interaction, etc It can be seen that it is so difficult to have foundation model which can be considered the perfect model to describe the almost true behavior of soils However, the study has tried to establish a new foundation model describing more behavior than other ones with aspiration having a contribution in both theory and practice Recommendation The orientation development of the dissertation will use real structure model to assess and verify again the parameter of the influence of foundation mass LIST OF PUBLICATIONS Journals and conferences in the country Hoang P Hoa, Pham D Trung and Nguyen T Phuoc, Overview of foundation models and propose a new foundation model applied in problem of analysis response of structures interaction with foundation, Vietnam Journal of Construction, ISSN 0866-0762, No 6, pp 47-50, 2015 Hoang P Hoa, Pham D Trung and Nguyen T Phuoc, The influence of foundation mass parameters on dynamic response of road-vehicles, Conference on Advances in Engineering for a Sustainable Development, University of Science and Technology, The University of Da Nang, ISBN 978-604-82-1805-8, pp 16-24, 2016 Pham D Trung, Hoang P Hoa and Nguyen T Phuoc, The experiment of influence of foundation mass on free vibration of beam, Vietnam Journal of the Builder, ISSN 0866-8531, No 11&12, pp 48-50&54, 2016 Journals and conferences abroad: Nguyen Trong P., Pham Dinh T., The influence of mass of twoparameter elastic foundation on dynamic responses of beam subjected to a moving mass, KSCE Journal of Civil Engineering (ISI-SCIE), pp.1-7, 2016 Pham D T., Hoang P H., Nguyen T P., Dynamic response of beam on a new foundation model subjected to a moving oscillator by finite element method, The 16th Asia Pacific Vibration Conference APVC2015, Bachkhoa Publishing House, Hanoi, Vietnam ISBN: 978- 604-938-726-5, pp 244-250, 2015 T P Nguyen, D T Pham, P H Hoang, A New Foundation Model for Dynamic Analysis of Beams on Nonlinear Foundation Subjected to a Moving Mass, Procedia Engineering (Scopus), ISSN 1877-7058, No 142, pp 165-172, 2016 T P Nguyen, D T Pham, P H Hoang, A dynamic foundation model for the analysis of plates on foundation to a moving oscillator, Structural Engineering and Mechanics, An International Journal, Technopress, (ISI-SCI), ISSN: 1225-4568, 59(6), pp.1019-1035, 2016 D T Pham, P H Hoang, T P Nguyen, Dynamic Response of Beam on a New Non-Uniform Dynamic Foundation Subjected to a Moving Vehicle Using Finite Element Method, International Journal of Engineering Research & Technology (IJERT), eISSN: 2278-0181, 6(3), pp 279-285, 2017 Trung D Pham, Hoa P Hoang, Phuoc T Nguyen, Experiments on influence of foundation mass on dynamic characteristic of structures, Structural Engineering and Mechanics, An International Journal, Technopress, (ISI-SCI), ISSN: 1225-4568, 65(5), pp 505-511, 2018