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Vibration Analysis of Timoshenko Beams on a nonlinear Elastic foundation

Tsinghua Science and Technology 2009年第3期14卷 322-326页

作者：莫怡华欧丽钟宏志 Department of Civil Engineering Tsinghua UniversityBeijing 100084 China School of Civil and Architectural Engineering Central South UniversityChangsha 410075 China

The vibrations of beams on a nonlinear elastic foundation were analyzed considering the effects of transverse shear deformation and the rotational inertia of beams. A weak form quadrature element method （QEM） is used for the vibration analysis. The fundamental frequencies of beams are presented for various slenderness ratios and nonlinear foundation parameters for both slender and short beams. The results for slender beams compare well with finite element results. The analysis shows that the transverse shear deformation and the nonlinear foundation parameter significantly affect the fundamental frequency of the beams.

关键词： weak form quadrature element method （QEM） nonlinear foundation vibration Timoshenko beam

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Limit point buckling of a finite beam on a nonlinear foundation

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Theoretical & Applied Mechanics Letters 2014年第3期4卷 18-24页

作者： Romain Lagrange Massachusetts Institute of Technology Department of MathematicsCambridgeMA 02139-4307 USA

In this paper, we consider an imperfect finite beam lying on a nonlinear foundation, whose dimensionless stiffness is reduced from 1 to k as the beam deflection increases. Periodic equilibrium solutions are found analytically and are in good agreement with a numerical resolution, suggesting that localized buckling does not appear for a finite beam. The equilibrium paths may exhibit a limit point whose existence is related to the imperfection size and the stiffness parameter k through an explicit condition. The limit point decreases with the imperfection size while it increases with the stiffness parameter. We show that the decay/growth rate is sensitive to the restoring force model. The analytical results on the limit load may be of particular interest for engineers in structural mechanics.

关键词： buckling imperfection finite beam nonlinear foundation limit point

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The Scheme to Determine the Convergence Term of the Galerkin Method for Dynamic Analysis of Sandwich Plates on nonlinear foundations

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Acta Mechanica Solida Sinica 2021年第1期34卷 1-11页

作者： Hong-Yan Chen Hu Ding Shao-Hua Li Li-Qun Chen Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai Institute of Applied Mathematicsand MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversitygShanghai 200444China State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures Shijiazhuang Tiedao UniversitxyShiyiazhuang 050043China

The vibration of a plate resting on elastic foundations under a moving load is of great significance in the design of many engineering fields,such as the vehicle-pavement system and the aircraft-runway system.Pavements or runways are always laminated structures.The Galerkin truncation method is widely used in the research of vibration.The number of truncation terms directly affects the convergence and accuracy of the response results.However,the selection of the number of truncation terms has not been clearly stated.A nonlinear viscoelastic foundation model under a moving load is established.Based on the natural frequency of linear undisturbed derivative systems,the truncation terms are used to determine the convergence of vibration response.The criterion for the convergence of the Galerkin truncation term is presented.The scheme is related to the natural frequency with high efficiency and practicability.Through the dynamic response of the sandwich beam under a moving load,the feasibility of the scheme is verified.The effects of different system parameters on the scheme and the truncation convergence of dynamic response are presented.The research in this paper can be used as a reference for the study of the vibration of elastic foundation plates.Especially,the model established and the truncation analysis method proposed are helpful for studying the vibration of vehicle-pavement system and related systems.

关键词： ndwich plate Galerkin method Convergence nonlinear foundation

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Dynamic Analysis and Numerical Simulation of a Kind of Arrestor Arresting Buckle Propagation by FEM

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China Ocean Engineering 1998年第3期13卷 323-332页

作者： Huang, YY Qian, Q Jin, T Huazhong Univ Sci & Technol Dept Mech Wuhan 430074 Peoples R China

For exact estimation of efficiency of a buckle arrestor, it is necessary to take the effect of structural inertia into account in the analysis of buckle propagation on elastic structures after meeting arrestors. Under this consideration, this paper deals with the dynamics of buckle arrest and its numerical simulation on the basis of the beam system model used by Chater and Hutchinson (1983). The FEM combined with an improving are-length control method is adopted to solve the dynamic equations describing the arresting of buckle propagation. A new group of parameters for arrestor design which differs greatly from that by the quasi-static analysis is obtained. The present results support the conclusion that the inertia of the beam cannot be neglected in such analysis.

关键词： buckle propagation arrestor beam nonlinear foundation finite element method

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