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NONLINEAR VIBRATION FOR MODERATE THICKNESS RECTANGULAR CRACKED PLATES INCLUDING COUPLED EFFECT OF elastic foundation

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Applied Mathematics and Mechanics(English Edition) 2005年第8期26卷 963-972页

作者： XIAO Yong-gang（肖勇刚） FU Yi-ming（傅衣铭） ZHA Xu-dong（查旭东） Department of Engineering Mechanics Hunan UniversityChangsha 410082 P. R. China College of Bridge and Structure Engineering Changsha University of Science and Technology Changsha 410076 P. R. China

Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-parameter foundation. Under the condition of free boundary, a set of trial functions satisfying all boundary conditions and crack＇s continuous conditions were proposed. By employing the Galerkin method and the harmonic balance method, the nonlinear vibration equations were solved and the nonlinear vibration behaviors of the plate were analyzed. In numerical computation, the effects of the different location and depth of crack, the different structural parameters of plates and the different physical parameters of foundation on the nonlinear amplitude frequency response curves of the plate were discussed.

关键词： moderate thickness rectangular plate elastic foundation crack nonlinear vibration

A Unified Dimensionless Parameter for Finite Element Mesh for Beams Resting on elastic foundation

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Computer Modeling in Engineering & Sciences 2020年第3期122卷 955-969页

作者： Ping Lou Xinlei Zhang F.T.K.Au Zixian Zhang Yi Huang School of Civil Engineering Central South UniversityChangshaChina. Key Laboratory of Heavy Railway Engineering Structure of Education Ministry Central South UniversityChangshaChina. Department of Civil Engineering University of Hong KongHong KongChina.

Discretising a structure into elements is a key step in finite element(FE)*** discretised geometry used to formulate an FE model can greatly affect accuracy and *** paper presents a unified dimensionless parameter to generate a mesh of cubic FEs for the analysis of very long beams resting on an elastic foundation.A uniform beam resting on elastic foundation with various values of flexural stiffness and elastic supporting coefficients subject to static load and moving load is used to illustrate the application of the proposed *** numerical results show that(a)Even if the values of the flexural stiffness of the beam and elastic supporting coefficient of the elastic foundation are different,the same proposed parameter“s”can ensure the same accuracy of the FE solution,but the accuracy may differ for use of the same element length;(b)The proposed dimensionless parameter“s”can indeed be used as a unified index to generate the mesh for a beam resting on elastic foundation,whereas the use of the same element length as a criterion may be misleading;(c)The errors between the FE and analytical solutions for the maximum vertical displacement,shear force and bending moment of the beam increase with the dimensionless parameter“s”;and(d)For the given allowable errors for the vertical displacement,shear force and bending moment of the beam under static load and moving load,the corresponding values of the proposed parameter are provided to guide the mesh generation.

关键词： Beam cubic finite element elastic foundation finite element mesh unified dimensionless parameter.

Vertical vibrations of elastic foundation resting on saturated half-space

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Applied Mathematics and Mechanics(English Edition) 2007年第9期28卷 1199-1207页

作者：王国才王哲孟凡丽 School of Civil Engineering and Architecture Zhejiang University of Technology

This paper is mainly concerned with the dynamic response of an elastic foundation of finite height bounded to the surface of a saturated half-space. The foundation is subjected to time-harmonic vertical loadings. First, the transform solutions for the governing equations of the saturated media are obtained. Then, based on the assumption that the contact between the foundation and the half-space is fully relaxed and the halfspace is completely pervious or impervious, this dynamic mixed boundary-value problem can lead to dual integral equations, which can be further reduced to the Predhohn integral equations of the second kind and solved by numerical procedures. In the numerical extortples, the dynamic colnpliances, displacements and pore pressure are developed for a wide range of frequencies and material/geometrical properties of the saturated soil-foundation system. In most of the cases, the dynamic behavior of an elastic foundation resting on the saturated media significantly differs from that of a rigid disc on the saturated half-space. The solutions obtained can be used to study a variety of wave propagation problems and dynamic soil-structure interactions.

关键词： saturated media elastic foundation vertical vibration dynamic colnplialice dual integral equations

ANALYSIS OF COUPLED-MODE FLUTTER OF PIPES CONVEYING FLUID ON THE elastic foundation

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Applied Mathematics and Mechanics(English Edition) 2000年第10期21卷 1177-1186页

作者：王忠民冯振宇赵凤群刘宏昭 School of Science Xi''an University of Technology 710048 Xi''an P R China Department of Basic Courses Xi''an Highway University 710064 Xi''an P R China School of Mechanical and Instrumnenal Engineering Xi''an University of Technology 710048 Xi''an P R China

The governing equation of solid-liquid couple vibration of pipe conveying fluid on the elastic foundation was derived. The critical velocity and complex frequency of pipe conveying fluid on Winkler elastic foundation and two-parameter foundation were calculated by po,ver series method. Compared,with pipe without considering elastic foundation, the numerical results show that elastic foundation can increase the critical flow velocity of static instability and dynamic instability of pipe. And the increase of foundation parameters may increase the critical flow velocity of static instability and dynamic instability of pipe, thereby delays the occurrence of divergence and flutter instability of pipe. For higher mass ratio beta, in the combination of certain foundation parameters, pipe behaves the phenomenon of restabilization and redivergence after the occurrence of static instability, and then coupled-mode flutter takes place.

关键词： elastic foundation pipe conveying fluid coupled-mode flutter stability power series method

A complex solution on the dynamic response of sandwich graphene-reinforced aluminum-based composite beams with copper face sheets under two moving constant loads on an elastic foundation

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International Journal of Mechanical System Dynamics 2023年第3期3卷 251-264页

作者： Mohammadreza Eghbali Seyed Amirhosein Hosseini Department of Mechanical Engineering University of ZanjanZanjanIran Department of Industrial Mechanical and Aerospace EngineeringBuein Zahra Technical UniversityQazvinIran

An analytical solution was used to investigate the elastic response of a sandwich beam with a graphene-reinforced aluminum-based composite(GRAC)on an elastic foundation using copper as the face layer of the functionally graded composite beam and a simply supported boundary ***'s higher-order shear deformation theory was utilized to derive the equations,which were solved in Laplace space and then converted into space–time using Laplace *** exact response of the GRAC sandwich beam was obtained by considering the displacement at the mid-span of the sandwich *** moving loads with different speed ratios were applied at a single point,and the effect of various parameters,including the spring constant,the speed ratio,the percentage of graphene,the moving load speed,and the distribution pattern,was *** study aimed to eliminate any overlap and improve the accuracy of the *** exact solving method presented has not been reported in other articles so ***,due to the difficulty of solving mathematical equations,this method is only applicable to simple boundary conditions.

关键词： GRAC beams moving load Laplace transform elastic foundation analytical solution aluminum-based

Semi-analytical approach for free vibration analysis of cracked beams resting on two-parameter elastic foundation with elastically restrained ends

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Frontiers of Mechanical Engineering 2014年第2期9卷 191-202页

作者： Alborz MIRZABEIGY Firooz BAKHTIARI-NEJAD Department of Mechanical Engineering Amirkabir University of Technology Hafez Ave Tehran 15914 Iran

In present study, free vibration of cracked beams resting on two-parameter elastic foundation with elastically restrained ends is considered. Euler-Bemoulli beam hypothesis has been applied and translational and rotational elastic springs in each end considered as support. The crack is modeled as a mass-less rotational spring which divides beam into two segments. After governing the equations of motion, the differential transform method （DTM） has been served to determine dimensionless frequencies and normalized mode shapes. DTM is a semi-analytical approach based on Taylor expansion series that converts differential equations to recursive algebraic equations. The DTM results for the natural frequencies in special cases are in very good agreement with results reported by well-known references. Also, the DTM procedure yields rapid convergence beside high accuracy without any frequency missing. Comprehensive studies to analyze the effects of crack location, crack severity, parameters of elastic foundation and boundary conditions on dimensionless frequencies as well as effects of elastic boundary conditions on cracked beams mode shapes are carried out and some problems handled for first time in this paper. Since this paper deals with general problem, the derived formulation has capability for analyzing free vibration of cracked beam with every boundary condition.

关键词： free vibration cracked beam elastic foundation restrained ends differential transform method

BUCKLING AND POST-BUCKLING OF ANNULAR PLATES ON AN elastic foundation

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Applied Mathematics and Mechanics(English Edition) 1991年第8期12卷 785-797页

作者：杨骁程昌钧 Department of Mechanics Lanzhou University Lanzhou

On the basis of von Karnmnequations, the axisymmetric buckling and post-buckling of annular plates on anelastic foundation is so wematically discussed byusing shooting

关键词： elastic foundation shooting method bifurcation solution,asymptotic formulae post-buckling analyses

GENERAL SOLUTION FOR DYNAMICAL PROBLEM OF INFINITE BEAM ON AN elastic foundation

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Applied Mathematics and Mechanics(English Edition) 1991年第7期12卷 633-637页

作者：郑小平王尚文陈百屏 Northwestern Polytechnical University Xi'an

Based on the theory of Eider-Bernoulli beam and Winkler assumption for elastic foundation, a mathematical model is presented. By using Fourier transformation for space variable, Laplace transformation for time variable and convolution theorem for their inverse transformations, a general solution for dynamical problem of infinite beam on an elastic foundation is obtained. Finally, the cases of free vibration,impulsive response and moving load are also discussed.

关键词： elastic foundation infinite beam dynamical problem,general solution integral transformation method

Thermal Buckling and Post-Buckling Behavior of Pined-Fixed Beams on Nonlinear elastic foundation

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Thermal Buckling and Post-Buckling Behavior of Pined-Fixed B...