Post-buckling And Free Vibration Of Elastic Foundation Beams And Circular Plates

Beams and plates are important basic structures in engineering.The mechanics behavior of beams and plates has important value in structural theory analysis and engineering application.There are components or structures subjected to the non-conservative force displayed attaching the structures in engineering applications,which makes a system become a non-conservative system.In this thesis,the shooting method and differential quadrature method are used to solve the post-buckling and free vibration of the beams and plates.The main works of this thesis has the following two aspects:1.Buckling and vibration of nonlinear elastic foundation beam under following loadBased on the geometrical nonlinear theory of the axially extensible Euler-Bernoulli beam,the buckling problem and vibration problem are established by the D’Alembert principle through the micro-element analysis.The beam is subjected to the tangential non-conservative following load and the nonlinear elastic foundation restraint.The small amplitude free vibration near the post-buckling is solved by the numerical shooting method.And the influence of the parameters of the foundation and the following load on the post-buckling characteristics and vibration of the beam are discussed.The post-buckling equilibrium path of the beam under the action of the following load and the relationship between the third order natural frequencies near the post-buckling with the load are discussed.2.Differential quadrature method for solving free vibration of medium circular plate in functionally graded materials.Based on the medium plate theory(Mindlin theory and Reissner theory),the control differential equation of axisymmetric free vibration of functionally graded material(FGM)medium plates established through Hamiltonian variation principle.The differential quadrature method(DQM)is used in solving the axisymmetric free vibration equation of the thick circular plate of the FGM with three boundary conditions.The governing equations and boundary conditions are separated into algebraic equations by differential quadrature method,and the problem of free vibration frequency is transformed into algebraic equation eigenvalue problem.The effects of graded index and thickness index on the zero dimension frequency are discussed.Compared with the results of other thesises,it turns out that the DQM method has more feasibility and accuracy.