Free Vibration And Thermal Shock Of Functionally Graded Beams And Circular Plates

At present, the problem of static deformation and dynamic response of functionally gradient material (FGM) structures that subjected to thermal and mechanical loading have been extensively investigated and become one of the most important key issues in solid mechanics and engineering. This thesis focuses on some mechanical problems of FGM structures that have not been studied until now. In this thesis, free vibration of FGM circular plates with/without thermal post-buckling deformation, dynamic response of FGM beam with thermal shock load and free vibration of delaminated FGM beam are studied involving the following three parts:1. Based on von Kaman's classical plate theory, governing equations for the small amplitude free vibration of FGM circular plates in the vicinity of the thermal post-bucking configuration that induced by a stable temperature filed are derived. By using shooting method to solve simultaneously the governing equations both for thermal post-buckling and vibration, numerical solutions of thermal post-buckling equilibrium paths and the first three natural frequencies depending on the temperature rise of the FGM circular plates are obtained. The effects of the parameters of material gradients, temperature field, and the boundary conditions on the responses of post-bucking and vibration of the plates are examined in detail. The characteristics of nonlinear temperature-dependent material properties of the functionally graded material are considered in the analysis.2. Based on Timoshenko beam theory, the problem of transient dynamic response of FGM beam that subjected to one dimensional thermal shock are investigated. The technique of Laplace transform and differential quadrature method (DQM) are performed to solve the thermal conduction equation and dynamic equations, respectively. The time depended deformation and stresses response of FGM beam are obtained. The effects of the parameters of material gradients and geometrical conditions of beam are analysed both in the cases of thermal loading from ceramic surface and metallic surface. A homogeneous beam that degradated from FGM beam is investigated by both DQM and Laplace transform method, so that a comparation could be done in order to testify the availability of DQM in this problem.3. Based on Tiomshenko beam theory, the governing equations of free vibration of FGM beam that with single delamination are established. A numerical method which is named Differential Quadrature Element Method (DQEM) is introduced to solve the governing equations. As a numerical experiment, the first eighth frequencys of FGM beam that with one delamination and two ends clamped are calculated. By contrast the results with that of perfect FGM beam, the effects of the length and position of delamination and the parameters of material gradients are discussed in detail.