Free Vibration And Stability Of Fuctional Graded Material Beams With Surface-bonded Piezoelectric Player

In recent years, the problem of static deformation and dynamic response of single-layer or multi-layer intelligent structures subjected to multiple loads have been extensively investigated and become one of the most important and key issues in solid mechanics and intelligent control field. In this thesis, responses of post-buckling and linear free vibration of FGM beams with surface-bonded piezoelectric layers are studied. The main content andresents are as following:1. By accurately considering the axial extension, governing equations for the small amplitude free vibration of functionally graded material Euler beams in the vicinity of thermal post-buckling configuration under thermal loadings, were formulated. 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 of the FGM beam depending on the temperature rise are obtained. The effect of the parameters of material gradients, temperature field on the responses of post-buckling and vibration of the beam are examined.2. Based on geometrically nonlinear theory for axial extensive Timoshenko beam, nonlinear governing equations, for functionally graded beams with surface-bonded piezoelectric layers subjected to thermo-electro-mechanical loadings were formulated. By using a shooting method, the obtained nonlinear boundary value problem was numerically solved and buckling and post-buckling response of the beams with the both ends fixed, subjected to transversely non-uniform heating and uniform electric field, were presented. Characteristic curves of the post-buckling deformation of the beam varying with thermal load, the electrical load, and the power law index are plotted. Numerical results show that the tensional force produced in the piezoelectric layers by the voltage can efficiently increase the critical buckling temperature and defer the thermal post-buckling to occur.3. Geometrically nonlinear deformation and free vibration for functionally graded beams with surface-bonded piezoelectric layers in the vicinity of the post-buckling configuration, subjected to thermo-electro-mechanical loadings were analysised quantitatively. For the small amplitude free vibration befor the pre-buckling, analytical solutions of the laminated beam with surface-bonded piezoelectric layers subjected to transversely non-uniform heating and uniform electric field were arrived at. By using a shooting method, the boundary value problems for the post-buckling and linear vibration of the beam with the ends fixed was numerically solved. Characteristic curves of the post-buckling deformation and the lower order frequencies versus thermal load, the electrical load, and the power law index are plotted. Influence of the inverse piezoelectric effect, the temperature rise and the properties of the material gradients on the deformation and vibration are discussed.