The Free Vibration Of Laminated Composite Plate In The Vicinity Of Thermal Post-buckled Static Equilibrium Configuration

On the basis of the classical theory of laminated composite plates and by using Galerkin method, thermal post-buckling, large amplitude vibration in the pre-buckled state and small amplitude vibration in the post-buckled state of the rectangular laminated plates subjected to uniform temperature rise are studied. The main contents are as following:1. Based on the classical theory of laminated composite plates and in the sense of von Karman's geometrically nonlinear equations, nonlinear dynamic governing equations, in terms of the middle plane displacements, for the composite laminated plates under mechanical and thermal loads are derived, in which the stretching-bending and the bending-twisting terms are included.2. On the assumption that the vibration response are harmonic, by using Kantorovich time averaging method in the time domain and Galerkin method in the special domain, large amplitude vibration of the symmetrically laminated composite plates in the pre-buckled state are analyzed. Characteristic curves of the fundamental frequency varying with the central amplitude are presented for some given values of the temperature rise. Numerical results show that the frequency increases with the increase of the central amplitude and decreases with the rise of temperature, monotonously.3. By using Galerkin method, small vibration of the uniformly heated laminated composite plates in the vicinity of the thermally post-buckling configuration is investigated. Firstly, the equilibrium paths, in terms of the dimensionless central buckling deflection and the thermal load parameter, are given for the symmetrically laminated rectangular plates. Effects of the geometric parameters and the boundary conditions on the equilibrium paths are examined. Then, for a special case, characteristic curves of the first four natural frequencies versus the temperature rise of the pre-buckled symmetric laminated plates are presented. Influences of the geometric, the othotropic and thermal load parameters on the frequencies are discussed in detail. Finally, the fundamental response of linear vibration of the thermally post-buckled plates is obtained. Variation of fundamental frequency with the temperature rise is shown numerically for different values of the aspect ratio and boundary conditions. From the results can be found that the frequency declines monotonously with the temperature rise and becomes zero at the critical temperature rise. However, thefundamental frequency becomes monotonously increasing functions of the temperature rise once the plate goes into the thermally post-buckling state.