Abstract
The parametric vibration and stability of the functionally graded ceramic-metal plate subjected to in-plane excitation is presented. Based on the stress–strain relationship and nonlinear geometric equations of nonhomogeneous materials, the nonlinear partial differential equations of this problem were derived by using principle of virtual work. For the simply supported rectangular plate, the displacement function was assumed and the nonlinear Mathieu vibrations equation of parametric excitation was obtained by using Galerkin method. The principal parametric resonance was analyzed. The multiscale method is used to obtain the frequency-response equation of the steady-state movement. Based on the Lyapunov stability theory, the critical conditions of steady-state solutions were deduced. Numerical examples are provided to investigate the amplitude curves of functionally graded plate and the influences of different frequency and excitation amplitude. The variations of resonance solution, stability, and bifurcation characteristics were analyzed.
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