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Vibration solutions of rectangular orthotropic plates by symplectic geometry method

Past researchers have treated the vibration problem of rectangular orthotropic Kirchhoff plates by using the semi-inverse method with trial functions which, however, do not always exist. In this study, free vibration and harmonic forced vibration are analysed using a unified method based on the symplectic method. Since only the fundamental equations are used, this method eliminates the need to select the trial function and hence avoids the limitation of the traditional semi-inverse method. Exact frequency equations are presented and the exact solution of natural frequency can be obtained. Furthermore, the analytical solution for free vibration, subject to appropriate modifications, is applied to determine the steady state solution for harmonic forced vibration. The proposed method can be extended to solve plate buckling problems. Tabulated numerical results show that the present method can furnish highly accurate and fast convergent solutions which should be useful as benchmarks.