Finding vibration mode functions satisfying both high-order partial differential governing equations and various non-Lévy-type boundary conditions is extremely challenging for the free vibration problems of func-tionally graded rectangular plates,making it difficult to analytically solve the problem with traditional methods.Herein,the newly developed Hamiltonian system-based symplectic superposition method was extended and successfully applied to analytical solutions to the free vibration problems of functionally graded rectangular plates.For the solution methodology,the original vibration problem was divided into sub-problems and the physical neutral plane was introduced to eliminate the stretching-bending coupling effect caused by the trans-versely non-uniform materials.The sub-problems were analytically solved with some mathematical techniques,i.e.,the variable separation and the symplectic eigenvector expansion,which are not applicable in the tradition-al Lagrangian system.The final solution to an original vibration problem was obtained through the superposition of sub-problems.The symplectic superposition method has the advantage of not requiring the pre-defined solu-tion forms,which overcomes the limitations of traditional semi-inverse methods and allows for obtaining analyt-ical solutions to more complex problems.Comparison of the obtained solutions with the numerical solutions proves the accuracy of the presented method.On this basis,quantitative parameter analyses on the natural fre-quencies were conducted to reveal the effects of boundary conditions,material distributions and aspect ratios.
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