Abstract
Analytic free vibration solutions of rectangular thin plates with two adjacent corners point-supported are obtained for the first time by using an up-to-date symplectic superposition method, which demonstrates the ability to yield solutions via step-by-step derivations from the governing equations, without predetermining any forms of solutions. The essential difference between the current method and the other ones is that the solution procedure is conducted in the symplectic space rather than in the classical Euclidean space. This extends the scope of application of eigen expansion and paves the way for more analytic solutions of similar problems. Comprehensive highly accurate numerical results are presented to show the validity of the current solutions and to provide the benchmarks for future comparison and verification of other methods.
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