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论文类型：期刊论文

发表时间：2016-01-15

发表刊物：APPLIED MATHEMATICAL MODELLING

收录刊物：SCIE、EI

卷号：40

期号：2

页面范围：984-992

ISSN号：0307-904X

关键字：Rectangular thin plate; Free vibration; Hamiltonian system; Symplectic superposition method

摘要：Analytic free vibration solutions of free rectangular thin plates with or without an elastic foundation are obtained by using an up-to-date Hamiltonian system-based symplectic superposition method. Such boundary value problems are known to be very difficult and they were generally solved by the approximate/numerical methods. The present analytic solutions are expected to be the benchmarks for future verification of other methods. The advantage of the method is that the solution procedure is conducted in the symplectic space, where the symplectic eigen expansion is valid and the predetermination of the solution form is avoided. This significantly extends the approach to the analytic solutions of similar problems. (C) 2015 Elsevier Inc. All rights reserved.