Analytical Forced Vibration Solutions of Orthotropic Cantilever Rectangular Thin Plates With the Symplectic Superposition Method

WANG Senlin; LI Jinbao; MA Hongyan; LI Rui

doi:10.21656/1000-0887.440277

Volume 45 Issue 9

Sep. 2024

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WANG Senlin, LI Jinbao, MA Hongyan, LI Rui. Analytical Forced Vibration Solutions of Orthotropic Cantilever Rectangular Thin Plates With the Symplectic Superposition Method[J]. Applied Mathematics and Mechanics, 2024, 45(9): 1117-1132. doi: 10.21656/1000-0887.440277

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Analytical Forced Vibration Solutions of Orthotropic Cantilever Rectangular Thin Plates With the Symplectic Superposition Method

doi: 10.21656/1000-0887.440277

State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Received Date: 2023-09-20
Rev Recd Date: 2023-10-26
Publish Date: 2024-09-01

Abstract

Abstract

The forced vibrations of orthotropic cantilever rectangular thin plates under harmonic loadings were investigated with the symplectic superposition method. The basic equations for the forced vibration of thin plates were introduced into the Hamiltonian system. The original problem was divided into some fundamental subproblems, and the analytical solutions of the subproblems were derived with the method of separation of variables and through eigenvector expansion in the symplectic space. The solution of the original problem was finally obtained by superposition. The main advantage of the symplectic superposition method is that the analytical solution can be obtained by step-by-step rigorous derivation, without any assumptions on the form of the solution, which breaks through the limitations of traditional semi-inverse methods. The numerical results calculated corresponding to different harmonic loads were compared with those obtained via the finite element method to verify the reliability and accuracy of the proposed method.
- symplectic superposition method,
- orthotropic thin plate,
- analytical solution,
- forced vibration

(Contributed by LI Rui, M.AMM Editorial Board)

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References(31)

References

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