On New Analytic Free Vibration Solutions of Doubly Curved Shallow Shells by the Symplectic Superposition Method Within the Hamiltonian-System Framework

被引:25
作者
Li, Rui [1 ,2 ]
Zhou, Chao [1 ,2 ]
Zheng, Xinran [1 ,2 ]
机构
[1] Dalian Univ Technol, Dept Engn Mech, State Key Lab Struct Anal Ind Equipment, Dalian 116024, Peoples R China
[2] Dalian Univ Technol, Int Res Ctr Computat Mech, Dalian 116024, Peoples R China
来源
JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME | 2021年 / 143卷 / 01期
基金
中国国家自然科学基金;
关键词
shallow shell; free vibration; analytic solution; symplectic superposition method; dynamics; SHEAR DEFORMATION-THEORY; ELASTICITY APPROACH; PLATES;
D O I
10.1115/1.4047701
中图分类号
O42 [声学];
学科分类号
070206 ; 082403 ;
摘要
This study presents a first attempt to explore new analytic free vibration solutions of doubly curved shallow shells by the symplectic superposition method, with focus on non-Levy-type shells that are hard to tackle by classical analytic methods due to the intractable boundary-value problems of high-order partial differential equations. Compared with the conventional Lagrangian-system-based expression to be solved in the Euclidean space, the present description of the problems is within the Hamiltonian system, with the solution procedure implemented in the symplectic space, incorporating formulation of a symplectic eigenvalue problem and symplectic eigen expansion. Specifically, an original problem is first converted into two subproblems, which are solved by the above strategy to yield the symplectic solutions. The analytic frequency and mode shape solutions are then obtained by the requirement of the equivalence between the original problem and the superposition of subproblems. Comprehensive results for representative non-Levy-type shells are tabulated or plotted, all of which are well validated by satisfactory agreement with the numerical finite element method. Due to the strictness of mathematical derivation and accuracy of solution, the developed method provides a solid approach for seeking more analytic solutions.
引用
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页数:14
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