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Research Papers

New Analytic Free Vibration Solutions of Rectangular Thick Plates With a Free Corner by the Symplectic Superposition Method

[+] Author and Article Information
Rui Li

State Key Laboratory of Structural Analysis for
Industrial Equipment,
Department of Engineering Mechanics,
and International Research Center for Computational Mechanics,
Dalian University of Technology,
Dalian 116024, China;
State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of
Science and Technology,
Wuhan 430074, China
e-mail: ruili@dlut.edu.cn

Pengcheng Wang

State Key Laboratory of Structural Analysis for
Industrial Equipment,
Department of Engineering Mechanics,
and International Research Center for
Computational Mechanics,
Dalian University of Technology,
Dalian 116024, China

Bo Wang

College of Engineering,
Peking University,
Beijing 100871, China

Chunyu Zhao

CAS Key Laboratory of Mechanical Behavior and
Design of Materials,
Department of Modern Mechanics,
University of Science and Technology of China,
Hefei 230027, China

Yewang Su

State Key Laboratory of Nonlinear Mechanics,
Institute of Mechanics,
Chinese Academy of Sciences,
Beijing 100190, China;
School of Engineering Science,
University of Chinese Academy of Sciences,
Beijing 100049, China
e-mail: yewangsu@imech.ac.cn

1Corresponding authors.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 10, 2017; final manuscript received January 4, 2018; published online xx xx, xxxx. Assoc. Editor: Izhak Bucher.

J. Vib. Acoust 140(3), 031016 (Feb 09, 2018) (9 pages) Paper No: VIB-17-1411; doi: 10.1115/1.4038951 History: Received September 10, 2017; Revised January 04, 2018

Seeking analytic free vibration solutions of rectangular thick plates without two parallel simply supported edges is of significance for an insight into the performances of related engineering devices and structures as well as their rapid design. A challenging set of problems concern the vibrating plates with a free corner, i.e., those with two adjacent edges free and the other two edges clamped or simply supported or one of them clamped and the other one simply supported. The main difficulty in solving one of such problems is to find a solution meeting both the boundary conditions at each edge and the condition at the free corner, which is unattainable using a conventional analytic method. In this paper, for the first time, we extend a novel symplectic superposition method to free vibration of rectangular thick plates with a free corner. The analytic frequency and mode shape solutions are both obtained and presented via comprehensive numerical and graphic results. The rigorousness in mathematical derivation and rationality of the method (without any predetermination for the solutions) guarantee the validity of our analytic solutions, which themselves are also validated by the reported results and refined finite element analysis.

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Figures

Grahic Jump Location
Fig. 1

Symplectic superposition for free vibration of a CCFF thick plate

Grahic Jump Location
Fig. 2

First ten mode shapes of a CCFF square thick plate with h/a = 0.2

Grahic Jump Location
Fig. 3

Convergence of the first and tenth normalized frequencies for CCFF, CSFF, and SSFF square plates with h/a = 0.2

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