Research Papers

Modal Analysis of General Plate Structures

[+] Author and Article Information
Hongan Xu

Department of Mechanical Engineering,
Wayne State University,
5050 Anthony Wayne Drive,
Detroit, MI 48202

W. L. Li

Department of Mechanical Engineering,
Wayne State University,
5050 Anthony Wayne Drive,
Detroit, MI 48202
e-mail: wli@wayne.edu

Jingtao Du

College of Power and Energy Engineering,
Harbin Engineering University,
Harbin 150001, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 19, 2011; final manuscript received June 27, 2013; published online November 26, 2013. Assoc. Editor: Massimo Ruzzene.

J. Vib. Acoust 136(2), 021002 (Nov 26, 2013) (11 pages) Paper No: VIB-11-1248; doi: 10.1115/1.4025876 History: Received October 19, 2011; Revised June 27, 2013

A general analytical method, referred to as the Fourier spectral element method, is presented for the dynamic analysis of plate structures consisting of any number of arbitrarily oriented rectangular plates. The compatibility conditions between any two adjacent plates are generally described in terms of three-dimensional elastic couplers with both translational and rotational stiffnesses. More importantly, all plates involved can be arbitrarily restrained along any edges in contrast to the commonly imposed condition: each plate has to be simply supported along, at least, one pair of parallel edges. Thus, plate structures here are not limited to Levy-type plates as typically assumed in other techniques. The flexural and in-plane displacement fields on each plate are analytically expressed as accelerated Fourier series expansions and the expansion coefficients are considered as the generalized coordinates to be determined using the familiar Rayleigh–Ritz technique. The accuracy and reliability of the present method are validated by both finite element analysis (FEA) and experimental data for box structures under various boundary conditions.

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Fig. 1

Schematic of a plate structure consisting of arbitrarily oriented plates

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Fig. 2

The coordinate transformation between two coupled plates

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Fig. 3

Coordinate systems defining the coupling or restraining springs

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Fig. 4

The construction of a box structure

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Fig. 5

Convergence of the natural frequencies predicted based on different truncation numbers: M = N = 5, 6, 7, 8, 9

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Fig. 6

The mode shapes for the free open box: the (a) 1st mode; (b) 2nd mode; (c) 3rd mode; (d) 4th mode; (e) 5th mode; (f) 6th mode; (f) 7th mode; and (f) 8th mode. Panel (a): calculated; panel and (b): measured.

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Fig. 7

The mode shapes for the open box under CSFF boundary conditions: the (a) 1st mode; (b) 2nd mode; (c) 3rd mode; (d) 4th mode; (e) 5th mode; (f) 6th mode; (f) 7th mode; and (f) 8th mode. Panel (a):Left—calculated; panel and (b): FEM.




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