Year: 2017
Author: Lingchang Meng, Fengming Li
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 6 : pp. 1485–1505
Abstract
The nonlinear transverse vibrations of ordered and disordered two-dimensional (2D) two-span composite laminated plates are studied. Based on the von Karman's large deformation theory, the equations of motion of each-span composite laminated plate are formulated using Hamilton's principle, and the partial differential equations are discretized into nonlinear ordinary ones through the Galerkin's method. The primary resonance and 1/3 sub-harmonic resonance are investigated by using the method of multiple scales. The amplitude-frequency relations of the steady-state responses and their stability analyses in each kind of resonance are carried out. The effects of the disorder ratio and ply angle on the two different resonances are analyzed. From the numerical results, it can be concluded that disorder in the length of the two-span 2D composite laminated plate will cause the nonlinear vibration localization phenomenon, and with the increase of the disorder ratio, the vibration localization phenomenon will become more obvious. Moreover, the amplitude-frequency curves for both primary resonance and 1/3 sub-harmonic resonance obtained by the present analytical method are compared with those by the numerical integration, and satisfactory precision can be obtained for engineering applications and the results certify the correctness of the present approximately analytical solutions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2016-0121
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 6 : pp. 1485–1505
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Ordered and disordered two-span composite laminated plates nonlinear vibration localization method of multiple scales primary and 1/3 sub-harmonic resonances.
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