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Nonlinear Vibrations of Two-Span Composite Laminated Plates with Equal and Unequal Subspan Lengths

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Mechanics of particles and systems

Published online by Cambridge University Press:  28 November 2017

Lingchang Meng  and
Fengming Li
Lingchang Meng
Affiliation:
College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China
Fengming Li*
Affiliation:
College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China
*
*Corresponding author. Email:[email protected] (F. M. Li)
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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.

Keywords

Ordered and disordered two-span composite laminated platesnonlinear vibration localizationmethod of multiple scalesprimary and 1/3 sub-harmonic resonances

MSC classification

Secondary: 70-08: Computational methods 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 6 , December 2017 , pp. 1485 - 1505
Copyright
Copyright © Global-Science Press 2017 

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