Volume 9, Issue 6
Nonlinear Vibrations of Two-Span Composite Laminated Plates with Equal and Unequal Subspan Lengths

Lingchang Meng & Fengming Li

Adv. Appl. Math. Mech., 9 (2017), pp. 1485-1505.

Published online: 2017-09

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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 plates, nonlinear vibration localization, method of multiple scales, primary and 1/3 sub-harmonic resonances.

  • AMS Subject Headings

70-08, 35Q72, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-1485, author = {Lingchang Meng , and Li , Fengming}, title = {Nonlinear Vibrations of Two-Span Composite Laminated Plates with Equal and Unequal Subspan Lengths}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2017}, volume = {9}, number = {6}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2016-0121}, url = {http://global-sci.org/intro/article_detail/aamm/10189.html} }
TY - JOUR T1 - Nonlinear Vibrations of Two-Span Composite Laminated Plates with Equal and Unequal Subspan Lengths AU - Lingchang Meng , AU - Li , Fengming JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1485 EP - 1505 PY - 2017 DA - 2017/09 SN - 9 DO - http://doi.org/10.4208/aamm.OA-2016-0121 UR - https://global-sci.org/intro/article_detail/aamm/10189.html KW - Ordered and disordered two-span composite laminated plates, nonlinear vibration localization, method of multiple scales, primary and 1/3 sub-harmonic resonances. AB -

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.

Lingchang Meng & Fengming Li. (2020). Nonlinear Vibrations of Two-Span Composite Laminated Plates with Equal and Unequal Subspan Lengths. Advances in Applied Mathematics and Mechanics. 9 (6). 1485-1505. doi:10.4208/aamm.OA-2016-0121
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