Nonlinear forced vibrations of completely free laminated composite rectangular plates are studied using multi-modal Lagrangian approach. Nonlinear higher-order shear deformation theory is used and the nonlinear response to transverse harmonic excitation in the frequency neighborhood of the fundamental mode is investigated. The numerical analysis is conducted in two steps. First, the plate displacements and rotations are expanded in terms of Chebyshev polynomials and a linear analysis is performed to obtain the natural frequencies and mode shapes. Then, the energy functional is discretized by using the natural modes of vibration and a system of nonlinear ordinary differential equations with cubic and quadratic nonlinear terms is obtained. A pseudo arc-length continuation and collocation scheme is employed to carry out a bifurcation analysis. A consistent reduced-order model necessary to capture the nonlinear dynamics of the plate is developed and the effect of number of modes retained in the numerical model is discussed.
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ASME 2013 International Mechanical Engineering Congress and Exposition
November 15–21, 2013
San Diego, California, USA
Conference Sponsors:
- ASME
ISBN:
978-0-7918-5625-3
PROCEEDINGS PAPER
Large Amplitude Vibrations of Laminated Rectangular Plates With Free Edges
F. Alijani,
F. Alijani
McGill University, Montreal, QC, Canada
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M. Amabili
M. Amabili
McGill University, Montreal, QC, Canada
Search for other works by this author on:
F. Alijani
McGill University, Montreal, QC, Canada
M. Amabili
McGill University, Montreal, QC, Canada
Paper No:
IMECE2013-62254, V04BT04A009; 8 pages
Published Online:
April 2, 2014
Citation
Alijani, F, & Amabili, M. "Large Amplitude Vibrations of Laminated Rectangular Plates With Free Edges." Proceedings of the ASME 2013 International Mechanical Engineering Congress and Exposition. Volume 4B: Dynamics, Vibration and Control. San Diego, California, USA. November 15–21, 2013. V04BT04A009. ASME. https://doi.org/10.1115/IMECE2013-62254
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