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Shock and Vibration
Volume 2017, Article ID 2189420, 9 pages
https://doi.org/10.1155/2017/2189420
Research Article

Geometrically Nonlinear Transient Response of Laminated Plates with Nonlinear Elastic Restraints

1Department of Engineering Mechanics, Beijing University of Technology, Beijing 100124, China
2College of Civil Engineering and Architecture, Hebei University, Baoding 071002, China

Correspondence should be addressed to Qingsheng Yang; nc.ude.tujb@gnaysq

Received 27 October 2016; Revised 21 December 2016; Accepted 4 January 2017; Published 19 January 2017

Academic Editor: Yuri S. Karinski

Copyright © 2017 Shaochong Yang and Qingsheng Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

To investigate the dynamic behavior of laminated plates with nonlinear elastic restraints, a varied constraint force model and a systematic numerical procedure are presented in this work. Several kinds of typical relationships of force-displacement for spring are established to simulate the nonlinear elastic restraints. In addition, considering the restraining moments of flexible pads, the pads are modeled by translational and rotational springs. The displacement- dependent constraint forces are added to the right-hand side of equations of motion and treated as additional applied loads. These loads can be explicitly defined, via an independent set of nonlinear load functions. The time histories of transverse displacements at typical points of the laminated plate are obtained through the transient analysis. Numerical examples show that the present method can effectively treat the geometrically nonlinear transient response of plates with nonlinear elastic restraints.