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Advances in Materials Science and Engineering
Volume 2018, Article ID 8162873, 12 pages
https://doi.org/10.1155/2018/8162873
Research Article

Free Vibrations and Nonlinear Responses for a Cantilever Honeycomb Sandwich Plate

1College of Mechanical Engineering, Beijing Information Science and Technology University, Beijing 100192, China
2College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China

Correspondence should be addressed to Junhua Zhang; moc.361@rauhjz

Received 11 July 2017; Accepted 22 November 2017; Published 6 March 2018

Academic Editor: Michael J. Schütze

Copyright © 2018 Junhua Zhang et al. 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

Dynamics of a cantilever honeycomb sandwich plate are studied in this paper. The governing equations of the composite plate subjected to both in-plane and transverse excitations are derived by using Hamilton’s principle and Reddy’s third-order shear deformation theory. Based on the Rayleigh–Ritz method, some modes of natural frequencies for the cantilever honeycomb sandwich plate are obtained. The relations between the natural frequencies and the parameters of the plate are investigated. Further, the Galerkin method is used to transform the nonlinear partial differential equations into a set of nonlinear ordinary differential equations. Nonlinear dynamic responses of the cantilever honeycomb sandwich plate to such external and parametric excitations are discussed by using the numerical method. The results show that in-plane and transverse excitations have an important influence on nonlinear dynamic characteristics. Rich dynamics, such as periodic, multiperiodic, quasiperiodic, and chaotic motions, are located and studied by the bifurcation diagram for some specific parameters.