A numerical approach is presented for linear and geometrically nonlinear forced vibrations of laminated composite plates with piezoelectric materials. The displacement fields are defined generally by high degree polynomials and the convergence of the results is achieved by increasing the degrees of polynomials. The nonlinearity is retained with the in-plane strain components only and the transverse shear strains are kept linear. The electric potential is approximated layerwise along the thickness direction of the piezoelectric layers. In-plane electric fields at the top and bottom surfaces of each piezoelectric sublayer are defined by the same shape functions as those used for displacement fields. The equation of motion is obtained by the Hamilton’s principle and solved by the Newmark’s method along with the Newton–Raphson iterative technique. Numerical procedure presented herein is validated by successfully comparing the present results with the data published in the literature. Additional numerical examples are presented for forced vibration of piezoelectric sandwich simply supported plates with either a homogeneous material or laminated composite as core. Both linear and nonlinear responses are examined for mechanical load only, electrical load only, and the combined mechanical and electrical loads. Displacement time histories with uniformly distributed load on the plate surface, electric volts applied on the top and bottom surfaces of the piezoelectric plates, and mechanical and electrical loads applied together are presented in this paper. The nonlinearity due to large deformations is seen to produce stiffening effects, which reduces the amplitude of vibrations and increases the frequency. On the contrary, antisymmetric electric loading on the nonlinear response of piezoelectric sandwich plates shows increased amplitude of vibrations.
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April 2010
Research Papers
Nonlinear Forced Vibrations of Laminated Piezoelectric Plates
Muhammad Tanveer,
Muhammad Tanveer
Department of Mechanical and Materials Engineering,
University of Western Ontario
, London, ON, N6A 5B9, Canada
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Anand V. Singh
Anand V. Singh
Department of Mechanical and Materials Engineering,
e-mail: avsingh@eng.uwo.ca
University of Western Ontario
, London, ON, N6A 5B9, Canada
Search for other works by this author on:
Muhammad Tanveer
Department of Mechanical and Materials Engineering,
University of Western Ontario
, London, ON, N6A 5B9, Canada
Anand V. Singh
Department of Mechanical and Materials Engineering,
University of Western Ontario
, London, ON, N6A 5B9, Canadae-mail: avsingh@eng.uwo.ca
J. Vib. Acoust. Apr 2010, 132(2): 021005 (13 pages)
Published Online: March 16, 2010
Article history
Received:
August 11, 2008
Revised:
November 26, 2009
Online:
March 16, 2010
Published:
March 16, 2010
Citation
Tanveer, M., and Singh, A. V. (March 16, 2010). "Nonlinear Forced Vibrations of Laminated Piezoelectric Plates." ASME. J. Vib. Acoust. April 2010; 132(2): 021005. https://doi.org/10.1115/1.4000768
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