Transient Response of Transversely Isotropic Composite Plates to a Point Source

[+] Author and Article Information
A. Mahmoud

Mechanical and Industrial Engineering Department,  University of Manitoba, Winnipeg, Manitoba R3T 5V6, Canadaumkotbam@cc.umanitoba.ca

A. H. Shah1

Civil Engineering Department,  University of Manitoba, Winnipeg, Manitoba R3T 5V6, Canadashah@cc.umanitoba.ca

S. B. Dong

Department of Civil and Environmental Engineering,  University of California at Los Angles, Los Angeles, CA 90095-1593dong@seas.ucla.edu


To whom correspondence should be addressed.

J. Appl. Mech 73(2), 338-341 (Jun 13, 2005) (4 pages) doi:10.1115/1.2070007 History: Received May 27, 2004; Revised June 13, 2005

In this paper, transient three-dimensional response of a transversely isotropic composite plate to a time varying point load is efficiently computed by reducing the elastodynamic equation through integral and coordinate transformations to a series of two-dimensional problems, each associated with a plane wave along a given direction in the plate. Discrete equations of a semi-analytical finite element model are solved for the thickness profile eigendata at a given frequency. Three-dimensional steady state responses in the wave number domain are formed by summing contributions from eigenmodes over propagation directions. The transient response is obtained by a numerical integration of inverse Fourier time transform of these steady state responses. Present results showed good agreement with data reported in the literature and confirmed previously observed phenomena.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Coordinate transformation into the traveling direction

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Figure 2

Variation of displacements along the x direction, 4mm from a vertical source in a unidirectional 1-mm-thick graphite/epoxy plate: (a) with number of sublayers (Nα=72); (b) with number of propagation directions (NE=10)

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Figure 3

Scaled normal top surface displacements along 45 deg from the x direction: a comparison between PWS (solid line) and Lih and Mal (dashed line)

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Figure 4

Snapshots, at t=1.9s, of top surface displacements along 45 deg, 0 deg, and 90 deg from the x direction




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