Transient Wave Propagation in a Symmetrically Layered Elastic Plate

[+] Author and Article Information
D. C. Viano

Biomedical Science Department, General Motors Research Laboratory, Warren, Mich.

J. Miklowitz

Division of Engineering and Applied Science, California Institute of Technology, Pasadena, Calif.

J. Appl. Mech 41(3), 684-690 (Sep 01, 1974) (7 pages) doi:10.1115/1.3423371 History: Received December 01, 1973; Revised March 01, 1974; Online July 12, 2010


The response of a symmetrically layered plate subjected to symmetric step normal line face loads is determined. The solution, which is based on the equations of motion from linear elasticity, is obtained in the form of an infinite series of integrals with each term being the contribution from a branch of the underlying frequency equation. Through numerical analysis several of the lower branches of the frequency equation, which depend on layered plate ratios (four material and one thickness) are evaluated and used to write the transient response in the near field. Integrations based on the first five branches show the dominance of the lowest mode in the solution. Applying arguments of stationary phase to the spectrum, yields low frequency-long wave and high frequency-short wave approximations for use in obtaining the far field-long time disturbance. The former governs a front running “head of the pulse” for the layered plate, and the latter, later arriving Rayleigh and Stoneley waves.

Copyright © 1974 by ASME
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