On the Nonlocal Theory of Wave Propagation in Elastic Plates

[+] Author and Article Information
J. L. Nowinski

Department of Mechanical and Aerospace Engineering, University of Delaware, Newark, Del. 19716

J. Appl. Mech 51(3), 608-613 (Sep 01, 1984) (6 pages) doi:10.1115/1.3167681 History: Received June 01, 1983; Revised December 01, 1983; Online July 21, 2009


Propagation of longitudinal waves in isotropic homogeneous elastic plates is studied in the context of the linear theory of nonlocal continuum mechanics. To determine the nonlocal moduli, the dispersion equation obtained for the plane longitudinal waves in an infinite medium is matched with the parallel equation derived in the theory of atomic lattice dynamics. Using the integroalgebraic representation of the stress tensor and the Fourier transform, the system of two coupled differential field equations is solved in the standard manner giving the frequency equations for the symmetric and antisymmetric wave modes. It is found that the short wave speed in the Poisson medium differs by about 13 percent from the speed established in the classical theory. A numerical example is given.

Copyright © 1984 by ASME
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