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TECHNICAL PAPERS

Asymptotics of Flexural Waves in Isotropic Elastic Plates

[+] Author and Article Information
N. A. Losin

10834 N. 32nd Lane, Phoenix, AZ 85029

J. Appl. Mech 64(2), 336-342 (Jun 01, 1997) (7 pages) doi:10.1115/1.2787312 History: Received September 13, 1995; Revised November 27, 1996; Online October 25, 2007

Abstract

The long and short-wave asymptotics of order O(k6 h6 ) for the flexural vibrations of an infinite, isotropic, elastic plate are studied. The differential equation for the flexural motion is derived from the system of three-dimensional dynamic equations of linear elasticity. All coefficients of the differential operator are presented as explicit functions of the material parameter γ = cs 2 /cL 2 , the ratio of the velocities squared of the flexural (shear) and extensional (longitudinal) waves. Relatively simple frequency and velocity dispersion equations for the flexural waves are deduced in analytical form from the three-dimensional analog of Rayleigh-Lamb frequency equation for plates. The explicit formulas for the group velocity are also presented. Variations of the velocity and frequency spectrums depending on Poisson’s ratio are illustrated graphically. The results are discussed and compared to those obtained and summarized by R. D. Mindlin (1951, 1960), Tolstoy and Usdin (1953, 1957), and Achenbach (1973).

Copyright © 1997 by The American Society of Mechanical Engineers
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