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RESEARCH PAPERS

Membrane and Flexural Waves on Thin Shells

[+] Author and Article Information
A. N. Norris, D. A. Rebinsky

Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08855-0909

J. Vib. Acoust 116(4), 457-467 (Oct 01, 1994) (11 pages) doi:10.1115/1.2930449 History: Received November 01, 1992; Revised May 01, 1993; Online June 17, 2008

Abstract

Membrane and flexural waves are limiting short wavelength solutions of the equations of motion for arbitrarily curved, smooth shells. Each distinct wave type is found using a geometrical or ray method based upon asymptotics in the small parameters h/R, where h is thickness and R a minimum radius of curvature. Useful, asymptotic formulae are found for the normal displacement associated with membrane waves, group velocities, and other physically significant quantities. Ray paths on a conical shell are illustrated for each wave type, and it is found that flexural rays form a caustic near the vertex.

Copyright © 1994 by The American Society of Mechanical Engineers
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