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


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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