The Effect of Spatial Distribution on Dynamic Snap-Through

[+] Author and Article Information
E. R. Johnson

Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, Va. 24061

I. K. McIvor

Department of Applied Mechanics and Engineering Science, University of Michigan, Ann Arbor, Mich. 48104

J. Appl. Mech 45(3), 612-618 (Sep 01, 1978) (7 pages) doi:10.1115/1.3424370 History: Received November 01, 1977; Revised March 01, 1978; Online July 12, 2010


The effect of the spatial distribution of impulsive loads on dynamic snap-through of a shallow circular arch is considered in detail. The Budiansky-Roth criterion is used to establish critical magnitudes of the load for many distributions by numerical integration of an approximate set of equations obtained by Galerkin’s method. It is necessary to distinguish between snap-through on the initial oscillation (immediate) and snap-through occurring during a finite time of the response. Critical magnitudes for both cases are compared to a distribution independent lower bound obtained from an analysis of the critical points. For all distributions considered the lower bound is a less conservative estimate of the critical magnitude for finite time snap-through than for immediate snap-through. The effect of small damping on this conclusion, however, remains an open question.

Copyright © 1978 by ASME
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