On a Class of Oscillations in the Finite-Deformation Theory of Elasticity

[+] Author and Article Information
J. K. Knowles

California Institute of Technology, Pasadena, Calif.

J. Appl. Mech 29(2), 283-286 (Jun 01, 1962) (4 pages) doi:10.1115/1.3640542 History: Received April 25, 1961; Online September 16, 2011


This paper treats the large-amplitude radial oscillations of a perfectly elastic, incompressible cylindrical tube of infinite length due to suddenly applied pressures on its lateral surfaces. The motion is studied for materials with essentially arbitrary strain-energy density. Sufficient conditions for periodic motions and a formula for the period of oscillation are given in terms of the strain energy. The results are specialized to the case of a rubberlike material of Mooney type, and asymptotic formulas are given for the case of a thin shell and for the case of small applied pressure.

Copyright © 1962 by ASME
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