Dynamic Stability of Transverse Axisymmetric Waves in Circular Cylindrical Shells

[+] Author and Article Information
J. H. Ginsberg

School of Mechanical Engineering, Purdue University, West Lafayette, Ind.

J. Appl. Mech 41(1), 77-82 (Mar 01, 1974) (6 pages) doi:10.1115/1.3423275 History: Received February 01, 1973; Revised April 01, 1973; Online July 12, 2010


Previous experiments [1] have indicated that axisymmetric waves may be unstable and that nonsymmetric waves may result. To show that it is possible for such a phenomenon to occur even in perfectly cylindrical shells, a new mechanism for the coupling of the two types of waves is determined. Relationships for the phase velocity of steady-state waves as a function of the amplitude of transverse displacement are obtained. The stability of the system is shown to be defined by an equivalent nonlinear system with two degrees of freedom. It is found that the stability limits are the bifurcation points in the amplitude-phase velocity diagram for the axisymmetric and nonsymmetric waves. The solution is a uniform asymptotic expansion of the modal series for the displacement components and retains all effects significant to the first approximation of the nonlinearity.

Copyright © 1974 by ASME
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