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.
On a Class of Oscillations in the Finite-Deformation Theory of Elasticity
J. K. Knowles
California Institute of Technology, Pasadena, Calif.
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Knowles, J. K. (June 1, 1962). "On a Class of Oscillations in the Finite-Deformation Theory of Elasticity." ASME. J. Appl. Mech. June 1962; 29(2): 283–286. https://doi.org/10.1115/1.3640542
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