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

James Knowles (1)

1 Caltech - Californian Institute of Technology

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 /he case of small applied pressure.

Domaines: Sciences de l'ingénieur [physics]

James Knowles. On a Class of Oscillations in the Finite-Deformation Theory of Elasticity. Journal of Applied Mechanics, 1962, 29 (2), pp.283-286. ⟨10.1115/1.3640542⟩. ⟨hal-01298777⟩