Abstract
This paper is concerned with the study of the amplitude of the steady-state vibration in a right finite cylinder made of a mixture consisting of three components: an elastic solid, a viscous fluid and a gas. An exponential decay estimate of Saint-Venant type in terms of the distance from one end of the cylinder is obtained from a first-order differential inequality for a cross-sectional area measure associated with the amplitude of the steady-state vibration. The decay constant depends on the excitation frequency, the constitutive coefficients and the first positive eigenvalue for the fixed membrane problem for the cross-sectional geometry. The paper also indicates how to extend the results to a semi-infinite cylinder.
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