Vibration of Thick Elastic and Viscoelastic Tubes. I: Harmonic Response

Abstract

The harmonic response of an infinitely long thick elastic tube is considered. Exact displacement and stress fields for steady‐state vibration are developed. Stiffness equations are derived, relating the internal and external boundary tractions and displacements. Assembly of these tube stiffness equations is used to evaluate the response of laminated tubular structures. The formulation is extended so that the behavior of viscoelastic tubes can also be determined. Comparisons are made with solutions based on thin‐shell theory, to assess how accurately shell theory models thick‐tube vibration. Distributions of displacement and normal stress through a laminated tubular structure are studied. The response of a tube with an elastic core and a viscoelastic tube also are investigated.