Acoustic propagation in finite length elastic cylinders. Part I: Axisymmetric excitation

Abstract

The acoustic propagation in a perfect finite length thin elastic cylinder is studied from an exact solution to the coupled elasto-acoustic equations of motion. Eigenfunction expansions are obtained for Koiter’s consistent shell equations and the Helmholtz equation governing the acoustic field. The acoustic pressure is expressed as the sum of modal acoustic pressures each factored by a normalized influence coefficient related to the corresponding generalized coordinate in the elastic cylinder eigenfunction. A set of nonlinear homogeneous algebraic equations in the generalized coordinates are obtained when satisfying the coupled equations and the compatibility condition at the fluid–cylinder interface. The method when applied to a clamped cylinder filled with water and excited by a plane wave demonstrates the existence of narrow nonresonant peaks in maximum cylinder displacement and a frequency range where the average response rises considerably.