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RESEARCH PAPERS

Dynamic Response of a Semi-Infinite Elastic Cylinder Containing an Acoustic Medium

[+] Author and Article Information
R. F. Carpenter, B. S. Berger

Department of Mechanical Engineering, University of Maryland, College Park, Md.

J. Appl. Mech 39(3), 682-688 (Sep 01, 1972) (7 pages) doi:10.1115/1.3422773 History: Received December 01, 1970; Revised October 01, 1971; Online July 12, 2010

Abstract

The solutions developed in this paper are based on the finite Hankel-Fourier-Laplace transform. The Love-Timoshenko shell equations are reduced through the application of the Fourier-Laplace transforms to the axial space and time variables. The equation of motion for the acoustic fluid contained within the shell are reduced through the application of the finite Hankel-Fourier-Laplace transform to the radial, axial spatial, and time variables. The boundary conditions at the fixed end of the semi-infinite shell are met through the application of loadings symmetric with respect to the origin and the application of a ring loading at the origin which is chosen so as to make the radial deflection there zero. Expressions are found for the transforms of the axial, tangential, and radial shell displacements, the axial, tangential, and radial fluid velocities, and the radiated fluid pressure. Numerical inversion of the Fourier-Laplace transform is accomplished in terms of a series of ultraspherical polynomials and Gauss-Hermite or Gauss-Laguerre quadrature.

Copyright © 1972 by ASME
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