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RESEARCH PAPERS

Nonmodal Solution of Spherical Shells With Cutouts Excited by High-Frequency Axisymmetric Forces

[+] Author and Article Information
M. C. Junger

Cambridge Acoustical Associates, Inc., Cambridge, Mass.

J. Appl. Mech 37(4), 977-983 (Dec 01, 1970) (7 pages) doi:10.1115/1.3408727 History: Received January 19, 1970; Revised March 13, 1970; Online July 12, 2010

Abstract

A closed-form solution is obtained for the high-frequency response of a thin spherical shell embodying a circular cutout and excited axisymmetrically by a concentrated radial force. The solution is constructed by combining the shell response to the radial exciting force with its response to radial, tangential, and moment line loads applied along the cutout boundary, these line loads being selected to match the boundary conditions. Concise expressions for the shell response are obtained by applying the Sommerfeld-Watson transformation to the slowly converging high-frequency modal series which is thereby reduced to only two terms, viz., an exponentially decaying near-field and a standing or propagating-wave field. These two terms are in the nature of the creeping waves commonly used to formulate electromagnetic or acoustic diffracted wave fields in the short-wavelength limit. The method is illustrated for the simple case of a circular cutout with a clamped boundary, but lends itself to more complicated boundary conditions, viz., intersecting shells or wave guides. The natural frequencies and mode shapes are found from a single, characteristic equation involving trigonometric functions.

Copyright © 1970 by ASME
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