Abstract

An integral transform technique is used to solve a boundary-value problem in which the partial differential equation is linear but the associated boundary condition is nonlinear. A spherical cavity in an infinite acoustic medium has an elastically supported boundary such that the pressure-displacement relation on the boundary is nonlinear. The response of the boundary to a plane shock wave which progresses across the cavity and envelops it is obtained by solving two auxiliary boundary-value problems with linear boundary conditions. Using influence coefficients obtained from these solutions, a nonlinear integral equation for the response of the actual boundary is obtained. The integral equation is solved numerically for a set of parameters, and curves for the pressure-time and displacement-time responses of the boundary are presented.

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