Abstract
The title problem is solved through extension of a method previously formulated for plane step-wave excitation, which employs generalized Fourier series augmented by partial closure of those series at early time. The extension encompasses both plane and spherical incident waves with step-exponential pressure profiles. The effects of incident-wave curvature and profile decay rate on response behavior are examined. A method previously developed for assessing the discrepancy between calculated and measured response histories is employed to evaluate the convergence of the truncated series solutions. Also studied is the performance of doubly-asymptotic approximations. Finally, the efficacy of modified Cesàro summation for improving the convergence of series solutions is examined. The documented computer program that produced the numerical results appearing in this paper, SPHSHK/MODSUM, may be down-loaded from the Web site http://saviac.xservices.com.