A Qualitative Appraisal of the Doubly Assymptotic Approximation for Transient Analysis of Submerged Structures Excited by Weak Shock Waves.

摘要

Using the problem of the transient response of a spherical elastic shell to the excitation of an incident plane step pressure wave as a test problem for the Doubly Asymptotic Approximation (DAA) method, a qualitative appraisal of this method is summarized as follows: (1) The DAA method, by the nature of its scheme is accurate for the prediction of early-time response; (2) If the intrinsic characteristic of the response of the submerged structure as manifested by its step response is of non-oscillatory nature or is dominated by non-oscillatory components, the DAA solution is not only accurate for late-time by design but also valid for intermediate-time responses; (3) If this intrinsic characteristic is of oscillatory nature or is dominated by oscillatory components, the DAA solution has faster oscillations (frequency distortion) and these oscillations are damped out much sooner than the real response. This indicates that the DAA formulation overestimates the fluid resistance to the structural oscillation; (4) The DAA solution underestimates the maximum oscillatory responses if they do not occur at early-time; (5) The DAA method is not useful for the prediction of the intermediate- and late-time oscillatory characteristics of the response, e.g., the structural vibration after the transit of the incident wave front; (6) Since (3) also represents an overstabilizing effect due to the fluid, the results will be doubtful if the DAA method is applied to analyze dynamic stability problems such as dynamic buckling of submerged shells and other nonlinear response problems.