Wave-number-based assessment of the doubly asymptotic approximation. II. Frequency and time domain response

Abstract

In part I, the surface variational principle (SVP) and the doubly asymptotic approximation (DAA) were used to generate alternative descriptions of the frequency domain wet surface impedance. These are used here to obtain alternative descriptions of the displacement field in slender hemicapped cylindrical shells. This field is represented as a decomposition into a two-dimensional wave-number space. The responses that are obtained are frequency domain transfer functions for a point force at the midplane, evaluated for a discrete set of frequencies. Solutions obtained from first- and second-order versions of DAA are compared to the SVP result. Then temporal responses are obtained by using an inverse fast Fourier transform to evaluate the convolution of the transfer functions with a prototypical temporal excitation. The results reveal that DAA and SVP differ most in the vicinity of fluid-loaded resonances. The largest disagreement is encountered for the axisymmetric portion of the response. It is shown that DAA often greatly underpredicts peak displacements and accelerations, but a few cases lead to overprediction.