Approximations for the two-dimensional Green’s function of a fluid-loaded plate

Abstract

Simple analytical formulas to predict the acoustic component of the two-dimensional (2-D) Green’s function of a fluid-loaded plate are presented. The formulas do not require any side computations such as numerical zero finding or numerical integrations. The simplest result obtained provides a good estimate of the Green’s function for a very broad range of frequencies, being degraded only near the coincidence frequency. A somewhat more complicated formula, almost uniformly valid in frequency, and yielding reasonable accuracy even at coincidence, is also presented. Numerical results comparing the asymptotic approximations to the ‘‘exact’’ Green’s function are presented, and show significant improvement over a basic steepest descents based approximation. For large values of x, very high accuracy can be achieved with relative errors of less than 0.1%. For other less stringent applications the approximations are accurate to within 10% at fairly small distances from the source, requiring only kfx>1 and k0x>0.5.