Acoustic radiation from an insonified elastic plate with a line discontinuity

Abstract

This paper deals with the development of analytic models for the prediction of the acoustic radiated field from an infinite elastic plate with a single line force and line moment impedance discontinuity due to an incident plane acoustic wave. The solution is in the form of a Fourier integral with a kernel having ten poles. The integral is evaluated by three methods. The first uses the steepest descent path (SDP) method, leading to a solution that decays as 1/(k0r)1/2. The second method used conformal transformations and the modified saddle point (MSP) method, where all ten poles of the integrand are factored out. This second method yields a solution that has complementary error functions and an asymptotic series in (k0r). The third method employs a transformation of the integrand to effect an efficient and fastly convergent numerical integration algorithm. In general, the MSP asymptotic series solution and the numerical integration yielded numerically identical results. However, while the SDP solution predicted a similar directivity function, it predicted numerically higher values than the MSP solution by as much as 20 dB for observers located close to the discontinuity. The three solutions converged for higher values of k0r, the convergence being slower for higher frequencies, especially above the coincidence frequency.