A hybrid solution for the response Green’s function of a fluid-loaded cylindrical shell

Abstract

A classical problem in structural acoustics is the response of a fluid-loaded cylindrical shell, with ring discontinuities or ring forces, to excitation by incident acoustic waves. The solution for these types of problems is generally formulated using integral transforms. The solution in the spatial domain is obtained by inverse transforming the wave-number solution. In past work, the inverse transform has been obtained by using either a contour integral approach or by introducing structural damping, thus removing the singularities from the integrand of the inverse transform. An alternative to these classical approaches, which does not require the introduction of structural damping, and therefore retains only the influence of the fluid loading on the response of the cylindrical shell, is a hybrid method which has previously been used for a fluid-loaded plate with a line discontinuity. Using this approach, the solution is not contaminated by the artificially introduced structural damping. Furthermore, the hybrid approach is more efficient computationally, especially when the evaluation of the response Green’s function is required. In this paper, the hybrid approach is applied to the solution of the displacement response Green’s function for a fluid-loaded cylindrical shell with a ring discontinuity, excited by an obliquely incident acoustic wave. The shell wall thickness to radius ratio is 0.01 and therefore thin shell equations of motion are used in the solution. The results presented are for the first circumferential mode (n=0). However, the approach can be used to generate results for other values of the circumferential mode number. At high frequencies, the results asymptotically approach those for a fluid-loaded plate. Also, for an axial load the results are in close agreement with results obtained on a shell with structural damping by other investigators.

The modeling of the radiation and response Green’s function of a fluid-loaded cylindrical shell with an external compliant layer

“…The denominator of the integrand, which is the characteristic equation of the fluid-loaded shell with an external compliant layer, becomes singular at its roots. Therefore, the integrand cannot be directly evaluated using an IDFT and an alternative approach, such as the hybrid numerical/ analytical method, 6,8 is required. In the hybrid method, the singularities that precluded the direct use of numerical integration are first removed from the integrand and their contribution evaluated using a contour integration.…”

“…6. Equation ͑12͒ includes excitation by incident pressure P i n and ring internal loads F U n , F V n , F W n , respectively, in the axial, tangential, and radial directions.…”

“…6 The solution for the response can be obtained for specific values of n, the circumferential mode number. Writing the equations of motion for particular circumferential mode n in matrix form 6 ͓S n ͑k,n͔͒ ΄ Ũ n Ṽ n W n…”