Abstract:

Using a finite-element formulation with infinite elements to approximate the external fluid, well-developed structural sensitivity analysis techniques can be applied to acoustic radiation and scattering problems. Changes to a nominal structure are introduced through a structural perturbation matrix, (epsilon)(Delta)S, which modifies the system matrix, S, of the nominal system. The perturbed surface pressures and normal velocities are expressed as a binomial series in (Delta)S. The convergence criteria for the series is examined for structural-acoustic systems. A perturbation consisting of a change in the Young's modulus is examined for two numerical examples. First, a one-dimensional problem of plane-wave scattering from a viscoelastic layer is examined. The results of the 1-D problem are then extended to the multidimensional problem of plane-wave scattering from a cylindrical shell. The perturbations consist of varying the Young's modulus of the layer and the shell. It is shown that the convergence of the binomial series is strongly linked to the amount of damping in the nominal system, but not to the damping in the perturbation. Furthermore, the use of a truncated series is shown to be a valid approximation in many cases, even when the series does not converge.