The wave superposition method has recently been advocated [Koopmann et al., ‘‘A method for computing acoustic fields based on the principle of wave superposition,’’ J. Acoust. Soc. Am. 86, 2433–2438 (1989)], as a reliable and accurate technique for computing the acoustic fields generated by arbitrary-shaped radiators; this study examines in depth the robustness and numerical stability of the method. The implementation of the method requires the placement of a finite number of point sources on a surface interior to the body of the radiator. The magnitude of these point sources can be evaluated in terms of the prescribed velocity distribution on the surface of the radiator. Once calculated, the magnitude of these point sources allow the pressure distribution exterior to the radiator to be evaluated. The first improvement made to the robustness of the method is the use of a hybrid combination of monopole and dipole sources; this modification allows the inherent problem of nonuniqueness of the method at certain frequencies to be overcome. Both discrete point and continuous source distributions are used to evaluate the method on a variety of test cases involving both spherical and prolate spheroid geometries. The prime motivation for using such a method is the avoidance of the singular integration inherent is the application of the normal boundary element methods, however, for the method to be successful, the resulting matrix approximations need to be well-conditioned. This numerical conditioning was found to be dependent not only on the position of the boundary and the source nodal points but also on the interpolation or the location of these sources on the retracted surface.

This work is concerned with the numerical modeling of elasto-acoustic problems applied to thin shells and specifically curved plates. A finite element formulation of the elastic problem is coupled to a variational boundary element solution of the acoustic problem. This solution to the acoustic problem, proposed by Mariem and Hamdi [J. B. Mariem and M. A. Hamdi, Int. J. Num. Methods. Eng. 24, 1251-1267 (1987) ], is implemented using high-order isoparametric elements, and attention is given to techniques of accelerating the numerical implementation for solutions at multiple frequencies. These techniques include a reduction in the problem size through the use of symmetry and, more importantly, the interpolation of the fluid impedance matrix within the frequency regime. The advantages in using this variational formulation are, first, the manner in which a highly singular integral operator is made amenable to numerical approximation, second, its application to nonclosed thin shells, and, third, its numerical implementation leads to the formulation of a symmetrical fluid matrix.

No abstract

The purpose of this paper is to clarify the question of nonexistence of solutions for the superposition method in acoustic radiation and scattering problems. Recently a number of authors have implemented this method and have claimed that nonexistence or nonuniqueness difficulties do not arise. Numerical evidence appears to support this view. However, this paper shows that the superposition method is a discrete approximation to an equation that does suffer from nonexistence of its solution at certain frequencies. Nonexistence of solutions is demonstrated with some numerical examples and an improved method is discussed.

A coupled boundary element/finite element technique originally developed for the analysis of open thin-shell problems, such as propeller blades, is used in this paper for the analysis of the fluid-filled elastic structures. For open thin-shell problems the question of nonuniqueness does not arise, however, it was thought at the time that such a formulation would prove to be nonunique for the analysis of closed fluid-filled submerged bodies. The work presented in this paper will demonstrate that, for submerged fluid-filled closed elastic bodies, this coupled formulation is unique throughout the entire frequency range. An advantage in implementing the variational form of the acoustic integral operator is that the resulting fluid matrix is symmetric. As such, the fluid/structural coupling is simplified, and the computational efficiency enhanced.