Journal of Computational Acoustics

The sound power radiated by a plane vibrating structure can be calculated by numerical integration of the Rayleigh integral or by means of finite and boundary element methods. However, these methods are usually time-consuming due to the numerical evaluation of surface integrals. This paper reviews and discusses an alternative numerical method (the lumped parameter model) to compute the sound radiation from planar structures which is based just on surface velocity information and a direct numerical evaluation of the radiation resistance matrix of the structure. As an example, the technique is applied to estimate the sound radiated from the structural axisymmetric modes of both clamped and simply-supported circular baffled plates.

A compact finite-difference scheme is presented in this paper for efficiently solving the variable Helmholtz equation. This scheme development involves relating the derivative terms, namely, u_xx and u_xxxx, to u at the two adjacent nodal points in order to yield a 3-point stencil implicit scheme. In addition to sixth-order accuracy, the proposed scheme can conditionally provide oscillation-free solutions using the underlying M-matrix theory. Computations have been carried out for several problems which are amenable to exact solutions. Agreement with the exact solutions is excellent even in a grid system involving fewer number of mesh points. Thus, the integrity of the compact scheme and the efficiency of the alternating direction implicit algorithm are demonstrated. The proposed scheme is applied to study the effect of variable wave number on the wave propagation characteristics for the problem, which is partly bounded by a scatter surface.

The one-dimensional analytical solutions are derived and three-dimensional substructure boundary element approaches are developed to predict and analyze the acoustic attenuation characteristics of straight-through perforated tube silencers and folded resonators without mean flow, as well as to examine the effect of nonplanar waves in the silencers and resonators on the acoustic attenuation performance. Comparisons of transmission loss predictions with the experimental results for prototype straight-through perforated tube silencers demonstrated that the three-dimensional approach is needed for accurate acoustic attenuation performance prediction at higher frequencies, while the simple one-dimensional theory is sufficient at lower frequencies. The BEM is then used to investigate the effects of geometrical parameters on the acoustic attenuation characteristics of straight-through perforated tube silencers and folded resonators in detail.

A semi-analytic method based on the propagation matrix formulation of indirect boundary element method to compute response of elastic (and acoustic) waves in multi-layered media with irregular interfaces is presented. The method works recursively starting from the top-most free surface at which a stress-free boundary condition is applied, and the displacement-stress boundary conditions are then subsequently applied at each interface. The basic idea behind this method is the matrix formulation of the propagation matrix (PM) or more recently the reflectivity method as wide used in the geophysics community for the computation of synthetic seismograms in stratified media. The reflected and transmitted wave fields between arbitrary shapes of layers can be computed using the indirect boundary element (BEM) method. Like any standard BEM methods, the primary task of the BEM-based propagation matrix method (thereafter called PM–BEM) is the evaluation of element boundary integral of the Green's function, for which there are standard method that can be adapted. In addition, effective absorbing boundary conditions as used in the finite difference numerical method is adapted in our implementation to suppress the spurious arrivals from the artificial boundaries due to limited model space. To our knowledge, such implementation has not appeared in the literature. Several examples are presented in this paper to demonstrate the effectiveness of this proposed PM–BEM method for modeling elastic waves in media with complex structure.

This study is concerned with the problem of acoustic scattering by a three-dimensional obstacle in a shallow water waveguide. A method coupling of the finite-element and natural boundary-element is analyzed and presented for solving the acoustic scattering problem numerically based on the Galerkin variational principle and the DtN mapping theory. The proposed method has the advantage of avoiding the absorbing boundary condition of the conventional finite-element method. Numerical examples are given of successful computational results for several 3D obstacles of various shapes.

The acoustic propagation problem is modeled via the parabolic approximation. The physical domain consists of the water column with a horizontal water–bottom interface and the bottom region consists of N-strata with horizontal interfaces. The computational domain is restricted to the water column, while the stratified bottom region is modeled by a nonlocal boundary condition applied along the water–bottom interface, and having the form of a Neumann to Dirichlet map (NtD). The discrete analog of the NtD has been implemented in a finite difference scheme for the general wide angle PE model, and successfully tested for several benchmark problems. The stratification of the media can be either physical, e.g. sediment formulation in the bottom, or artificial/computational, e.g. forced by sparse distribution of environmental data measurements in the water column. It should be emphasized that the sound speed may vary from layer to layer, but is constant within each layer. The proposed NtD map can be used in geoacoustic inversion via the optimal control adjoint method.

This paper presents an integrated simulation method for investigating nonlinear sound beams and three-dimensional (3D) acoustic scattering from any combination of complicated objects. A standard finite-difference simulation method is used to model pulsed nonlinear sound propagation from a source to a scattering target via the Khokhlov–Zabolotskaya–Kuznetsov equation. Then, a parallel 3D acoustic simulation method based on the finite integration technique is used to model the acoustic wave interaction with the target. Any combination of objects and material layers can be placed into the 3D simulation space to study the resulting interaction. Several example simulations are presented to demonstrate the simulation method and 3D visualization techniques. The combined simulation method is validated by comparing experimental and simulation data and a demonstration of how this combined simulation method assisted in the development of a nonlinear acoustic concealed weapons detector is also presented.

A finite difference (FD) method is developed and analyzed for the Helmholtz equation in a radially symmetric waveguide. The resulting algorithm can be used to solve for sound intensities in complex models that may include high material contrasts and arbitrary bathymetry. An analysis of the effect of grid discretization on the results indicates that numerical dispersion is significant within one-third of a wavelength from a point source and decreases beyond that. Numerical results are presented and compared to wide-angle parabolic equation (PE) solutions and analytic solutions, where available. Comparison with analytic results indicates that the FD method accurately solves for the acoustic wave field at all propagation angles and is more accurate than the PE method near the source. Results are also shown for models in which mode coupling occurs near the source.