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The shear waves have been taken into consideration to deduce the theoretical model of the scattering of isotropic circular solid cylinders in a fluid medium. The theoretical analysis has been done based on the wave equation and the three classical boundary conditions. The analytical solution of the far-field pattern for this scattering issue has been derived and the pressure in the scattered wave can be given. And the finite element method (FEM) has been used to solve the underwater acoustic scattering problems. Numerical solution of the resulting was discussed in three directions. The following work is to study the scattering problems of collection of cylinders with arbitrary cross-sections and any numbers. The conclusions drawn in this paper could contribute to explore the acoustic propagation characteristics of the two-phase media.

In this paper we study a mathematical model to describe a three dimensional acoustic scattering problem associated to a "vibrating" obstacle that is a bounded simply connected domain contained in the three dimensional real Euclidean space whose shape changes in time. In particular we propose a numerical method based on a perturbation series and the operator expansion method to solve the mathematical model considered. This method makes possible to obtain highly parallelizable algorithms able to compute the solution of the problem considered order by order in perturbation theory, and able to obtain the required solution of the scattering problem summing up the perturbation series. Really impressive speed up factors are observed and reported when the algorithm is executed on the Chiba Cluster, a parallel machine of the Argonne National Laboratory, USA. We validate the mathematical model and the numerical method proposed solving some test problems. The quantitative character of the numerical results obtained is established. The results obtained on the test problems are discussed both from the numerical and the physical point of view. In particular we show that the Doppler spectrum associated to the far field patterns of the scattered acoustic fields depends mainly from the incoming wave and from the excited vibrational modes (Figs. 9–13). The website: shows some Applets relative to the numerical examples.

The problems of acoustic waves scattered by scatterer immersed in unbounded domain is an essential ingredient in the study of acoustic-structure interaction. In this paper the problems of acoustic scattering in an infinite exterior region are investigated by using a fractal two-level finite element mesh with self-similar layers in the media which encloses the conventional finite element mesh for the cavity. The similarity ratio is bigger than one so that the fractal mesh extends to infinity. Because of the self-similarity, the equivalent stiffness (mass) matrix of one layer is proportional to the others. By means of the Hankel functions automatically satisfying Sommerfeld's radiation conditions at infinity, the different unknown nodal pressures on different layers are transformed to some common unknowns of the Hankel coefficients. The set of infinite number of unknowns of nodal pressure is reduced to the set of finite number of Hankel's coefficients. All layers have the same matrix dimension after the transformation and the respective matrices of each layer are summed. Due to the proportionality, the infinite number of layers can be summed in closed form as the entries of each matrix are in geometric series. That is, processing one layer is enough to virtually represent a set of infinite number of layers covering an infinity domain. No new elements are created. Numerical examples show that this method is efficient and accurate in solving unbounded acoustic problems.

This paper shows that under the assumption of the out-going radiation conditions at infinity, the time-harmonic acoustic scattered field off a sound-soft solid in a shallow ocean with a fluid-like seabed is unique in . Here M₁ is the water part, M₂ the seabed, the waveguide and Ω the solid object. The associated modal problem is studied and a representation formula for the solution in terms of the Green's function is derived.

A dual-primal variant of the FETI-H domain decomposition method is designed for the fast, parallel, iterative solution of large-scale systems of complex equations arising from the discretization of acoustic scattering problems formulated in bounded computational domains. The convergence of this iterative solution method, named here FETI-DPH, is shown to scale with the problem size, the number of subdomains, and the wave number. Its solution time is also shown to scale with the problem size. CPU performance results obtained for the acoustic signature analysis in the mid-frequency regime of mockup submarines reveal that the proposed FETI-DPH solver is significantly faster than the previous generation FETI-H solution algorithm.

The current work describes the application of high-order numerical techniques to single or multiple overset curvilinear body-fitted grids, demonstrating the feasibility of direct computations of noise radiated by flows around complex non-Cartesian bodies. Flows of both physical and industrial interest can be investigated with this approach. We first rapidly describe the numerical techniques implemented in our curvilinear simulations. The explicit high-order differencing and filtering schemes are presented, as well as their application to the curvilinear Navier–Stokes equations. We then present brief results of various 2-D acoustic simulations. First the flow around a cylinder, and the associated acoustic field, are described. The diameter-based Reynolds number Re_D = 150 is under the critical Reynolds number of the onset of 3-D phenomena in the vortex-shedding. Simulation results can thus be meaningfully compared to experimental measurements. A case of acoustic scattering is then examined. A non-compact monopolar source is placed half way between two differently sized cylinders. A complex diffraction pattern is created, and resulting RMS pressure data are compared to the analytical solution. Finally the noise generated by a low Reynolds number laminar flow around a NACA 0012 airfoil is presented.

Coupled finite-infinite element computations are very efficient for modeling large scale acoustics problems. Parallel algorithms, like sub-structuring and domain decomposition methods, have shown to be very efficient for solving huge linear systems arising from acoustics. In this paper, a coupled finite-infinite element method is described, formulated and analyzed for parallel computations purpose. New numerical results illustrate the efficiency of this method for academic test cases and industrial problems alike.

A broadband multilevel fast multipole algorithm (MLFMA) for the acoustic scattering from a sound-hard obstacle is presented. The formulation is based on the Burton–Miller boundary integral equation and Galerkin's method, avoiding any hypersingular integral operators. The resulting matrix equation has good iterative properties for all frequencies and avoids the interior resonance problem. The main novel feature is the use of a broadband MLFMA to accelerate the iterative generalized minimal residual (GMRES) solver. The algorithm is based on a combination of Rokhlin's translation formula for large division cubes and the spectral representation of the Green's function for cubes smaller than one half wavelength, thereby avoiding the sub-wavelength breakdown of the high-frequency MLFMA.

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.

A novel boundary element method based on subdivision surfaces is applied to simulate wave scattering problems governed by the Helmholtz equation. The Loop subdivision scheme widely used in the CAD (computer aided design) field is applied to represent the geometric model and approximate physical field variables. The novelty of this work is that it is the first time to apply the fast multipole method for subdivision surface boundary element method to accelerate the solution of the system of equations. It is demonstrated that the subdivision surfaces boundary element method based on the Loop subdivision scheme performs well in terms of accuracy, and automatically provides multiresolution subdivision hierarchy models to meet the requirements of different precision. This approach is then applied to several real-world applications to illustrate the potential for integrated engineering analysis.

The interaction between the sound field outside an elastic structure and its boundary is of paramount importance in the field of acoustics. This paper describes the global acoustic impedance in the form of impedance integral operator and impedance matrix for the analysis of elastic structures. In general, the excitation applied locally to the structure can induce vibration on the entire structure surface and hence the global acoustic impedance is introduced to characterize the relationship between the resultant sound pressure and acoustic particle velocity. The main advantage of the global acoustic impedance over the local acoustic impedance is that it facilitates improved physical insights into the sound field due to the presence of excitation sources. Furthermore, the acoustic impedance of an elastic spherical shell in matrix form is solved and analyzed by solving the finite element equation of structural dynamics with programming techniques. The impedance matrix is subsequently taken as the boundary condition to investigate the acoustic scattering from the elastic shell structure using the acoustic boundary element method. Explanations for the difference between the acoustic scatterings calculated based on the global acoustic impedance and the local acoustic impedance are offered.

The elevation of ocean waves is always modeled in linear theory as a superposition of the sinusoidal components with crests and troughs of identical heights. However, under some circumstances, the wave amplitude is outside the linear range and presents as a weakly nonlinear asymmetrical waveform with sharper crests and shallower troughs. We studied the impact of the weakly nonlinear effect of ocean waves in deep and intermediate waters on acoustic scattering from the surface of the ocean using two rough surface models with fractal geometry and power law spectral behavior in the equilibrium range. The classic Weierstrass–Mandelbrot function was used to model the linear waves and a new fractal function, the fractional Weierstrass function developed in studies of electromagnetism, was used to model the weakly nonlinear waves. We evaluated these two models using the Pierson–Moskowitz spectrum and the incident wavelength. The bistatic scattering strength was obtained via a numerical method based on the “exact” solution of the integral equation. The weakly nonlinear phenomenon led to a very small reduction in the narrow area around the specular reflection angle and a small increase in the remaining wide area, including the backpropagation area with a scattering angle $<90^{\circ }$. The differences in backscattering strength between the two models were similar to the bistatic scattering strength in the backpropagation area and did not depend on the incident grazing angle.

Acoustic and elastic metamaterials have shown potential for many different applications in wave manipulation and structural isolation. Minimization of a scattered wave field has been identified as an important use for such materials, and a wide variety of designs have been proposed for this purpose. Several of these designs face practical challenges (e.g. pentamode designs, which are difficult to manufacture), and many others involve numerous tunable parameters and a large design parameter space (e.g. distributions of resonators), making global search-based optimization less tractable and raising the need for gradient-based methods. In this work, gradient-based optimization governed by partial differential equations (PDEs) is used to optimize acoustic channels in a coiled-space metastructure layer surrounding a rigid acoustic scatterer. The optimization technique is chosen to more feasibly search the design parameter space, and the acoustic channel design is chosen to exploit sound speed optimization as a proxy for channel length optimization to give practically achievable structures. Results are presented for both a single plane wave direction and multiple plane wave directions, as well as for both a single frequency and multiple frequencies. The equivalence of sound speed optimization and channel length optimization is demonstrated for a feasible design minimizing the scattered pressure field. Designs with various numbers of optimized channels are also considered.

In this study, we focus on the prediction of the pressure field scattered from an immersed cylindrical shell partially coated by a soft rubber, impacted by an acoustic plane wave. As the coating covers only a partial portion along the circumference of the shell, the considered system is not axisymmetric. As a result, a spectral (Fourier) resolution of the mathematical problem would induce the coupling of the different circumferential orders, which can lead to prohibitive computing times. To circumvent this issue, the reverse Condensed Transfer Function (rCTF) method has recently been developed to decouple vibroacoustic subsystems initially coupled along lines or surfaces. From an analytical model of the fully coated shell impacted by the acoustic plane wave and a finite element (FE) model of the missing coating material, the rCTF approach predicts the vibroacoustic behavior of the coated shell with a voided section instead of the removed part. This voided section can then be filled by a FE model of the water domain replacing the removed coating material, using the direct CTF approach. The principle of the rCTF approach, some numerical validations, and results for the scattering from the partially coated shell are presented in this paper.