Journal of Computational Acoustics

Solution of wide-band underwater acoustic problems with the classical Normal Mode method in the frequency domain needs to solve the problem repeating for every frequency component of the wide-band source signal. In this paper, a direct and causal analytical Time Domain Normal Mode Method is presented for arbitrary time-dependent acoustic sources for a single layered isovelocity waveguide. An incomplete separation of variables technique is used to solve the inhomogeneous wave equation, directly in the time domain. Therefore, it becomes possible to calculate the time domain acoustic pressure in a single run.

Jet's sound-field emitted by a large scale source modeled as a wave packet is considered. Attention is given to nonlinear propagation effects caused by the source's supersonic Mach number and high amplitude. The approach of the Westervelt equation is adapted to derive a new set of weakly nonlinear sound propagation equations. An optimized Lax–Wendorff scheme is proposed for the newly derived equations. It is shown that these equations can be simulated using a time step close to the CFL limit even for high amplitudes unlike the conventional finite-difference simulation approach of the Westervelt equation. Two- and three-dimensional sound propagations were simulated for symmetric and asymmetric supersonic wave packets. It is seen that nonlinearity in the sound field is affected by the wave packet form, an effect that cannot be captured by a 1D propagation equation. High skewness in the pressure fluctuation and its time derivative were found near the Mach direction, showing crackle-like features. Pressure time history and frequency spectra are also investigated.

In this work, new absorbing boundary conditions (ABCs) for a wave equation with a temperature-dependent speed of sound are proposed. Based on the theory of pseudo-differential calculus, first- and second-order ABCs for the one- and two-dimensional wave equations are derived. Both boundary conditions are local in space and time. The well-posedness of the wave equation with the developed ABCs is shown through the reduction of the original problem to an equivalent one for which the uniqueness and existence of the solution has already been established. Although the second-order ABC is more accurate, the numerical realization is more challenging. Here we use a Lagrange multiplier approach which fits into the abstract framework of saddle point formulations and yields stable results. Numerical examples illustrating stability, accuracy and flexibility of the ABCs are given. As a test setting, we perform computations for a high-intensity focused ultrasound (HIFU) application, which is a typical thermo-acoustic multi-physics problem.

In this paper we consider the propagation of Lamb waves in a poroelastic plate containing a linear crack, the special case where the surface of the plate is unloaded, by employing the Wiener-Hopf technique.

The problem we solve here is a mathematically interesting toy problem. Physically speaking the more reasonable problem would be to consider there to be fluid pressure on both sides of the plate. This problem can be solved using the solution we derive here and will be presented in a subsequent work. Also dealt in this paper are the characteristic equations for a viscous fluid Biot systems and the orthogonality relations for a free boundary poroelastic slab.

Photoacoustic generation using an optical fiber is a promising approach to meet the challenges in most advanced ultrasonic non-destructive testing (NDT) applications. The energy-absorption layer coated on the fiber endface plays an important role in converting the laser energy into heat and exciting the acoustic wave. The selection of the absorption material and the optimization of the structure dimension are the keys for achieving high energy-conversion efficiency. A 2D-axisymmetric finite element analysis (FEA) model was established to simulate the photoacoustic generation process using a newly developed absorption material, polydimethylsiloxane/gold nanoparticle (PDMS/Au NPs) nanocomposites, with different thicknesses and laser pulse durations. The experimental results obtained using a similar set-up show a similar trend predicted by this FEA simulation. The FEA results provide practical clues to the design of the fiber-optic photoacoustic generator.

The two-sided second-order Arnoldi algorithm is used to generate a reduced order model of two test cases of fully coupled, acoustic interior cavities, backed by flexible structural systems with damping. The reduced order model is obtained by applying a Galerkin–Petrov projection of the coupled system matrices, from a higher dimensional subspace to a lower dimensional subspace, whilst preserving the low frequency moments of the coupled system. The basis vectors for projection are computed efficiently using a two-sided second-order Arnoldi algorithm, which generates an orthogonal basis for the second-order Krylov subspace containing moments of the original higher dimensional system. The first model is an ABAQUS benchmark problem: a 2D, point loaded, water filled cavity. The second model is a cylindrical air-filled cavity, with clamped ends and a load normal to its curved surface. The computational efficiency, error and convergence are analyzed, and the two-sided second-order Arnoldi method shows better efficiency and performance than the one-sided Arnoldi technique, whilst also preserving the second-order structure of the original problem.

Finite element analysis of transient acoustic phenomena on unbounded exterior domains is very common in engineering analysis. In these problems there is a common need to compute the acoustic pressure at points outside of the acoustic mesh, since meshing to points of interest is impractical in many scenarios. In aeroacoustic calculations, for example, the acoustic pressure may be required at tens or hundreds of meters from the structure. In these cases, a method is needed for post-processing the acoustic results to compute the response at far-field points. In this paper, we compare two methods for computing far-field acoustic pressures, one derived directly from the infinite element solution, and the other from the transient version of the Kirchhoff integral. We show that the infinite element approach alleviates the large storage requirements that are typical of Kirchhoff integral and related procedures, and also does not suffer from loss of accuracy that is an inherent part of computing numerical derivatives in the Kirchhoff integral. In order to further speed up and streamline the process of computing the acoustic response at points outside of the mesh, we also address the nonlinear iterative procedure needed for locating parametric coordinates within the host infinite element of far-field points, the parallelization of the overall process, linear solver requirements, and system stability considerations.