Journal of Theoretical and Computational Acoustics

In this paper, we consider the general idea of Digital Sound Reconstruction (DSR) and analyze its inherent limitations. Based on this discussion, a new method which we call Advanced Digital Sound Reconstruction (ADSR) is introduced and analyzed in detail. This method aims to overcome the problems of classical DSR by introducing shutter gates and focuses on sound generation in the low-frequency domain. Combining the idea of classical DSR with a redirection mechanism leads to a gain of 20dB per decade regarding the sound pressure for decreasing frequency values. We present multiple array designs and possible embodiments for ADSR as well as an in depth view of excitation and optimization approaches. Finally, numerical investigations are used in order to demonstrate the potential of ADSR especially in the mid- to low-frequency range.

The Partition of Unity Finite Element Method (PUFEM) shows promise for modeling wave-like problems in the mid-to-high frequency range, allowing to capture several wavelengths in a single element. Despite the increasing attention it received in acoustics and in structural dynamics, its efficacy to deal with coupled problems has not been addressed. The main challenge in this case is to be able to represent different types of physical waves accurately, knowing that the wavelengths can be very different and vary differently, exemplified by the dispersion of flexural waves in a solid. Without a proper handling of the coupling between the coupled media, at best the number of degrees of freedom (DoF) will not be optimal, at worst the coupled model will not converge. Techniques like mesh refinement, wave enrichment and compatible or incompatible meshes might offer a potential solution to the problem, but the model usually needs to be adjusted through a time consuming trial-and-error procedure. To tackle the problem, this paper considers a 2D coupled vibro-acoustic problem, in which the structural and acoustic domains, modeled with PUFEM, are coupled using compatible and incompatible meshes based on different coupling strategies. Numerical analyses show that the proposed method outperforms the classical finite element method by several orders of magnitude in terms of number of DoF. Recommendations are proposed on the technique to choose depending on the frequency range of interest in relation to the critical frequency of the structure to ensure the best convergence rate. Finally, an application example is presented to highlight the performance of the proposed method.

Pseudospectral time domain (PSTD) methods are widely used in many branches of acoustics for the numerical solution of the wave equation, including biomedical ultrasound and seismology. The use of the Fourier collocation spectral method in particular has many computational advantages. However, the use of a discrete Fourier basis is also inherently restricted to solving problems with periodic boundary conditions. Here, a family of spectral collocation methods based on the use of a sine or cosine basis is described. These retain the computational advantages of the Fourier collocation method but instead allow homogeneous Dirichlet (sound-soft) and Neumann (sound-hard) boundary conditions to be imposed. The basis function weights are computed numerically using the discrete sine and cosine transforms, which can be implemented using $O(NlogN)$ operations analogous to the fast Fourier transform. Practical details of how to implement spectral methods using discrete sine and cosine transforms are provided. The technique is then illustrated through the solution of the wave equation in a rectangular domain subject to different combinations of boundary conditions. The extension to boundaries with arbitrary real reflection coefficients or boundaries that are nonreflecting is also demonstrated using the weighted summation of the solutions with Dirichlet and Neumann boundary conditions.

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.

Step discontinuities, which are formed in pipeline repair and maintenance, will introduce additional wave scattering in the pipeline diagnosing work. Therefore, an analytical model is established in this paper to investigate the longitudinal wave scattering from a step discontinuity and the influence of discontinuity material on the scattering characteristics in water pipelines. In the model, axial wavenumber, displacement and stress profiles of the unblemished pipeline and discontinuity sections are calculated by a multi-layered cylindrical waveguide model. To concatenate these sections and predict the overall influences of the discontinuity, the mode matching method is applied by enforcing the flexible axial boundary conditions with an extended bi-orthogonality relation. Based on the established model, numerical calculations are carried out to investigate the reflection/transmission characteristics when discontinuity material and attenuation are considered. Both finite element method (FEM) software and laboratory experiments are also conducted for modeling verification: the maximum root mean square errors of the predicted reflection and transmission coefficients are 0.01 and 0.1 compared with FEM and experiment results, respectively. It indicates the proposed model is accurate in predicting the wave scattering from a step discontinuity in a water pipeline with the influence of discontinuity material accounted for. In addition, this pure analytical model introduces advantages in computational cost when modeling long pipelines compared with existing FEM packages.

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.