After the parabolic equation method was initially applied to scalar wave propagation problems in ocean acoustics and seismology, it took more than a decade before there was any substantial progress in extending this approach to problems involving solid layers. Some of the key steps in the development of the elastic parabolic equation are discussed here. The first breakthrough came in 1985 with the

A possible medium is considered with a large number of diverse but possibly similar relaxation processes. The equations for single spatially located relaxation processes of general type are developed and extended to a large spatially extended system. Each process is characterized by a relaxation time and a relaxation strength and is excited by the local pressure in an incident acoustic wave. A constant

The numerical solution of the elastodynamic problem with kinematic boundary conditions is considered using mixed finite elements for the space discretization and a staggered leap-frog scheme for the discretization in time. The stability of the numerical scheme is shown under the usual CFL condition. Using the general form of Robin-type boundary conditions some cases of debonding and the resulting acoustic

A hybrid computational method is proposed for three-dimensional structural-acoustic radiation in shallow water, which combines the wave superposition method (WSM) with the adjustable Green function and the multi-physical-coupled finite element method (FEM). A low-frequency acoustic model in the near field is established by the FEM to discretize the continuous and arbitrary-shaped radiator, and the

Solving an acoustic wave equation using a parabolic approximation is a popular approach for many existing ocean acoustic models. Commonly used parabolic equation (PE) model programs, such as the range-dependent acoustic model (RAM), are discretized by the finite difference method (FDM). Considering the idea and theory of the wide-angle rational approximation, a discrete PE model using the Chebyshev

A modified Helmholtz equation least-square (HELS) method is developed to reconstruct vibroacoustic quantities on an arbitrarily shaped vibrating structure. Unlike the traditional nearfield acoustical holography that relies on the acoustic pressures collected on a hologram surface at a short stand-off distance to a target structure, this modified HELS method takes the partial normal surface velocities

This paper presents an optimal design method for the acoustic stealth shape for a bottom object with relatively lower echo strength (ES), based on the physical acoustics method (PAM) and genetic algorithm (GA). Specifically, the performance of the PAM was evaluated with acoustic scattering from a Manta-like object, using two-dimensional (2D) axisymmetric calculation method. In the optimization method

This study proposes an optimization approach to maximize the transmission loss (TL) of a muffler by optimizing the thickness of the embedded porous layer. The objective function, i.e. the TL value, is computed by the four-pole parameters based on the boundary element analysis, and the thicknesses assigned to the discretized elements are naturally chosen as the design variables, resulting in a continuous

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

An inversion scheme based on time-warping is presented for estimating the attenuation coefficient of a sediment bottom using a single vector sensor, restricted to shallow water and using low-frequency impulsive sources. The attenuation information is extracted from the modal phase difference between pressure and vertical velocity. The method is derived from Pekeris waveguide theoretical equations and

This paper presents a methodology that enables one to trace back the forced-vibroacoustic components (F-VAC) that are responsible for acoustic radiation from an arbitrarily shaped structure. This methodology relies on a modified Helmholtz equation least-square (HELS) method that takes partial normal surface velocities obtained by using a laser vibrometer and partial acoustic pressures measured using

The implicit frequency dependence of linear systems arising from the acoustic boundary element method necessitates an efficient treatment for problems in a frequency range. Instead of solving the linear systems independently at each frequency point, this paper is concerned with solving them simultaneously at multiple frequency points within a single iteration scheme. The proposed concept is based on

A discussion is given of early literature pertaining to the theory of vibration from the time of Pythagoras up through 1750. The paper attempts to give an analytical interpretation to early anecdotal works concerning Pythagoras and to publications of Galileo, Huygens, Hooke, Taylor, John Bernoulli, Leibniz and Euler. To bridge the “culture gap,” mathematical developments by the latter cited authors

Biot’s theory of porous media is discussed critically, with emphasis on the first 1956 JASA paper that purports to apply for low frequencies. It is pointed out that the use of two and only two displacement fields has a certain arbitrariness, and that models with additional displacement fields are possible. Biot’s expression for the strain-energy per unit volume is justified in part, but it is pointed

Several methods for handling sloping fluid–solid interfaces with the elastic parabolic equation are tested. A single-scattering approach that is modified for the fluid–solid case is accurate for some problems but breaks down when the contrast across the interface is sufficiently large and when there is a Scholte wave. An approximate condition for conserving energy breaks down when a Scholte wave propagates

In acoustics, knowledge of the impulse response of a system is often important. While impulse responses may be measured, they may also be predicted using numerical methods. This work considers the generation of impulse responses from frequency-domain finite element solutions. It is shown that these impulse responses, obtained by inverse Fourier transformation, are noncausal. Through error analysis

In low Mach number aeroacoustics, the well-known disparity of scales allows applying hybrid simulation models using different meshes for flow and acoustics, which leads to a fast computational procedure. The hybrid workflow of the perturbed convective wave equation involves three steps: (1) perform unsteady incompressible flow computations on a subdomain; (2) compute the acoustic sources and (3) simulate

In this paper, a semi-analytical framework, based on the scaled boundary finite element method (SBFEM), is proposed, to study interior acoustic problems in the mid-frequency range in two and three dimensions. The SBFEM shares the advantages of both the finite element method (FEM) and the boundary element method (BEM). Like the FEM, it does not require the fundamental solution (Green’s function) and

A complete and formal theoretical derivation of the equations of motion and the stress–strain relations in Carcione–Leclaire three-phase theory is presented. The Lagrangian formulation is obtained on the basis of the potential and kinetic energies. We provided a new and more clear method to express the kinetic and potential energy density in an elastic solid. In particular, the deduction of the kinetic

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

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

Stoneley wave velocity variation is analyzed by solving the modified Scholte secular equation for velocity of Stoneley waves, allowing to find dependency of the Stoneley wave velocity on the Wiechert parameter and construct a set of inequalities that confines region of existence for the appropriate root of the secular equation. Numerical analysis for Stoneley wave velocity dependence on the Wiechert

An efficient and accurate method for calculating the sound radiated by a baffled circular rigid piston is using spherical harmonics, and the solution is a series containing the integral of spherical Bessel functions. The integral is usually calculated with the generalized hypergeometric functions in existing literatures, which shows poor convergence at middle and high frequencies due to the overflow

The field of aeroacoustics has gained much attention since the well-known acoustic analogies were first published in the 1950s. In parallel, the continuous growth of computational resources has enabled researchers and engineers to investigate phenomena involving flow-induced noise or sound propagation effects related to arbitrary velocity fields. To describe the latter mentioned physical processes

A fast method for calculating sound radiation/reflection directivities at high resolution in the infinite far field is proposed with the use of the fast multipole boundary element method (FMBEM). This method calculates directivities using direction-dependent coefficients called outgoing coefficients, which are obtained in the calculation process of the matrix-vector products in the FMBEM. Since the

Vibrating structures are often mounted on or located near a passive plane surface with finite acoustic impedance, and hence the acoustic pressures measured in a half-space bounded by the surface consist of both the direct radiation from the structure and the reflection from the boundary surface. In order to visualize the direct radiation from the source into free space, a reconstruction method based

Acoustical properties of the sea bottom can be described using geoacoustic (GA) models. Most existing propagation models use GA parameters as the bottom properties. It is difficult to obtain GA parameters for a layered bottom because of inter parameter coupling. These problems can be solved by inverting the model-independent reflective parameters P and Q. For a multilayered bottom, a sound field computation

Reliable acoustic path (RAP) is a direct path used for sound propagation between a shallow source and a deep receiver in deep water. The RAP environment can provide a high signal-to-noise ratio (SNR) environment for source localization, so it has been widely studied for underwater passive detection. Active detection can be used for source localization during the descent of a vertical line array (VLA)

Due to the dispersion of normal modes in shallow water, there exist regular striations on the interference spectrogram in space-frequency domain. Based on the range-frequency domain striations, waveguide invariant can be estimated with the prior knowledge of source range. Utilizing striations along the array, Rouseff and Zurk [J. Acoust. Soc. Amer.130 (2011) EL76–EL81] proposed the striation-based

The application of a boundary element technique in combination with a contour integral approach to the numerical analysis of acoustic resonances in exterior configurations is investigated in this paper. Similar to the boundary element analysis of exterior acoustic radiation or scattering problems, spurious eigenfrequencies also turn up in the boundary element solution to exterior acoustic resonance

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

The asymptotic rate of convergence of the Legendre–Galerkin spectral approximation to an atmospheric acoustic eigenvalue problem is established, as the dimension of the approximating subspace approaches infinity. Convergence is in the H1 Sobolev norm and is based on the existing theory [F. Chatelin, Spectral Approximations of Linear Operators (SIAM, 2011)]. The assumption is made that the eigenvalues

The Fast Multipole Boundary Element Method (FMBEM) reduces the O(N2) computational and memory complexity of the conventional BEM discretized with N boundary unknowns, to O(NlogN) and O(N), respectively. A number of massively parallel FMBEM models have been developed in the last decade or so for CPU, GPU and heterogeneous architectures, which are capable of utilizing hundreds of thousands of CPU cores

This paper is concerned with the spectral characteristics of leak noise at the source relevant to fluid dynamics for natural gas pipelines. Comparison is made between the flow field characteristics for the buried and above-ground pipelines to demonstrate the differences in aero-acoustics generation mechanism. The fundamental spectral parameters including the sound pressure level (SPL) and power spectral

The problem is the scattering of a plane sound wave at a rough water-air interface. The purpose of this paper is to describe in detail the method and demonstrate its work with simple examples. The main advantage of this approach is that there are no limits on the relation between the shape of the surface and the incident wave, so we can consider large Rayleigh parameter, shading, multiple scattering

A high-order large eddy simulation (LES) code based on the flux reconstruction (FR) scheme is further developed for supersonic jet simulation. The FR scheme provides an efficient and easy-to-implement way to achieve high-order accuracy on an unstructured mesh. The order of accuracy and the shock capturing capability of the solver are validated with the isentropic Euler vortex and Sod’s shock tube problem

A novel method to solve exterior Helmholtz problems in the case of multipole excitation and random input data is developed. The infinite element method is applied to compute the sound pressure field in the exterior fluid domain. The consideration of random input data leads to a stochastic infinite element formulation. The generalized polynomial chaos expansion of the random data results in the spectral

In this paper, a coupled finite/infinite element method is applied for computing eigenfrequencies of structures in exterior acoustic domains. The underlying quadratic eigenvalue problem is addressed by a contour integral method based on resolvent moments. The numerical framework is applied to an academic example of a hollow sphere submerged in water. Comparisons of the computed eigenfrequencies to

Material and geometrical parameters of tires involve some degree of uncertainty mainly related to production processes. Accordingly, the associated structural responses are affected by these uncertainties. In this study, a novel theoretical ring model is presented to describe the in-plane and out-of-plane vibrations as well as the steady-state response of tires, and then to evaluate the influence of

In this paper, a half-space fast multipole BEM is developed for the simulation of three-dimensional acoustic problems above an infinite impedance plane. The half-space impedance Green’s function involving a complex line source is used, so that both mass-like and spring-like impedance boundary conditions on the infinite plane can be explicitly satisfied and the infinite plane is not required to be discretized

Green’s functions for acoustic problems is the fundamental solution to the inhomogeneous Helmholtz equation for a point source, which satisfies specific boundary conditions. It is very significant for the integral equation and also serves as the impulse response of an acoustic wave equation. They are important for acoustic problems that involve the propagation of sound from the source point to the

This paper makes the first attempt to propose a novel hybrid collocation solver based on the generalized finite difference method (GFDM) and singular boundary method (SBM) to analyze underwater acoustic radiation and propagation around the thin plate structures excited by simple harmonic force under shallow sea environment. In the proposed hybrid solver, the meshless GFDM is employed to obtain the

A shape optimization approach based on isogeometric wideband fast multipole boundary element method (IGA WFMBEM) in 2D acoustics is developed in this study. The key treatment is shape sensitivity analysis by using the adjoint variable method under isogeometric analysis (IGA) conditions. A set of efficient parameters of the wideband fast multipole method has been identified for IGA boundary element

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

Finite element methods are progressively being utilized to assist in the continuous development of loudspeakers. The core of this paper is the method of lumping certain parts of the finite element model, creating a significant reduction in the model complexity that allows for e.g. faster structural optimization. This is illustrated in the paper with a loudspeaker example where the electromagnetic parts

A combined Finite Element Method with Normal Mode (FEM-NM) is proposed for calculation of the acoustic field radiated by a three-dimensional structural source in shallow water. The FEM is used to calculate the near range acoustic field, then the modes expansion at the vertical and azimuthal direction is performed at a certain coupling range. Hence, the true three-dimensional acoustic field at any range

Surface waves have been extensively studied in earthquake seismology. Surface waves are trapped near an infinitely large surface. The displacements decay exponentially with depth. These waves are also named Rayleigh and Love waves. Surface waves are also used for nondestructive testing of surface defects. Similar waves exist in finite width three-dimensional plates. In this case, displacements are

We consider the problem of imaging extended reflectors in three-dimensional acoustic waveguides using a planar array that is parallel to the waveguide’s cross-section. Our data consist of the multiple-frequency array response matrix. To form an image, we back-propagate a projection of the data on the propagating modes in the waveguide. The projection operator is adequately defined for any array-aperture

Surface waves have been extensively studied in earthquake seismology. Surface waves are trapped near an infinitely large surface. The displacements decay exponentially with depth. These waves are also named Rayleigh and Love waves. Surface waves are also used for nondestructive testing of surface defects. Similar waves exist in finite width three-dimensional plates. In this case, displacements are

A combined Finite Element Method with Normal Mode (FEM-NM) is proposed for calculation of the acoustic field radiated by a three-dimensional structural source in shallow water. The FEM is used to calculate the near range acoustic field, then the modes expansion at the vertical and azimuthal direction is performed at a certain coupling range. Hence, the true three-dimensional acoustic field at any range

Scattering of sound by a target can be described as a wave radiated by virtual point sources inside the target. In the Rayleigh scattering regime, the strength of the virtual sources can be calculated analytically. When a target is located close to the ocean surface or another reflecting boundary, reflections of the incident and single-scattered waves from the boundary lead to multiple scattering from

In this paper, we consider the numerical solution of the time-dependent wave equation in a semi-infinite waveguide. We employ the Double Absorbing Boundary (DAB) method, by introducing two parallel artificial boundaries on the side where waves are outgoing. In contrast to the original implementation of the DAB, where the numerical solution involved either a low-order finite difference scheme or a low-order

A new efficient method for the simulation of sound radiation from large vibrating structures with the Finite Element Method (FEM) is proposed. The acoustic radiation from the major radiating panels is simulated separately for each panel, using customized fluid domains that are weakly coupled to the vibrating structure. Thereby, a significant reduction of the model order is achieved, maintaining at

The Viscous Grain Shearing (VGS) theory predicts the existence of a compressional wave and a shear wave in an unconsolidated marine sediment. Although it is known that, subject to certain constraints, the shear wave satisfies causality, the causal nature of the compressional wave is less well understood. In this paper, the VGS compressional-wave speed and attenuation are examined in three frequency

Conventional finite-difference or pseudo-spectral viscoacoustic modeling methods use uniform, rectangular grids to simulate wave propagation, leading to severe spurious diffractions at the surface topography. To overcome the problem, we mesh the velocity and quality factor (Q) models into curvilinear grids and map the models and the first-order velocity-stress viscoacoustic equation into an auxiliary

The radiated acoustic waves from impact pile driving produce high noise level into the water which may cause damage to marine mammals living close to the offshore construction location. In this paper, a linear, axisymmetric finite element (FE) model is applied to predict pile driving noise in the water. Measurement from bottom-mounted hydrophone deployed at a site 230 m from the source is used to validate

We derive a formula for the gradients of the total scattering cross-section (TSCS) with respect to positions of a set of cylindrical scatterers. The analytic form enhances modeling capability when combined with optimization algorithms and parallel computing. As application of the method, we consider a gradient-based minimization of TSCS for a set of cylindrical obstacles by incrementally repositioning

A method is presented for the closed-form evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such integrals on a plane element, and used to develop a criterion for the selection of quadrature rules. The analytical approach is based on an optimized expansion of

Computational speeds are compared for modern implementations of three parabolic equation approximations. The split-step c0-insensitive model is 3.7 and 5.5 times faster than the finite-difference model OWWE and finite-element model RAM, respectively. Calculations are made between a source and receiver separated horizontally by 1000km at 600m depth near the minimum of sound speed in the deep ocean.

Propagation of Lamb waves in both laminated and functionally graded (FG) composites is analyzed. Anomalous dispersion at high frequencies is observed revealing substantial discrepancy in the high frequencies asymptotes for quasi-flexural and quasi-symmetric fundamental modes. The applied methodology is based on a variant of sextic complex formalism.