Journal of Computational Acoustics

Applications of high-amplitude acoustic or ultrasonic waves in industrial processing require a good knowledge of the nonlinear pressure field, as well as the heat produced by the wave. In this article a new time-domain algorithm solving a second-order nonlinear wave equation written in Lagrangian coordinates and valid for any fluid is presented. The new model is compared with two others which were previously developed, corresponding to the two other possible physical approaches. This paper discusses the limits of application of every approach and the suitability of every one to model nonlinear acoustic waves in resonators. Conclusions about the applicability of the physical models are given. The time-domain character of the models allows the development of a new algorithm to calculate the temperature evolution inside a resonator due to acoustic losses. This algorithm is presented here and applied to strongly nonlinear waves for which the nonlinear attenuation is dominant. Several kinds of time functions for excitation can be considered in the models. The strongly nonlinear resonator response to a short pulsed signal is analyzed to show the efficiency of the time-domain numerical model.

In this paper, we proposed a unified formulation to explain the reason why spurious eigensolution occurs in the eigenproblem of interior acoustics using the real-part and imaginary-part BEMs and why fictitious frequency occurs in exterior acoustics using the complex-valued BEM. Both the two problems stem from the rank deficiency of the influence matrix. Based on the circulant properties and degenerate kernels, an analytical study in a discrete system for a circular cavity is conducted. The Fredholm alternative theorem is employed to study the rank-deficiency problems in conjunction with singular value decomposition updating technique. The spurious and fictitious boundary modes are found to locate in the column vectors of left unitary matrix. Also, the effects of different types of boundary condition on the spurious and fictitious solutions using direct and indirect methods are discussed. The mathematical and physical meanings for the nontrivial boundary solution in spurious eigensolution and fictitious frequency are explained. Numerical experiments are found to agree with the analytical predictions.

In this paper we investigate the unknown body problem in a waveguide. The Rayleigh conjecture states that every point on an illuminated body radiates sound from that point as if the point lies on its tangent sphere. This conjecture is the cornerstone of the intersecting canonical body approximation ICBA for solving the unknown body inverse problem. Therefore, the use of the ICBA requires that an analytical solution be known exterior to the sphere in the waveguide, which leads us to analytically compute the exterior solution for a sphere between two parallel plates. A least-squares matching of theoretical acoustic fields against the measured, scattered field permits a reconstruction of the unknown object.

In many applications, and in particular in seismology, realistic propagation media disperse and attenuate waves. This dissipative behavior can be taken into account by using a viscoacoustic propagation model, which incorporates a complex and frequency-dependent viscoacoustic modulus in the constitutive relation. The main difficulty then lies in finding an efficient way to discretize the constitutive equation as it becomes a convolution integral in the time domain. To overcome this difficulty the usual approach consists in approximating the viscoacoustic modulus by a low-order rational function of frequency. We use here such an approximation and show how it can be incorporated in the velocity-pressure formulation for viscoacoustic waves. This formulation is coupled with the fictitious domain method which permits us to model efficiently diffraction by objects of complicated geometry and with the Perfectly Matched Layer Model which allows us to model wave propagation in unbounded domains. The space discretization of the problem is based on a mixed finite element method and for the discretization in time a 2nd order centered finite difference scheme is employed. Several numerical examples illustrate the efficiency of the method.

This paper examines a two-dimensional deep-water waveguide in a range-dependent medium. Solutions of the homogeneous Helmholtz equation concentrated near the waveguide axis and which decrease exponentially outside a strip containing the axis are constructed. These solutions have the form of exponentials multiplied by parabolic cylinder functions whose arguments are an infinite series in powers of ω^-1/2, where ω is a cyclic frequency. Coefficients of these series are found from a recurrent system of differential equations up to terms allowing to get a residual (difference between the left-hand side of the Helmholtz equation and zero) of order ω^-1/2. Arbitrary constants of general solutions of arising differential equations are calculated going over to the limiting case of a range-independent medium. Numerical simulations are carried out for a deterministic model of a range-dependent ocean, where the range-dependence results for change in geographic location. Parameters of this medium model are matched with the AET experiment.

Experiments from several shallow-water areas are summarized. Coherent sound transmission results, particularly wavenumber spectra, are compared to range-dependent calculations that use oceanographic and geophysical characteristics from measurements and archives as bounded inputs to the propagation codes. In general excellent agreement was obtained between the measured and calculated results for both narrowband and broadband transmissions between 50 Hz and 1 kHz to ranges of 40 km. A relative signal gain (RSG) method for the estimation of horizontal coherence length was applied to measured RSG results and yielded coherence lengths on the order of 30λ at 400 Hz at distances of 40 km. Perturbation theory was applied to the shallow-water waveguide under the condition of adiabatic normal modes and expressions were derived for the phase structure function that was simplified by the use of Gaussian correlation functions. These analytical results, along with estimates of the variances of the environmental variables permitted the estimation of the coherence function and the RSG. The calculated coherence function and RSG were found to be consistent with measured RSG and replica correlation results. The fluctuations in the oceanic water volume were found to be the dominant factor in the loss of coherence.