Journal of Computational Acoustics

In this review paper, the use of the Time Reversal (TR) method as a computational tool for solving some classes of inverse problems is surveyed. The basics of computational TR are explained, using the scalar wave equation as a simple model. The application of TR to various problems in acoustics and elastodynamics is reviewed, in a selective and biased way as it leans on the author's personal view, referring to representative articles published on the subject.

An acoustic wave equation for pressure accounting for viscoelastic attenuation is derived from viscoelastic equations of motion. It is assumed that the relaxation moduli are completely monotonic (CM). The acoustic equation differs significantly from the equations proposed by Szabo (1994) and in several other papers. Integral representations of dispersion and attenuation are derived. General properties and asymptotic behavior of attenuation and dispersion in the low and high-frequency range are studied. The results are compatible with experiments. The relation between the asymptotic properties of attenuation and wavefront singularities is examined. The theory is applied to some classes of viscoelastic models and to the quasi-linear attenuation reported in seismology.

A model for nonlinear sound wave propagation for the trumpet is proposed. Experiments have been carried out to measure the sound pressure waveforms of the and notes played forte. We use these pressure measurements at the mouthpiece as an input for the proposed model. The compressible Euler equations are used to incorporate nonlinear wave propagation and compressibility effects. The equations of motion are solved using the discontinuous Galerkin method (DGM) and the suitability of this method is assessed. The third spatial dimension is neglected and the consequences for such an assumption are examined. The numerical experiments demonstrate the validity of this approach. We obtain a good match between experimental and numerical data after the dimensionality of the problem is taken into account.

We propose a new method for calculating dispersion spectra of shear waves in the two-dimensional free phononic plates made of solid matrix with periodically distributed inclusions and in the waveguides composed of a phononic layer between two periodic substrates. The method proceeds from the propagator M which involves exact integration in the depth coordinate. Because the components of M can be very large, the dispersion equation for a free plate is recast in terms of the resolvent of propagator R = (αI - M)^-1 (α is a constant) which is numerically stable. The resolvent is the central object of the method. Another key tool, which comes into play in the case of a waveguide, is a projector P expressed as a contour integral of the resolvent of the substrate. The projector allows to extract the "physical" modes decreasing into the depth of the substrates without solving the wave equation. The resulting dispersion equation for a waveguide defined via the projectors for the substrates and the resolvent for the enclosed layer is numerically stable. We provide several options for the calculation of the resolvent and projector. Besides, special attention is given to derivation of the dispersion equations for the uncoupled symmetric and antisymmetric dispersion branches in the case of mirror-symmetric structures.