Showing papers in "Wave Motion in 1987"

TL;DR: In this article, a theory for the propagation of pulses in anisotropic elastic media is described, which provides a convenient method to describe the evolution and change of shape of an ultrasonic pulse as it traverses a piecewise homogeneous solid.

TL;DR: In this article, the authors proposed a differential operator to obtain the continuity of fields at the internal junction of the two materials which cover each face of the wedge, based on a function related to the Maliuzhinets function.

TL;DR: In this article, a plane sound wave is incident upon two semi-infinite rigid plates, lying along y = 0, x > 0 and y = -h, x < 0, respectively, where (x, y) are two-dimensional Cartesian coordinates.

TL;DR: In this article, the behavior at caustics is analyzed for weakly nonlinear wave solutions of hyperbolic equations, and it is shown that short waves, weak enough to be governed by linear or weakly nonsmooth geometrical optics away from caustic, are governed by a linear theory at and near caustices.

TL;DR: In this article, the authors studied the effect of the fourth-order Schrodinger equation on two-dimensional evolution of uniform Stokes waves and found that the narrower instability region and the presence of a higher-order dispersion term tend to delay the trend toward chaos.

TL;DR: In this paper, the propagation of time-harmonic longitudinal waves in a solid containing a periodic distribution of cracks is investigated in a two-dimensional configuration, where cracks are parallel to the x-axis, and their centers are located at positions x=2ml, y=2nd (m, n=0, ± 1, ± 2,…).

TL;DR: In this article, a plane wave incident obliquely onto the open end of a wide parallel-plane waveguide generates an interior field that resembles a geometric optical sheet beam whose initially well-defined shape gets diffused after undergoing multiple reflection.

TL;DR: In this paper, a modification of the null field approach is used to study the scattering of elastic waves by non-planar cracks, where a fictitious surface is added to the crack so that a convenient closed surface is obtained and the surface fields on this closed surface are expanded in vector spherical harmonics.

TL;DR: In this paper, the concept of energy velocity for linear dispersive waves is discussed in the uniaxial case and the identification of energy velocities with the kinematic concept of group velocity is not valid.

TL;DR: In this article, a continuum theory for transient wave propagation in three-dimensional composite materials is given, which provides a set of governing equations for the prediction of dynamic response of elastic composites to impulsive loadings.

TL;DR: In this article, the seismic response of an elastic dipping layer is studied and the excitation is given by a prescribed antiplane motion of the base which is assumed to be rigid.

TL;DR: In this paper, a new numerical method for calculating the properties of waves on surfaces of inhomogeneous elastic materials of any anisotropy is presented. But the method uses the wave equation with the elastic moduli and mass density assumed to be functions of position and the displacement field is expanded in a series of Laguerre functions.

TL;DR: In this article, the interplay between ray fields and mode fields, on the excitation mechanism of each, and on their properties when the field incidence angle is strongly oblique, was studied.

TL;DR: In this paper, it was shown explicitly that the matrix B, which plays a central role in surface wave existence theory, is positive definite at zero velocity, and that B is a positive definite matrix.

TL;DR: In this article, four two-dimensional configurations are considered for diffraction and corner reflection of an ultrasonic displacement pulse, and the results are presented as full-field snapshots of the displacement fields at specified times, and as time histories of the particle velocity at the midpoint of the transducer-specimen interface at x =− H, y = H.

TL;DR: In this paper, a system of two KdV equations coupled by small linear dispersive terms is considered, which describes the resonant interaction of two transverse gravity internal wave modes in a shallow stratified liquid.

TL;DR: In this paper, the authors studied the two-dimensional, steady-state problem of the scattering of waves in a homogeneous, isotropic, linear-elastic wedge where the wedge angel is less than 180°.

TL;DR: In this article, a simple model of this variation is used to determine the reflection and transmission coefficients for a vertical plane barrier of finite depth, where the incident plane wave has its crests parallel to the plate and the fluid is of infinite depth.

TL;DR: In this article, a parametric inverse based on the asymptotic series is discussed, with attention given to the effects of additive noise, and the classic Mie series and the approximation to the reflection are used.

TL;DR: In this article, an analogue of the mild-slope equation is obtained for small-amplitude water waves propagating across a shearing current, which is shown to conserve wave action flux.

TL;DR: In this article, Tiersten's perturbation boundary conditions are generalized to the case of a piezoelectric substrate with a sinusoidally corrugated surface.

TL;DR: In this article, the modified Burgers equation governs the propagation of a weakly nonlinear slow magnetoacoustic wave near the equilibrium state with zero transverse magnetic field, and the reductive perturbation method is used to show that this is the case.

TL;DR: Several concepts familiar to the literature of quantum mechanics are discussed in the context of the more general one-way wave theories encountered in ocean acoustics and seismology as mentioned in this paper, where the authors discuss the following:

TL;DR: In this paper, the transient motion of a dislocation starting from rest and moving in an arbitrary rectilinear motion in an anisotropic solid is analyzed by transform techniques and inversion according to the Cagniard-de Hoop technique.

TL;DR: In this article, the Christoffel equations for electroacoustic waves in unbounded piezoelectric crystals are solved in the limits of weak and strong electromechanical coupling and for the case where the unstiffened elastic constants satisfy the conditions of elastic isotropy.

TL;DR: In this paper, the problem of wave generation in a deep, long channel by an oscillating pressure patch is analyzed, and a modified dispersion relationship, which incorporates a phase shift in the wave frequency is presented.

TL;DR: In this paper, the Sturm-Liouville problem is reduced to the matrix potentials of the normal (progressive) modes and attenuated standing waves, which are then used to determine the elastic parameters and the density.

TL;DR: In this paper, the Infeld-Rowlands method was used to derive a linear dispersion relation expressed as a cubic equation in gw1 for generalized Kortewegde Vries ((ut+α1umux+α2unux+uxxx)x+α3uyy = 0) waves with respect to 2D longitudinal disturbances.

TL;DR: In this article, the authors deal with the third-order resonant interaction between a quartet of linearly damped waves, one of which is continuously forced, and show that the system has only one steady state that consist of only the forced wave.