In this case, the wave pattern after the cumulation of the reflected wave at the symmetry axis is the most complicated since the wave interacts with the set of transverse waves
which were formed in the conic expansion part (see Figures 3(d) and 3(e)).
At first, the propagation velocity of longitudinal [C.sub.L] and transverse waves
([C.sub.T]) was determined--Figure 8.
Original waveforms and basic characteristic information of the microseismic wave case, for example, the arrival time of the longitudinal wave (P wave), the arrival time of the transverse wave
(S wave) and the peakparticle velocity (PPV), are shown in Figure 4.
The [u.sup.v] displacement wave equations can be expressed as a longitudinal wave equation for the dilatation [epsilon] and a transverse wave
equation for the rotation tensor [[omega].sup.[mu]v] .
On the other hand, when the propagating elastic wave is an ultrasonic transverse wave
, the deformation in the elastic medium can be defined as u = 0, v = v(x, t), and w = 0.
The fact that plasmas and a Slinky[R] suspended from a ceiling by an array of strings are both systems where their respective wave characteristic equations have been modified to include a linear restoring force, explains the analogy found between the dispersion relation for transverse electromagnetic radiation in the former one and the dispersion relation for transverse waves
in the latter one (Crawford, 1968).
Propagation of transverse waves
in elastic micropolar porous semispaces is discussed by Hsia et al.
For orthotropic materials such as wood, where mechanical properties in the perpendicular directions are unique and independent, the speed of longitudinal and transverse waves
in each of the principal axes depends on the density, the direction of propagation, and elastic constants .
The following dimensionless variables and constants are introduced: x = [x.sub.1]/1, y = [y.sub.1]/1, [x.sub.0] = h/1, [[kappa].sup.2] = [c.sub.1]/[c.sub.2] = ([lambda] + 2[mu])/[mu], [tau] = [c.sub.1]t/1 where [c.sub.1] and [c.sub.2] are the phase velocities of longitudinal and transverse waves
for considered material of the plate, [lambda] and [mu] are elastic moduli (Lame constants).
The problem of wave propagation in a rotating random infinite magnetothermoviscoelastic medium was studied and a coupled dispersion relation for longitudinal and transverse waves
was deduced to determine the effect of viscoelasticity, relaxation times, and rotation on the phase velocity of the coupled waves .
Since the wave speed of the transverse waves
in the front plate is much smaller than the longitudinal wave speed, the shear wave arrives at the specimen plane at approximately 1 ps after the arrival of the loading compressive pulse at the specimen plane.
where [a.bar] is waves coupling coefficient, which indicates the proportion mixes E and H type waves in hybrid modes; [[A.bar].sub.1], [[B.bar].sub.1]--unknown amplitude coefficients; [J.sub.m]([[k.bar].sup.g.sub.[perpendicular to].sub.1,2]r) is the Bessel cylindrical function of the first kind m-th order; [[k.bar].sup.g.sub.[perpendicular to].sub.1,2]r - first and second internal transverse waves
numbers normalized to radius r; m = 0, 1, 2, ...