Transient Wave Propagation Problems Research Articles

In-Plane and Shear-Bending Impact of Laminated Composite Plates

The accuracy of the lamination theory in transient wave propagation problems was studied. In-plane and shear-bending impact experiments were conducted with graphite epoxy angle-ply and cross-ply plates. The measured strain histories of these plates were compared with the theoretical predictions of the lamination theory. The results show that, under the given loading conditions, the lamination theory adequately predicts wave velocities and strains in symmetric angle-ply and cross-ply graphite epoxy plates.

Shear waves in an elastic wedge

An elastic wedge of interior angle χπ is subjected to spatially uniform but time-dependent shear tractions, which are applied to one or both faces of the wedge, parallel to the line of intersection of the faces. The transient wave propagation problem is solved by taking advantage of the dynamic similarity which characterizes problems without a fundamental length in the geometry. The shear stress τθz is evaluated, and it is found that the singularity near the vertex of the wedge is of the form r(1/χ)−1/(1 − χ). The results show that the stress is not singular for interior angles less than π. As a special case we obtain the dynamic shear stress generated by the sudden opening of a semi-infinite crack in a homogeneously sheared unbounded medium.

Transient Shear Waves in Two Joined Elastic Quarter Spaces

A half space composed of two joined elastic quarter spaces of different material properties is subjected to time-varying shear tractions, which are applied parallel to the plane of juncture. The method of homogeneous solutions is used to solve the transient wave-propagation problem for the case that the surface tractions vary in time as Dirac delta functions. For surface tractions varying in time as Heaviside step functions, Duhamel superposition is employed to derive closed-form expressions for the shear stress in the plane of juncture. The interface shear stress shows a logarithmic singularity at the free surface.

Elastic Wave Propagation in Rods of Arbitrary Cross Section

A study is made of the problem of transient elastic wave propagation when a load is applied to one end of an infinitely long rod of arbitrary cross section. Fourier and Laplace transforms aid in developing a general solution in the form of a sum over all modes of harmonic wave propagation and integrals over all wavelengths. An expansion at long wavelength reveals two types of modes of propagation which are called longitudinal and radial shear modes. For a suddenly applied pressure, the long-distance, long-time response is found to be an integral of the Airy integral.

A STUDY OF TWO‐DIMENSIONAL HEAD WAVES IN FLUID AND SOLID SYSTEMS

The problem of transient wave propagation in a three‐layered, fluid or solid half‐plane is investigated with the point of view of determining the effect of refracting bed thickness on the character of the two‐dimensional head wave. The “ray‐theory” technique is used to obtain exact expressions for the vertical displacement at the surface caused by an impulsive line load. The impulsive solutions are convolved with a time function having the shape of one cycle of a sinusoid. The multiple reflections in the refracting bed are found to affect the head wave significantly. For thin refracting beds in the fluid half‐space the character of the head wave can be completely altered by the strong multiple reflections. In the solid half‐space the weaker multiple reflections affect both the rate of decay of the amplitude of the head wave with distance and the apparent velocity of the head wave by changing its shape. A comparison is made of the results for the solid half‐space with previously published results of model experiments.