One-Dimensional Pulse Propagation in an Obliquely Laminated Half Space

Abstract

A solution is presented for the response of a periodically laminated half space to a suddenly applied surface pressure. The lamination angle is arbitrary. Dispersion due to the structure of the composite is included by using a continuum theory that approximately models such behavior. The predominant long-time far-field solution is obtained using the head-of-the-pulse technique. This solution is contrasted with the first-order approximation obtained when the composite is represented by an equivalent homogeneous anisotropic elastic medium. Both theories yield a response to the step load consisting of two pulses, each traveling with a separate velocity. For the anisotropic elasticity theory, the pulses are simple steps, while for the dispersive theory, oscillations are superposed on the steps. The character of these oscillations is highly dependent on the lamination angle and other properties of the composite, particularly for the slower pulse. Representative numerical examples are presented.