Dispersive Pulse Propagation Parallel to the Interfaces of a Laminated Composite

Abstract

This paper presents a theoretical analysis of the geometric dispersion of transient stress waves in a linearly elastic laminated composite. The loading is a uniform pressure of step-function time-dependence, applied to a half space. The laminates are perpendicular to the half-space boundary. The mathematical treatment is borrowed from the theory of wave propagation in rods. Fourier transforms are applied to time and the coordinate in the propagation direction. Inversion of the spatial transform by residues yields a formal solution in the form of an infinite series of integrals. Each of these integrals is the contribution to the transient response from a mode of sinusoidal wave propagation. Application of the saddle-point technique for long-time asymptotic approximation indicates that the low-frequency portion of the integral from the first mode gives the dominant contribution, called the head-of-the-pulse approximation. The form of the expression for the head-of-the-pulse approximation leads to the definition of a characteristic dispersion time τ. Since τ is a single quantity which describes the dispersion of the wave, it simplifies parametric studies. A closed-form algebraic expression for τ is presented, which has a simple dependence on the propagation distance and spacing of the laminates. Numerical examples for boron-epoxy and glass-epoxy laminates are given.