Analysis of transient Lamb waves generated by dynamic surface sources in thin composite plates

TLDR: In this paper, a theoretical analysis is carried out in an effort to understand certain unusual properties of transient guided waves produced in a thin unidirectional graphite/epoxy composite plate by a localized dynamic surface load.

Abstract: A theoretical analysis is carried out in an effort to understand certain unusual properties of transient guided waves produced in a thin unidirectional graphite/epoxy composite plate by a localized dynamic surface load. The surface motion is calculated using an approximate plate theory, called the shear deformation plate theory (SDPT), as well as a recently developed finite element analysis (FEA), for their mutual verification. The results obtained by the two methods are shown to have excellent agreement. An interesting, nearly periodic "phase reversal" of the signal with propagation distance is observed for each propagation direction relative to the fiber direction. For clarification, a closed form analytical expression for the vertical surface displacement in an aluminum plate to an impulsive point force is obtained using the steepest descent method. It is found that the strong dispersion of the first antisymmetric waves at low frequencies is the main reason behind the phase reversal. This is verified further by measuring the surface response of a relatively thick aluminum plate to a pencil lead break source. The understanding developed in the paper is expected to

Figures

FIG. 6. Time history of vertical surface displacement in a 1-mm-thick unidirectional graphite/epoxy composite plate under uniformly distributed load on a circle of 2.5-mm radius, for propagation along 0°~SDPT!.

FIG. 7. Time history of vertical surface displacement in a 1-mm-thick aluminum plate subjected to~a! a point load and~b! a uniformly distributed load on a 2.5-mm radius~SDPT!.

FIG. 8. Time history of vertical surface displacement in a 3.1-mm-th aluminum plate to a pencil lead break source.

FIG. 3. Time history of vertical surface displacement a 1-mm-thick unidirectional graphite/epoxy composi plate subjected to a point load from SDPT~first row! and FEM~second row!.

FIG. 2. Time history and spectrum of the source arbitrary units.

FIG. 4. Dispersion curves for unidirectional graphite/epoxy composite p of 1-mm thickness for different propagation direction wrt the fibers cal lated from SDPT.