Transient Waves from Acoustic Emission Sources in Isotropic Plates Using a Higher Order Extensional and Bending Theory.

Abstract

This dissertation presents a derivation for the transient wave response of an infinite isotropic plate to a general acoustic emission (AE) point source discontinuity loading, based on third-order plate theory. The calculation of the wave response is facilitated by employing the concept of a seismic moment tensor (or derived “equivalent†body-forces) to describe the loading from highly localized displacement discontinuities on a fracture surface. Further, the body forces from 3-D elasticity are converted to plate loadings for use in the plate theory wave equations of motion. The transient wave response can be detected as AE signals using piezoelectric sensors. In particular, time-dependent surface strains can be readily obtained experimentally. Therefore the results emphasize the calculation of the surface strains for potential comparison with future experiments. The calculated transient response, which represents waves propagating from a general AE point source in the plate, is expressed in an explicit integral form. It is shown that the transient response, which is given by double inverse Fourier transforms, can be simplified into a finite series involving inverse Hankel transforms which only require one-dimensional inversions for an isotropic plate. Thus numerical evaluation of the transient wave is more robust and accurate than that generated using two-dimensional inverse transforms and also, asymptotic solutions can be readily obtained. Nine types of AE sources representing different micro-damage mechanisms and their corresponding plate loads are discussed. Numerical results for four types of AE point sources with a Heaviside time history loading are presented. The long-term goal of the development, having established a relationship between disturbance and response, is to monitor responses in a structure and be able to determine the source, i.e. damage, type and location by solving the inverse problem in real time. What is new and different from previous work upon which this is building is that the extensional formulation is evaluated for general AE loading, and a higher order bending theory is developed and evaluated. Additionally, the polar conversion reduction to a single variable spatial integration is implemented for both theories.