Numerical Evaluation of a Band-Limited Green’s Function Using the Finite Element Method for Acoustic Emission Analysis

Abstract

The ability to model transient wave propagation in solids and determine the Green’s function plays a major role in improving the reliability of quantitative source characterization of acoustic emission. In this work, the finite element method is employed to determine a numerical solution of the Green’s function of an isotropic plate due to a point source applied normally to the surface. The advantage of using the finite element method is that it can be extended to model realistic geometries that cannot be treated analytically. The numerical results presented here are based on a two-dimensional axisymmetric transient finite element analysis. A limited bandwidth approximation of a delta function is used (Hanning function) for modeling the source. Hence the solution is called the band-limited Green’s function. The exact analytical solutions of the Green’s function of an isotropic infinite plate are used to validate the numerical solutions. Further analysis is carried out to investigate the effects of varying the spatial resolution of the finite element model on the accuracy of the solutions. Finally, it is demonstrated how the results of the band-limited Green’s function can be used to accurately convolve the response of an arbitrary source function.