Numerical modeling of laser acoustic waves using finite element method and fast integral wavelet transform

The objective of this dissertation is to use the generalized theory of thermoelasticity to model laser-induced ultrasound. The need for establishing functional correlation between laser input parameters, material properties, and ultrasonic displacements motivated this work. By incorporating an analytical description of a laser heat source which exhibits the spatial as well as temporal characteristics of the laser pulse, comprehensive modeling of laser ultrasonic displacement histories is obtained using the dynamic finite element method. Validation of the model is performed through comparing the temporal and spectral characteristics of analytical waveforms to experimentally acquired signals. An integral wavelet transform algorithm using the compactly supported semi-orthogonal linear spline wavelet is applied to examine the spectral attributes of both numerical and experimental waveforms in the time-frequency domain. This dissertation shows the capabilities of the proposed modeling approach and demonstrates the proficiency of applying the wavelet transform to process complex NDE signals.;A generalized characteristic equation applicable to both classical and generalized theories of thermoelasticity is derived to investigate the feasibility and applicability of thermoelastic theories in describing thermo-mechanical wave propagation. As a result, the theory suitable for modeling laser-induced mechanical responses is identified. The effects of relaxation time constants on wave dispersion characteristics are also investigated.;Studies of surface waves generated with four different laser spot sizes and three levels of laser energy inputs in plates of various thicknesses show good agreement between finite element and experimental waveforms. The capability of the model to predict laser ultrasound associated with both dispersive and non-dispersive waves is demonstrated. Inconsistencies between numerical and experimental waveforms are noticed and explanations of probable causes are given. It is shown that ultrasonic waveforms are strong functions of laser energy density and changes in plate thickness and that there is an energy density threshold below which certain modes cannot be initiated. Finally, it is pointed out that this modeling approach can be easily extended to include anisotropic materials and layered composites.