Identification of the Orthotropic Elastic Tensor of Composites Using Full Field Lamb Wave Energy Velocities and Dispersion Curves

Abstract

A multi-objective inversion procedure is proposed based on 3D Lamb wave dispersion curves and energy velocity matching to identify the elastic stiffness tensor of orthotropic composite plates. To validate the procedure, finite element model simulations and experimental measurements have been conducted on an aluminum and a composite plate by using piezoelectric actuator broadband signals. Experimentally, the in-plane and out-of-plane velocity components on the surface of these plates were measured using a 3D Infrared Scanning Laser Doppler Vibrometer. By exploiting Fourier Transform, the measured space-time domain data is converted into the frequency-wavenumber domain, from which dispersion curves are extracted. To identify the energy velocity, Short Time Fourier Transform and linear Radon transformation have been applied. Then, image processing is used both for dispersion and energy velocity curves to match the amplitude of the in-plane and out-of-plane velocities on the surface of the plate. The Semi Analytical Finite Element method (SAFE) was selected as the forward model to be embedded in an inversion algorithm due to its accuracy and robustness. Using a multi-objective genetic algorithm, the elastic tensor is calculated by simultaneously minimizing the error between (i) the measured and calculated dispersion curves on one hand, and (ii) the measured and calculated energy velocity slowness curves on the other hand for every in and out of plane velocity measurement. The mean values of the pareto front are selected as optimum parameters. The reconstructed elastic stiffness properties show good agreement with less than 6% average deviation.