Characterization of the full complex-valued stiffness tensor of orthotropic viscoelastic plates using 3D guided wavefield data

A two-stage inversion scheme is proposed to determine the full set of 9 complex-valued stiffness properties of orthotropic viscoelastic plates using their 3D surface velocity response to a broadband vibrational excitation. A combination of the hybrid TLS-ESPRIT and IWC method is employed to the extract complex-valued wavenumber-frequency pairs corresponding to relevant Lamb wave and shear horizontal plate waves from the data from surface velocity response. Particle swarm optimization is chosen to inversely determine the plate's orthotropic viscoelastic properties using the semi-analytical finite element method as a forward model to compute the real and imaginary parts of the wavenumbers. The inversion procedure first identifies the elastic parameters by matching the real wavenumber values, followed by the characterization of the viscoelastic properties which are merely linked to the imaginary wavenumber values. To validate the accuracy of the proposed method, a series of numerical simulations of 3D wavefield data using a finite element model (COMSOL) is conducted, as well as broadband experimental measurements obtained by means of a 3D Infrared Scanning Laser Doppler Vibrometer. It is shown that the inverted orthotropic viscoelastic properties based on the virtual wavefield data are in close agreement with the target values, showing a mean relative error of less than 2% and 5% error on the elastic and viscous properties, respectively. Additionally, the median absolute deviations are negligible, showing the robust convergence of the inversion procedure to a global minimum, and giving confidence to apply the method on experimental wavefield data in order to reveal the full (unknown) C-tensor for material characterization. The proposed characterization method can be used for various orthotropic viscoelastic materials, including metal sheets, carbon/epoxy laminates, and wooden plates.