Transient Vibro-Thermography and Nonlinear Resonant Modes

Abstract

Transient vibro-thermography for nondestructive evaluation and super-resolution imaging of material defects invariably employs nonlinear contact dynamics involving the ultrasonic actuator (horn) and the surface of the target structure. It produces nonlinear resonant modes of vibration in the target structural component. Vibration-induced heat generation is one phenomenon involved here. However, the contribution of nonlinear vibration on the thermal signature is poorly understood. In this study, we consider a metallic component with a thin-walled cavity as a representative sharp feature tuned to the main excitation frequency of the ultrasonic actuator. We have developed a mathematical model to simulate transient thermal signature of structural discontinuity/cavity/defect. The model incorporates a coupled thermo-viscoelastic heat generation process in the bulk material based on the Helmholtz free energy formulation. To capture the source of nonlinear resonant modes, we incorporate the stick-separation contact dynamics due to the ultrasonic horn and the target structural component. Commercial finite element simulation (comsol multiphysics) is used to quantitatively understand the nonlinear vibration response and the thermal transport behavior of the target structure with the cavity. The proposed model accounts for the effects of both the normal and the shear components of deformation contributing on heat generation and captures the nonlinear modal contribution on the heat flux map. The study shows how the geometric feature and material parameters produce an evolution of the nonlinear subsuper harmonics along with the primary harmonics tuned to the excitation frequency. Results obtained from numerical simulations are compared with the experimental results.