Nonlinear Ultrasonic Waves for Structural Health Monitoring

Nonlinear ultrasonic waves in solids have shown good sensitivity to quasi-static stresses. The stress sensitivity of elastic waves is typically associated to finite strains (e.g. theory of acoustoelasticity). In the case of waveguides, classical nonlinear theories for guided waves are still based on the assumption of finite strains. In the case of constrained solids subjected to thermal excursions, however, there are theoretically no finite strains (for perfectly-constrained solids) associated with thermal stresses. A new model is therefore needed to justify the existence of wave nonlinearities in this case of stress without strain. This problem is solved on the basis of the interatomic potential of the solid that indicates a “residual” strain energy, due to the prevented thermal expansion, that is at least cubic as a function of strain. The cubic relationship between strain energy and strain produces second-harmonic generation of propagating elastic waves. Consequently, a nonlinear wave equation can be derived. The solution to this equation leads to a new nonlinear parameter for double harmonic generation that is directly related to the thermal stresses in the structure. The present study finds applications in the monitoring of thermal stresses in buckling-prone structures, such as continuously-welded railroad tracks and pipelines.