Application of nonlinear ultrasonic waves to characterize hysteretic materials

This study investigates the mechanics and mathematical fundamentals of the propagation of ultrasonic waves in nonlinear (hysteretic in this example) media. The resulting mathematical models, that are hyperbolic systems of conservation laws, are solved numerically. A variety of numerical methods such as Gudonov Schemes, Flux Limiter Schemes, and the Central Scheme approach (each based on the conservation property) are used to solve these hyperbolic systems. The numerical results are interpreted using signal-processing tools such as the Fast Fourier Transformation (FFT) in order to analyze and physically interpret any nonlinear effects. For example, higher harmonics are excited, and their location and amplitude are used to infer material properties. Furthermore, the development of shock and rarefaction waves (both purely nonlinear dynamical effects) are studied.