Optimized excitation sources and exact solutions for ultrasonic field propagation in a nonlinear medium with hysteretic behavior

Ultrasonic wave propagation in a microhomogeneous material with hysteretic strain-stress behavior was studied by the application of a Lie group algebraic method in order to find optimized excitation sources. Starting from previously published work (V. Gusev, J. Acoust. Soc. Am., vol.107, no.6, p.3047-3058, 2000), the particle velocity of an ultrasonic wave propagating in the nonlinear medium is described, avoiding the absolute term. This algebraic method provides a class of exact solutions for particle velocity in a nonlinear medium.