Energy conservation and pulse propagation in an elastic medium with quadratic nonlinearity

Abstract

A sinusoidal acoustic tone-burst launched into an elastic medium with weak quadratic nonlinearity is shown to generate a right-triangular static displacement pulse, when conservation of energy is properly imposed on the model equations. The right-triangular displacement profile is shown to occur whether the tone-burst is modeled with displacement-prescribed or traction-prescribed boundary conditions. Definitive experimental evidence is presented confirming the model predictions. Theoretical arguments and experimental evidence are also presented showing that, contrary to the assertion of Qu et al. [J. Acoust. Soc. Am. 131, 1827 (2012)], the right-triangular shape is not in violation of causality.