Nonlinear ultrasonic resonators: a numerical analysis in the time domain

In the framework of the study of nonlinear acoustic phenomena arising in high-power ultrasonic resonators, this paper deals with the numerical prediction of the behaviour of strongly nonlinear waves in resonators. In particular three-dimensional cavities in complex modal configurations are analyzed. The main motivation of this work is the understanding and optimisation of high-power ultrasonic applications in fluids. Based on conservation laws written in Lagrangian coordinates and the isentropic state equation, several evolution equations (one-dimensional, two-dimensional, three-dimensional and axisymmetric) are proposed and numerically solved in the time domain. No restriction on nonlinearity level is imposed. These developments allow the simulation of the time evolution of the pressure distribution inside the cavity, as well as the harmonics distribution. Distortion, nonlinear attenuation and rms pressure can be studied. Periodic (continue) and pulsed signal excitation are possible. Some results referred to complicated nonlinear waves are presented.