High order approximate solution of nonlinear acoustic equation:development and validation

For the nonlinear acoustic wave equation,the commonly used second harmonic solution is not accurate enough,which causes a big error in measuring the material nonlinearity.Using perturbation method,nonlinear acoustic wave equation can be expanded into a series of inhomogeneous partial differential equations.The special solution forms of the high harmonics are formulated according to the properties of the low harmonic solutions.Then the high-order harmonic solutions are obtained with symbol calculation tool.Thus the high order approximate solution of the second harmonic can be achieved by summing up all of the second harmonic solutions.To verify the high order approximate solution,nonlinear acoustic experiments are carried out in water.The results show that the relative amplitude of the second harmonic increases firstly and then decreases with the propagation distance and the excited primary amplitude.The high order approximate solution can make up for the theory deficiency of the second harmonic perturbation solution,can broaden experimental range in measuring the material nonlinearity and can improve the accuracy of the measured nonlinearity by making full use of the experimental data.