Axial nonlinear field of a vibrating circular transducer

The on-axis cumulative growth of nonlinear effects resulting from a monochromatic excitation of a circular source mounted in an infinite rigid baffle is analyzed by perturbation analysis. The first order (linear) signal is the summation of two propagating planar waves: one emanating from the center of the source and the other originating from the source boundary. The mutual nonlinear interaction and propagation of these two waves are analyzed on the basis of the nonlinear wave equation governing the velocity potential. Nonuniform validity of the pressure expression is corrected by the method of renormalization and thereby obtaining uniformly accurate expression in the near as well as far fields. Asymptotic trends at long range are derived which resulted in a Fourier series description for the pressure signal. The results yield a computationally efficient model that can predict the spectral components as well as the temporal waveform. The predicted results are compared favorably with experimental observations over a wide range of variable parameters.