A cylindrical expansion of the audio sound for a steerable parametric array loudspeaker

Abstract

In this work, a cylindrical expansion for the audio sound generated by a steerable baffled parametric array loudspeaker (PAL) based on the phased array technique is derived from the Westervelt equation. The expansion is a series of twofold summations with uncoupled angular and radial components in the cylindrical coordinate system. The angular component is determined by the trigonometric functions, and the radial component is an integral containing the Bessel functions and an arbitrary excitation velocity profile. The numerical results for a typical steerable PAL are presented and compared to those obtained using the convolution model. It is found that the prediction of the audio sound using the proposed cylindrical expansion improves the agreement with the experimental results when compared to the existing models. This is because no further approximations are required in the cylindrical expansion of the quasilinear solution of the Westervelt equation, whereas the complex near field nonlinear interactions between the ultrasonic waves cannot be correctly captured in a convolution model. The proposed cylindrical expansion does, therefore, provide an alternative approach to modeling a phased array PAL and high accuracy with a relatively low computational cost.

Extended convolution model for computing the far-field directivity of an amplitude-modulated parametric loudspeaker

“…On the other hand, the convolution model may not capture the complex near field nonlinear interactions between the ultrasonic waves [24]. Therefore, a cylindrical expansion for the ultrasound was introduced when the radiating surface of the ultrasonic emitter was modeled as a baffled phased ultrasonic source [25]. The resultant directivity model improves the accuracy of the convolution model but increases the computation complexity greatly.…”