Nonlinear coupling between radial and axial vibrations during single-axis acoustic levitation in mid-air

Abstract

In this paper, a nonlinear dynamic model of single-axis standing-wave acoustic levitation is studied theoretically and experimentally to explore the effect of nonlinear coupling between radial and axial vibrations. The model makes it possible to predict loss of levitation stability for a levitating spherical particle in response to forced axial vibration via nonlinear coupling. We first present the acoustic radiation force acting on a spherical particle levitated in a three-dimensional standing wave field using the framework of acoustic potential theory. The radiation force is expanded into a power series and truncated at cubic nonlinearities with respect to the small displacements of the sphere motion. In this way, it is possible to account specifically for the nonlinear coupling term in the equation of motion. In order to validate the coupling effect, the asymptotic solutions of the equation of motion with an axial excitation force are derived and compared with experimental measurements. In the validation experiment, a mechanical shaker generates the axial vibration of a polystyrene sphere. We show that, theoretically, the natural radial frequency decreases due to the axial vibration because of nonlinear coupling, eventually leading to dynamic destabilization of the radial equilibrium state. The critical value of the axial vibration amplitude for the radial instability provided by the truncated nonlinear model depends only on the wavelength of the sound and the geometry of the standing wave field. This simple stability criterion predicts well the maximum experimental amplitude at which the levitation fails.