Saddle-Node Bifurcations and Design Parameters for Single-Axis Acoustic Levitators

Abstract

Acoustic levitation (Aclev) is an important tool to noncontact handling of containerless objects. In the recent years, many devices have been successfully developed due to the stable behavior of the Aclev devices. As a result, most of the works on Aclev concentrate on numerical simulations or experimental tests to study the geometry and arrangements of the acoustic emitters, or the influence of various types of perturbations, and most of the mathematical models consider only the acoustic potential. In this work, the nonlinear equation of motion for a levitated particle immersed in a single-axis acoustic field is developed considering dissipative forces. The parameter space is searched for the existence of equilibrium points bifurcations, and a design range for the Aclev device gains is determined from the equilibrium point existence condition, providing hints in order to improve the stability gain margin and, consequently, the robustness to perturbations. In addition, the dynamical behavior of the Aclev device concerning the gains is studied considering also the micro-gravity situation. Numerical simulations corroborate the analytical results.