Uncertainty Analysis of a Near-Field Acoustic Levitation System

Abstract

Near-field acoustic levitation is a physical phenomenon that occurs when a planar object is placed in the proximity of a vibrating surface. Consequently, a thin layer of ambient gas, commonly referred to as squeeze film, is trapped in the clearance between a vibrating surface and an adjacent planar object performing its levitation. Mathematically, this phenomenon is described by using the Reynolds equation, which is derived from the Navier–Stokes momentum and continuity equations. The equation of motion that represents the dynamic behavior of the levitated object is also considered. However, the performance of the near-field acoustic levitation can be significantly affected by uncertainties on its geometrical parameters and operating conditions. Thus, the present contribution aims to evaluate the influence of uncertain parameters on the resulting levitation force. For this purpose, the differential evolution algorithm is associated with two strategies (inverse reliability analysis and effective mean concept). This multi-objective optimization problem considers the maximization of the levitation force associated with the maximization of both the reliability and robustness coefficients. Numerical simulations demonstrated the sensitivity of each uncertain parameter associated to the obtained levitation forces. As expected, it was verified that the levitation force decreases as the considered reliability and robustness coefficients increases.