Sound Field Design for Transducer Array-Based Acoustic Levitation

Doctoral thesis, 2022

Acoustic levitation is a technique where sound waves are used to hold an object at a designated position, suspending it against other external forces and keeping it stable in the desired position. Transducer arrays are an arrangement of many loudspeaker elements, tuned such that the array creates a sound field that is too complicated for the individual elements to produce on their own. Sound field design refers to the process of prescribing some target criteria for a sound field, describing these criteria mathematically, and apply some method to produce a sound field with these criteria fulfilled.

This thesis is about combining these three concepts. The necessary criteria for levitation to take place are described, using radiation pressure from sound waves in air as the physical mechanism by which the levitation forces are produced. Ultrasonic transducer arrays are modeled using analytical descriptions for the wave propagation, as well as for the predictions of the radiation forces on spherical objects of various sizes. The sound fields required to successfully levitate objects are obtained by numerically optimizing the magnitudes and phases of the elements in the mono-frequent transducer arrays. This is achieved by deriving design criteria from intuitive considerations of the conditions needed for levitation, quantifying these criteria as a
single valued cost function which is minimized with a Quasi-Newton method.

The thesis is focused on two main aspects: how to define a suitable cost function for a single levitation trap, and how to levitate multiple objects via mutual quiet zones. The design criteria for a trap are described using a vector field approach, representing properties of the force field with invariant quantities evaluated at the desired levitation position. These quantifiers are scaled by the characteristic quantities of the system and transformed to a satisficing cost function, which avoids over-optimization by reducing the prioritization of a particular criterion when closer to fulfilled. Multiple objects are levitated by superposing sound fields with mutual quiet zones, i.e. each sound field has a trap for one object and quiet zones where all the other objects will be.