Titolo della tesi: Wave body non-linear interaction and radiation pressure in acoustics
The aim of the research is to investigate the effect of the radiation pressure phenomenon on light-weight bodies and controlling their movement in space. The application of this novel technology could support several interesting applications, including contact-less actuators, contact less manipulators, powering micro-vehicles that lack their own on-board motors, and acoustic recharging power for batteries of wireless devices.
The actuation mechanism, specifically the non-linear acoustic field, is clarified and theoretically described. The conventional linear acoustic theory is insufficient in this context. In the linear regime, only small oscillations of the body under the influence of an impinging wave are expected, without any potential for producing long stroke motion. Non-linear effects are essential to generate a drift motion of the body, namely the net effect of radiation pressure. To this end, a very general and rigorous formulation of the acoustic problem based on Hamilton’s principle has been developed. The resulting equations are highly non-linear, and numerical finite difference simulations of such an acoustic field interacting with a moving body present considerable challenges. The nature of radiation pressure has been examined to clarify its nature. The historical debate between tensorial and scalar form is analyzed in detail, providing an additional contribution in terms of clarity regarding the various hypotheses presented historically. This exploration emphasizes the distinctions and implications of each perspective, enhancing understanding of the foundational principles. The analysis aims to clarify misconceptions and consolidate knowledge surrounding these concepts, contributing to ongoing discussions in the field.
On the other hand, based on the mechanism of wave-body interaction supported by Hamilton’s principle, the radiation force phenomenon is treated as an "actuator" that connects electronically controlled loudspeaker acoustic emissions with the net force acting on the body. In this context, the objective is to move a light-weight body along a specified trajectory in one-dimensional space by varying the pressure level emitted by a piston using non-linear control theory. Achieving real-time control necessitates establishing a relationship through a semi-analytical method capable of providing instantaneous values for the radiation pressure on the body. For this purpose, a perturbative approach was employed to find an approximate solution to the problem with second-order accuracy.
Initially, the case of a rigid body was analyzed; subsequently, a body represented by an impedance was studied in detail. Once the physical model was established, it became possible to implement a predictive control strategy that modifies amplitude and frequency parameters to consistently achieve optimal force required for guiding the object along a defined trajectory.
To compare the semi-analytical results with the exact expressions, a finite difference (FD) scheme was implemented using one of the most robust methods for compressible flows, the Rusanov method. This method proved to be decisive in conducting a validation and comparison campaign among the results obtained for different cases. This treatment is unique because, in addition to deriving and formalizing a new method to find the expression of radiation pressure on a perfect reflective body, a numerical validation was first conducted, comparing results with formulas present in the literature (including models by Rayleigh, King, Westervelt, Beyer, and Hasegawa). Following this, an engineering application was developed based on these concepts, implementing a controller capable of moving a small object at will under the influence of the acoustic wave.