To understand the propagation of acoustic wave fields in heterogeneous media, it is important to have knowledge about the underlying physical mechanisms of these fields. During this course, the acoustic field equations (equation of motion and equation of deformation) will be derived, and it will be shown how the acoustic field is described via a pressure and a velocity wave field. Next, linearized versions of the field equations are used to derive a wave equation for linear acoustics. A similar approach is used to show how the Westerveld equation used for non-linear acoustics may be obtained. Next, different solution methods for modelling acoustic wave fields in heterogeneous media will be explained, as well as the concepts behind Kirchhoff Integrals, Rayleigh I and II, and evanescent waves. Finally, the ideas behind imaging and (non-linear) inversion for quantitative imaging are explained.
Today’s precision piezoelectric acoustic wave devices require many common features such as high Q, low power, small size, and stringent requirements on frequency stability, temperature stability, and force sensitivity. Since the devices are employed as elements of frequency standards and detection, their frequency performances have to be maintained by precision designs, manufacturing, and operations. Consequently, the analysis and design of these piezoelectric devices would need 2-D or 3-D models that are accurate in terms of the resonator geometry, mountings and material properties. Furthermore, we would also need models for nonlinear analysis that include effects such as (1) temperature sensitivity, (2) applied forces from environmental vibrations, (3) harmonic generation, and (4) intermodulation. These models are useful for design and analysis of acoustic resonators because we have been successful in extracting their electrical circuit parameters and identifying the major factors impacting their precision frequency performances.
The course will first focus on the primary aspects of accurate linear finite element modeling, such as the frequency spectra and quality factor Q as functions of resonator geometry and mountings. Comparisons of model results with the relevant experimental results are presented. Next the nonlinear finite element modeling of these devices are discussed. Both linear and nonlinear material properties and deformations are taken into account. The linear and nonlinear material constants for common piezoelectric materials are discussed and presented. The nonlinear behavior of quartz resonators such as their frequency-temperature behavior, force-frequency effects, and nonlinear resonance including the Duffing effect will be presented. If time permits, nonlinear frequency response modelling for force frequency effects, harmonic generation and intermodulation of BAW and SAW resonators will be presented and compared to experimental results.
Acoustic tweezers are devices that use configurable ultrasonic acoustic fields to trap and then manoeuvre small objects. In order to develop devices and strategies for dexterous manipulation in these devices we must understand: the underlying physics that produces the acoustic radiation force, the acoustic fields that cause trapping and how these fields can be generated in practice.
In this course the physical principles that lead to Gor’kov equation (which determines the forces on objects much smaller than the acoustic field’s wavelength) will be described and the equation derived. Alternative scattering regimes, for larger objects will also be considered using ray acoustics. The various methods and devices that have been designed to dexterously manipulate microparticles will be reviewed.
Acoustic tweezers have been successfully designed for operation in liquid (typically water) and air. This course will identify the particular requirements and challenges in each regime. Including: design of transducers, safety considerations, dynamics of particles in the medium and appropriate control methods. Examples of recent applications will be discussed in context of the described theory and methods.
The organizers gratefully acknowledge the generous support provided by the following