Ultrasonic cavitation is a well-known phenomenon that plays an important role in several physical systems and its applications are commonly utilized in different fields of physics and technology. The cavitation phenomena can be described by means of a field theory that should be able to predict the values of the macroscopic quantities, introducing physical parameters specifically for the bubbly liquid to be considered as a continuum; while on the other hand, the goal is to solve the problem of single bubble dynamics in an ultrasonic field as a starting point towards a multibubble theory. Usually the theory of single bubble dynamics in ultrasonic cavitation is constructed by primarily imposing the conditions of spherical symmetry on the bubble interface and a viscoelastic liquid, thus obtaining a significant simplification of the equations of motion and a single nonlinear equation for the interface. This approach can be satisfactory in several cases, but the situations in which the bubble deviates from its spherical shape (i.e. the collapse on a rigid boundary) and the problem of the stability of the interface motion, which turns out to be very important in sonoluminescence, cannot be treated by this theory. In the field of ultrasonic cavitation numerical analysis is a further means of investigation besides the analytical approach and experimental measurements, and it is necessary at least for two reasons. Specifically, an exact analytical treatment of the equations that model this phenomenon is substantially impossible due to their high nonlinearity; and furthermore the typical order of magnitude of the measurable quantities (object sizes in the range of microns, time intervals in the range of microseconds with nanosecond resolution) makes experiments difficult to perform. Hence we numerically analyze the relationships between amplitude and frequency by the use of SPECTRA PLUS software. The method is tested analyzing forced oscillations of cavitation bubbles excited by ultrasonic standing waves at different pressure amplitudes, showing characteristic behaviour of nonlinear dynamical systems; frequency spectra are obtained, stability analysis is performed. It is important to note that we observe subharmonic behaviour of the volume mode of the bubble prior to the instabilities due to shape modes. If one further increases the value of pressure amplitudes, one can clearly observe surface instabilities and deformations that lead to the destruction of the bubble. This evidence may suggest that the subharmonic behaviour leads to chaos in ultrasonic cavitation.

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