Spontaneous pattern formation in an acoustical resonator

Abstract

A dynamical system of equations describing parametric sound generation (PSG) in a dispersive large aspect ratio resonator is derived. The model generalizes previously proposed descriptions of PSG by including diffraction effects, and is analogous to the model used in theoretical studies of optical parametric oscillation.A linear stability analysis of the solution below the threshold of subharmonic generation reveals the existence of a pattern forming instability, which is confirmed by numerical integration. The conditions of emergence of periodic patterns in transverse space are discussed in the acoustical context.

Bistable and dynamic states of parametrically excited ultrasound in a fluid-filled interferometer

“…This fact, different to the bistability of the fundamental mode, is also present in the fully dispersive cavity, as shown in [10,12].…”

“…This theory has been also applied to the interferometer case [7,12,13,14], but the agreement with the experiment [7] was mainly qualitative. The discrepancies can be interpreted in terms of the influence of the first higher harmonics (those with higher amplitudes) on the parametric process, introducing additional features that can not be captured by the fully dispersive model.…”

Measurement of the frequency dependence of the ultrasonic parametric threshold amplitude for a fluid-filled cavity

“…These frequencies ͑ 1 and 2 ͒ occur at approximately half the drive frequency ͑2͒ in such a manner that 1 + 2 Ϸ 2. 11,12 Parametric excitation is possible only if the energy input to the system due to periodic variation of its resonant frequencies reaches a critical threshold value that is large enough to overcome the energy dissipated by the system. Therefore, the amplitude of the varying parameter must satisfy a threshold condition.…”

Spatio-Temporal Dynamics in Parametric Sound Generation

“…Nevertheless, higher harmonics can be controlled using additional dispersion mechanisms, such as bubbly fluids or walls with selective (frequency dependent) absorption, or a waveguide cavity [3]. This theory has been also applied to the interferometer case [4] , but the agreement with the experiment [2] was mainly qualitative. This theory has been also applied to the interferometer case [4] , but the agreement with the experiment [2] was mainly qualitative.…”