Optimized Shapes of Ocsillating Resonators for Generating High-Amplitude Pressure Waves
It is well known that the resonator geometry strongly influences the resonant frequencies of an acoustical resonator and the generated nonlinear standing pressure waveform. Maximizing the ratio of maximum to minimum gas pressure at an end of an oscillating resonator by optimizing the cavity contour is investigated numerically. A quasi-Newton type scheme is used to find optimized axisymmetric resonator shapes to achieve the maximum pressure compression ratio. The acoustical field is solved using a one-dimensional model, and the resonance frequency shift and hysteresis effects are obtained through an automation scheme based on continuation methods. Results are presented from optimizing cone, horn-cone, and cosine resonator geometries. Significant performance improvement is found in the optimized shapes over others previously published. Different optimized shapes are found when starting with different initial guesses, indicating multiple local extrema. The numerical model is validated by comparing with the experimental results of a horn-cone shaped resonator.