Shock-free, forced oscillations of an air column in a closed tube

Abstract

This paper reports generation of high-amplitude, shock-free oscillations of an air column in a closed tube of uniform cross section. The air column is driven sinusoidally by the bellows mounted at one end of the tube at a frequency equal or close to the resonance frequency of the lowest mode. The shock-free oscillations are achieved by connecting an array of Helmholtz resonators to the tube axially. The array of resonators gives rise to wave dispersion, which changes the sound speed in this tube to depend on the frequency and makes the tube dissonant by avoiding coincidence of the higher-harmonic frequencies of excitation and the resonance ones of the higher modes. Each resonator is identical and small in a sense that the cavity’s volume is chosen much smaller than the tube’s volume per axial spacing between neighboring resonators, while the natural frequency of the resonator is chosen even higher than the lowest resonance frequency. Frequency response is obtained and compared with the theory up to the resonance frequency of the third mode. It is observed that the shock-free oscillations are realized at the sound pressure level of 170 dB where the shock would emerge unless the array were connected.