Experiments of high-amplitude and shock-free oscillations of air column in a tube with array of Helmholtz resonators

This experimental study is made to verify the weakly nonlinear theory for high-amplitude and shock-free oscillations of an air column developed in the previous paper [Sugimoto et al., J. Acoust. Soc. Am., 114, 1772-1784 (2003)]. The experiments use a new tube and resonators designed so as to not only avoid higher harmonic resonances and evanescences but also reduce the values of the coefficient of Q in the amplitude equation, and a rubber diaphragm sandwiched by circular plates to drive the air column. The steady-state pressure field in the tube and in the cavities of the resonators is measured, from which Fourier coefficients are obtained. In spite of nonlinearity, higher harmonics are suppressed significantly as designed, and the frequency response measured shows quantitatively good agreement with the one predicted up to about 170 dB (SPL). The first harmonics and the nonoscillatory component in the pressure field are well predicted, though the second harmonics show a quantitative discrepancy with the theory. In view of the good agreement of the frequency response, it is concluded that the theory is valid and useful enough to provide guidelines in designing the tube with the array of resonators. (c) 2005 Acoustical Society of America.