Calculation of the Response of an Impulsively Excited Oscillator in an Infinite Acoustic Fluid

The response of an impulsively excited single-degree-of-freedom oscillator submerged in an infinite acoustic fluid is considered. The character of the response is determined by the quantity ka; k is the wave number associated with the in-vacuo natural frequency of the oscillator, and a is a characteristic structural dimension. For low-frequency oscillators (ka ≪ 1), the response consists of two parts. The first is the usual hydrodynamic solution in which the effect of the fluid on the structure is that of an added mass. The second is much smaller (of order ka) and is significant only in a “boundary layer” in time of order a/c, with c the fluid sonic velocity. For high-frequency oscillators (ka ≫ 1), the principal effect of the fluid is a decay of oscillator vibration due to sound radiation.