Effect of mean flow on responses of a fluid-loaded plate

Abstract

Asymptotic solutions to the dynamic and acoustic responses of a fluid-loaded infinite plate subject to a time-dependent line force excitation in mean flow are obtained. Results show that mean flow has a significant effect on the plate traveling waves, the modification factor being α2(1∓M)8 when the excitation frequency is above the plate coincidence frequency, where α is the fluid-loading factor, M is the mean flow Mach number, and minus and plus signs indicate upstream and downstream propagating waves, respectively. At the coincidence frequency, the amplitudes of traveling waves are modified by mean flow by (c0+c1M+c2M2), where cj, j=0, 1, and 2 are α-dependent constants. For light fluid loading, for example, an air/steel interface, α≊6.5×10−4, the leading term of the traveling wave is proportional to α−4/3M2. For heavy fluid loading, for example, a water/steel interface, α≊0.133, the leading term is proportional to α−2/3M. Below the coincidence frequency, the effect of mean flow on plate traveling waves is insignificant. Mean flow also changes the radiated acoustic pressures. In particular, the amplitudes of the leaky waves are modified by mean flow, to the leading order of a small value of α, by (√Ω±M)2[4Ω√(Ω±M)2−1]−1, where Ω is the ratio of the excitation frequency to the plate coincidence frequency. The effect of mean flow on the cylindrical waves depends on Ω. When Ω≳1, the peak amplitudes of the cylindrical waves are modified by mean flow by √(1−Ω−1)±2Ω−1/2M−M2, and the beam angles are rotated by θb=sin−1(M∓Ω−1/2). When Ω<1, the effect of mean flow on the cylindrical waves is greatly decreased. Mean flow modifies the wave numbers of the traveling waves and acoustic waves as well. As a result, the waves propagating in the upstream direction are squeezed and those in the downstream direction are relaxed in space.