Sound radiation from two semi-infinite dissimilar plates subject to a harmonic line force excitation in mean flow. I. Theory

Abstract

Formulations are derived for predicting sound radiation from two semi-infinite dissimilar plates subject to a line force excitation at the joint in the presence of mean flow using the Wiener–Hopf technique and Fourier transformations. The acoustic pressure is solved in the frequency-wave-number domain first in terms of the decomposition factors and parameters associated with displacements, slopes, bending moments, and shear forces at the joint of two plates. The decomposition factors are evaluated via contour integrations, and the parameters are determined by a set of simultaneous equations derived from boundary conditions and the finiteness requirement imposed at the joint. It is shown that the set of equations reduces to a 2×2 matrix for a welded joint, a 3×3 matrix for a hinged joint, and a 4×4 matrix for a free–free joint, i.e., two plates being mechanically unconnected. The frequency-domain acoustic pressure is subsequently obtained by taking an inverse Fourier transformation and evaluated by using the residue theory and contour integrals along the branch cut. Asymptotic behaviors of the plate flexural displacement and radiated acoustic pressure in the frequency-wave-number domain are obtained. Effects of mean flow on resulting sound radiation are examined.