Vibroacoustic response of an eccentric hollow cylinder

The linear 3D elasticity theory in conjunction with the classical method of separation of variables and the translational addition theorem for cylindrical wave functions are employed to investigate the three-dimensional steady-state sound radiation characteristics of an arbitrarily thick eccentric hollow cylinder of infinite length, submerged in an unbounded ideal acoustic medium, and subjected to arbitrary time-harmonic on-surface mechanical drives. The spatial Fourier transform along the shell axis and Fourier series expansion in the circumferential direction are utilized to obtain a formal integral expression for the radiated pressure field in the frequency domain. The method of stationary phase is subsequently implemented to evaluate the integral for an observation point in the far field. The analytical results are illustrated with numerical examples in which air-filled water-submerged concentric and eccentric steel cylinders are driven by harmonic concentrated radial and transverse surface loads. Effects of excitation and cylinder eccentricity on the far-field radiated pressure amplitudes/directivities are discussed and contributions from pseudo-Rayleigh, whispering gallery, and axially guided waves are examined through selected spatial dispersion patterns. Limiting cases are considered and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data in the existing literature.