Three dimensional non-axisymmetric transient acoustic radiation from an eccentric hollow cylinder

Abstract

Theoretical analysis and detailed numerical simulations are presented for three-dimensional non-stationary vibroacoustic response of a doubly fluid-loaded infinitely long eccentric hollow elastic circular cylinder of arbitrary wall thickness, under arbitrary non-axisymmetric time-dependent on-surface mechanical drives. The formulation is based on the Navier equations of linear elasticity for the solid material, the wave equation for the internal and external fluid domains, the classical method of separation of variables, and the translational addition theorem for cylindrical wave functions. Laplace transform with respect to the time coordinate, Fourier transform with respect to the axial coordinate, and Fourier series expansion in the circumferential direction, are employed to obtain the transformed solutions in the form of partial-wave expansions of transcendental functions. A set of equally spaced virtual sources are assumed along the axial direction, and semi-analytical solutions are obtained in the Laplace domain as discrete summations of simple two dimensional solutions with different axial wave numbers. Time domain solutions are subsequently calculated by using Durbin’s numerical inverse Laplace transform scheme. The analytical results are illustrated with numerical examples in which air- or water-filled concentric and eccentric steel cylinders, submerged in water, are driven by a pair of equal and opposite external radial point loads of finite duration described by a Ricker pulse. Some interesting features of the transient fluid–solid interaction problem such as the generation of shell-induced circumnavigating waves, appearance of multiple high/low amplitude pressure spots in the internal fluid, and formation of non-propagating evanescent waves in the external fluid are noted using appropriate 2D images of the three dimensional sound fields. 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.