Greenʹs matrix and the boundary integral equation method for the analysis of vibration and energy flow in cylindrical shells with and without internal fluid loading

This paper presents several aspects of the dynamics of a cylindrical shell with and without heavy internal fluid loading, which have not been studied before in detail. Firstly, a consistent formulation of boundary integral equations for a shell of finite length is derived based on the energy conservation principle and the reciprocity theorem. This derivation naturally leads to identification of principal components of the energy flux through an arbitrary cross-section of a shell and to formulation of Greenʹs matrix for an infinitely long shell at each individual circumferential wave number. Secondly, an inspection into the energy re-distribution between several transmission paths in a near field (in a boundary layer at the vicinity of a loaded cross-section) is performed, which sheds light on the role of evanescent waves in motions of a driven shell. Thirdly, the influence of excitation conditions on steady fluctuations of the overall energy flow between transmission paths in a far field is explored for the case, when several propagating waves exist in a shell both with and without internal fluid loading. Besides, a systematic verification of the solution offered by the boundary equations method is given through comparison of eigenfrequencies with those computed in finite element modelling for various boundary conditions. Analysis of dispersion curves and input mobilities is also presented.