Bi-orthogonality conditions for power flow analysis in fluid-loaded elastic cylindrical shells: Theory and applications

The paper addresses the classical problem of time-harmonic forced vibrations of a fluid-loaded cylindrical shell considered as a multi-modal waveguide carrying infinitely many waves. Firstly, a modal method for formulation of Green’s matrix is derived by means of modal decomposition. The method builds on the recent advances on bi-orthogonality conditions for multi-modal waveguides, which are derived here for an elastic fluid-filled cylindrical shell. Subsequently, modal decomposition is applied to the bi-orthogonality conditions to formulate explicit algebraic equations to express the modal amplitudes independently of each other. Secondly, the method is verified against results available in the literature and the convergence is studied as well. Thirdly, the work conducted in the same references is extended by employing this method to assess the near field energy distribution when the coupled vibro-acoustic waveguide is subjected to separate pressure and velocity acoustical excitations. Further, it has been found and justified that the bi-orthogonality conditions can be used as a ’root finder’ to solve the dispersion equation. Finally, it is discussed how to predict the response of a fluid-filled shell when an excitation is imported from CFD-modelling of an operating pump.