Modeling Fluid-Filled Cylindrical Shells with Wave Finite Elements
Sousa, R.W.O. (Rayston Werner Oliveira Sousa)1; Mencik, J.-M. (Jean-Mathieu Mencik)2; Dos Santos, J.M.C. (Jose Maria Campos dos Santos)1
1 University of Campinas-UNICAMP; 2 INSA Centre Val de Loire, Université François Rabelais de Tours
doi:10.20906/CPS/CILAMCE2017-0608
Resumo
The Wave Finite Element (WFE) method is a numerical approach to calculate the wave propagation along periodic structures, which is based on the Finite Element (FE) model of a structure slice. In this work, the WFE method is applied to calculate the vibroacoustic response of cylindrical shells filled with acoustic fluids, e.g., gas pipelines or exhaust pipes. For this purpose, the FE mesh of a slice is considered which involves 2D flat shell elements for the structure part (cylindrical shell) and 3D acoustic elements for the acoustic part (fluid). The transfer matrix of the slice links the solid/acoustic quantities on the right boundary to those on the left boundary. Computing the eigenvalues and eigenvectors of the transfer matrix yields, from Bloch's theorem, the wave parameters - expressed in terms of wavenumbers - and the wave shapes, respectively. In fact, the vectors of wave shapes constitute a vector basis which is well suited to express the displacements and pressures in fluid-filled cylindrical shells. The proposed strategy reduces considerably the computational times when compared to the FE method. In the present approach, a symmetric formulation based on displacements and velocity potentials as field variables is applied, which is well suited to express a transfer matrix which is symplectic. This numerically provides the usual properties that waves should occur in pairs, i.e., right-going and left-going wave modes. The proposed WFE-based approach is validated by analyzing the vibroacoustic response of a cylindrical shell filled with an acoustic fluid of finite length and subject to harmonic mechanic/acoustic loads. Dispersion curves are assessed and compared with analytical theories. Additional experiments are made to highlight the relevance of the proposed method in terms of accuracy and CPU time savings, in comparison with FE analysis.
Palavras-chave: wave finite element method; fluid-structure interaction; cylindrical shell; wave propagation