Natural neighbour Galerkin computation of the vibration modes of fluid‐structure systems

Abstract

PurposeThis paper seeks to extend the application of the natural neighbour Galerkin method to vibration analysis of fluid‐structure interaction problems.Design/methodology/approachThe natural element method (NEM) which is a meshless technique is used to simulate the vibration analysis of the fluid‐structure interaction systems. The method uses the natural neighbour interpolation for the construction of test and trial functions. Displacement variable is used for both the solid and the fluid domains, whereas the fluid displacement is written as the gradient of a potential function. Two classical examples are considered: free vibration of a flexible cavity filled with liquid and vibration of an open vessel containing liquid. The corresponding eigenvalue problems are solved and the results are compared with the finite element method (FEM) and analytical solutions to show the accuracy and convergence of the method.FindingsThe performance of the NEM is investigated in the computation of the vibration modes of the fluid‐structure interaction problems. Good agreement with analytical and FEM solutions are observed. Through the notable obtained results, it is found that the NEM can also be used in vibration analysis of fluid‐structure interaction problems as it has been successfully applied to some problems in solid and fluid mechanics during the recent years.Originality/valueIn spite of notable achievements in solving some problems in solid and fluid mechanics using NEM, the vibration analysis of fluid‐structure interaction problems, as considered in this paper, has not been investigated so far.