Finite element analysis of the vibrations of waveguides and periodic structures

Abstract

Many structural components can be regarded as waveguides. They are uniform in one direction so that the cross section of the waveguide has the same physical and geometric properties at all points along the axis of the waveguide. In this paper a method is presented to calculate the forced response of such a structure using a combination of wave and finite element (FE) approaches. The method involves post-processing a conventional, but low order, FE model in which the mass and stiffness matrices are typically found using a conventional FE package. A section of the waveguide is meshed and the eigenvalues and eigenvectors of the resulting transfer matrix found. The eigenvectors form a set of basis functions for the analysis of the structure as a whole, allowing the global dynamic stiffness matrix to be built easily and then the forced response to be calculated very efficiently. The main advantage of the approach over the alternative waveguide/FE approach often termed the spectral FE method, is that conventional FE packages can be used to form the stiffness and mass matrices so that structures with complex geometries or material distributions can be analysed with relative ease. To demonstrate the efficacy of the method examples of the forced response for a finite beam and plate-strip are presented.