Finite element analysis of frequency spectra for elastic waveguides

The finite element theory is presented for the analysis of the dispersive characteristics of elastic waveguides of arbitrary cross-section. The necessary mass and stiffness properties of circular core, circular sleeve, rectangular, and triangular elements are developed. The practical application of these new elements is demonstrated in the calculation of frequency spectra for circular, square, and triangular waveguides and for a fiber reinforced composite. The dispersive characteristics of the composite material are determined from a formulation which models the fiber as a cylinder and the surrounding matrix material as a rectangular section. The numerical results obtained by the finite element analysis are also compared with the available results from other methods.