Numerical investigation of dispersion relations for helical waveguides using the Scaled Boundary Finite Element method

In this paper, the dispersion properties of elastic waves in helical waveguides are investigated. The formulation is based on the Scaled Boundary Finite Element method (SBEFM). With a set of orthogonal unit basis introduced as the contravariant basis, the helical coordinate is firstly considered, where components of tensor retain the dimension of original quantity. Based on the strain-displacement relation, the eigenvalue matrix is obtained about wavenumbers and frequencies. The cross section of the waveguides is discretized by using high-order spectral elements. Moreover, the formulated linear matrix is utilized to design efficient and accurate algorithms to compute the eigenvalues of helical waveguides. Compared with the Pochhammer-Chree curves, the convergence and accuracy of the SBFEM are discussed. Finally, we give some dispersion curves for a wide range of lay angles and analyze in detail properties of cut-off frequency, mode separation and mode transition for elastic wave propagation in the helical waveguides. (C) 2013 Elsevier Ltd. All rights reserved.