Signal Wrap-Around Free Spectral Element Formulation For Multiply Connected Finite 1-D Waveguides

Abstract

This paper presents a novel spectral element formulation based on Numerical Laplace Transforms for the wave propagation of multiply connected finite 1-D waveguides, based on the first order shear deformation theory. The present formulation overcomes the severe short-comings of Fourier transform based spectral element formulation which has serious problems associated with the signal wrap-around while analysing finite domain structures. The real part of the Laplace variable which provides damping to the wavenumber solution, is characterized by Wilcox and Wedepohl approaches. The effect of this damping alters the wave dispersion and introduces certain interesting phenomenon that is not seen in the undamped waveguides. Problems involving wave propagation analysis are solved on finite multiply connected waveguides of varied complexity to demonstrate the efficiency of the formulated element. In most of the examples, the presence of signal wrap-around in Fourier domain based spectral element is brought out. With this approach, any large structural network, consisting of 2-D either metallic or composite finite length waveguides, under high frequency impact loading can be analyzed with very low computational cost.