Numerical modeling of wave propagation for damped elbow pipes using Fourier-Legendre spectral element method in polar coordinates

Wave propagation in damped elbow pipes is investigated with the Fourier-Legendre spectral element method. The damped steady-state dispersion relationship is constructed by the frequency-wavenumber spectral decomposition of the governing wave equation, based on the strain-displacement relation of the ring coordinate. Then, the discretization formulation is obtained via the Legendre spectral element method where high-order spectral elements of polar coordinates are introduced to keep this finite element model consistent with the structures geometry. Finally, we give some dispersion curves of energy velocity and attenuation on damped elbow pipes with different curvatures in the ring wavenumber-frequency space.