Computation of dispersion curves for embedded waveguides using a dashpot boundary condition.

In this paper a numerical approach is presented to compute dispersion curves for solid waveguides coupled to an infinite medium. The derivation is based on the scaled boundary finite element method that has been developed previously for waveguides with stress-free surfaces. The effect of the surrounding medium is accounted for by introducing a dashpot boundary condition at the interface between the waveguide and the adjoining medium. The damping coefficients are derived from the acoustic impedances of the surrounding medium. Results are validated using an improved implementation of an absorbing region. Since no discretization of the surrounding medium is required for the dashpot approach, the required number of degrees of freedom is typically 10 to 50 times smaller compared to the absorbing region. When compared to other finite element based results presented in the literature, the number of degrees of freedom can be reduced by as much as a factor of 4000.