Numerical and analytical calculation of modal excitability for elastic wave generation in lossy waveguides

In the analysis of elastic waveguides, the excitability of a given mode is an important feature defined by the displacement-force ratio. Useful analytical expressions have been provided in the literature for modes with real wavenumbers (propagating modes in lossless waveguides). The central result of this paper consists in deriving a generalized expression for the modal excitability valid for modes with complex wavenumbers (lossy waveguides or non-propagating modes). The analysis starts from a semi-analytical finite element method and avoids solving the left eigenproblem. Analytical expressions of modal excitability are then deduced. It is shown that the fundamental orthogonality property to be used indeed corresponds to a form of Auld's real orthogonality relation, involving both positive- and negative-going modes. Finally, some results obtained from the generalized excitability are compared to the approximate lossless expression.