Abstract
In many applications, one is interested in estimating the wave speed in materials or structures for which the wave equation cannot be solved analytically. This work is concerned with studying wave propagation in tendons and ligaments, where material anisotropy, nonlinearity, prestress, and non-ideal boundary conditions make an analytical solution impractical. In these cases, the finite element method can be used to simulate the structure in time and then extract wave motion, but this is computationally expensive, both in the simulation and for post processing. This work exploits the duality between modes of vibration and traveling waves to show how one can perform a semi-analytical dispersion analysis. The proposed method is then applied to models of tendons and ligaments of varying complexity and is found to provide significant insights into the nature of wave propagation and the expected dispersion behavior.
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