Abstract
We consider three dimensional finite element computations of thermoelastic damping ratios of arbitrary bodies using Zener’s approach. In our small-damping formulation, unlike existing fully coupled formulations, the calculation is split into three smaller parts. Of these, the first sub-calculation involves routine undamped modal analysis using ANSYS. The second sub-calculation takes the mode shape, and solves on the same mesh a periodic heat conduction problem. Finally, the damping coefficient is a volume integral, evaluated elementwise. In the only other decoupled three dimensional computation of thermoelastic damping reported in the literature, the heat conduction problem is solved much less efficiently, using a modal expansion. We provide numerical examples using some beam-like geometries, for which Zener’s and similar formulas are valid. Among these we examine tapered beams, including the limiting case of a sharp tip. The latter’s higher-mode damping ratios dramatically exceed those of a comparable uniform beam.
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Basak, A., Nandakumar, K. & Chatterjee, A. Decoupled three-dimensional finite element computation of thermoelastic damping using Zener’s approximation. Meccanica 46, 371–381 (2011). https://doi.org/10.1007/s11012-010-9318-8
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DOI: https://doi.org/10.1007/s11012-010-9318-8