Predictive Elastothermodynamic Damping in Finite Element Models Using a Perturbation Formulation

Abstract

A method is presented by which elastothermodynamic damping can be included in finite element formulations for design analysis. In this method, elastothermodynamic damping theory is combined with a perturbation method previously developed for viscoelastic modeling. A key aspect of this approach is that it projects elastothermodynamic damping onto the undamped mode shapes of the structure. A finite element formulation is developed and presented for beams in both bending and extension. The finite element formulation creates nonsparse, nonsymmetric damping and stiffness matrices. Results with this method for various cases are discussed. After validation against the classic Zener model damping prediction, the method is applied to the analysis of damping in a three-dimensional truss. The results show that elastothermodynamic damping is higher for modes with a larger portion of their strain energy due to local member bending rather than extension. Through examples it is shown that to maximize elastothermodynamic damping in a truss, both the member cross section and the truss mode shapes must be considered.