Finite element modeling of frequency-dependent material damping using augmenting thermodynamic fields

Abstract

A new method of modeling frequency-dependent material damping in structural dynamics analysis is reported. Motivated by results from materials science, augmenting thermodynamic fields are introduced to interact with the usual mechanical displacement field. The methods of irreversible thermodynamics are used to develop coupled material constitutive relations and partial differential equations of evolution. These equations are implemented for numerical solution within the computational framework of the finite-element method. The method is illustrated using several examples including longitudinal vibration of a rod, transverse vibration of a beam, and vibration of a large space truss structure.