On the strength of mechanical and thermal damping in linear materials

This paper gives a criterion for distinguishing between various types of linear models for elastic and thermoelastic behavior. The models are all dissipative and the steady-state periodic limit for periodic input can be defined. Associated with this limit is a scalar function of frequency which could be determined experimentally. Its behavior for large frequency determines the strength of the damping. Both fibers and one-dimensional bars are considered. The models include Kelvin—Voigt materials, viscoelastic models with regular and singular kernels as well as standard thermoelasticity. It is found that strength of damping increases the order of singularity in the viscoelastic models. Thermoelastic damping is shown to be weak and to be of the same order as for elastic models with smooth kernels.