Characterization and Synthesis of Rayleigh Damped Elastodynamic Networks

We consider damped elastodynamic networks where the damping matrix is assumed to be a non-negative linear combination of the stiffness and mass matrices (Rayleigh damping). We give here a characterization of the frequency response of such networks. We also answer the synthesis question for such networks, i.e., how to construct a Rayleigh damped elastodynamic network with a given frequency response. The characterization and synthesis questions are sufficient and necessary conditions for a frequency dependent matrix to be the frequency response of a Rayleigh damped network. We only consider the non-planar case.