Characterization and Synthesis of Rayleigh Damped Elastodynamic Networks

TL;DR

This paper characterizes the frequency response of Rayleigh damped elastodynamic networks and provides a method for synthesizing such networks with a specified response, revealing limitations in realizability.

Contribution

It offers a new characterization of Rayleigh damped networks' frequency response and addresses the synthesis problem, highlighting constraints on realizability.

Findings

Not all damped networks can be realized with fixed proportional damping.

Provides a characterization of the frequency response for Rayleigh damped networks.

Shows limitations in synthesizing networks with given responses.

Abstract

We consider damped elastodynamic networks where the damping matrix is assumed to be a non-negative linear combination of the stiffness and mass matrices (also known as Rayleigh or proportional 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. Our analysis shows that not all damped elastodynamic networks can be realized when the proportionality constants between the damping matrix and the mass and stiffness matrices are fixed.