Analysis of proportional damping or Rayleigh damping on damped and undamped systems

Abstract

Damping mechanisms have been active areas of research for a long time in history, despite this its understanding is still rudimentary as compared to the other traits of modeling. The actual problem is that even now it is not clear, which state variables are relevant for the computation of damping forces, which makes it very difficult to model in Finite Element Method. To remedy this, a well-known method is used, called ‘Proportional damping’ (Rayleigh damping) and used for the modeling of viscous damping, initially established for undamped systems, but can be used for the analysis of damped systems as well. Proportional damping is used to model the energy dissipation characteristics of complex engineering structures as well as solve multiple dynamic problems. It plays very important role in modeling damping on an industrial scale. So, Rayleigh damping is proved to be an effective way of considering damping for structure's analysis. To completely analyze the proportional damping, damping parameters are attained for two multiple degrees of freedom systems and Rayleigh damping parameters will be extracted for attained damping values during the research to demonstrate the theoretical approach of Proportional damping. The aim of this paper is to analyze Rayleigh damping or Proportional damping and have an overview of its effects and its importance in structures, along with explaining its advantages and disadvantages.