Taking into Account Uncertainties to Analyze the Robustness of an Energy Pumping System

Abstract

Energy pumping is defined as the irreversible energy transfer from one structure (linear and the socalled primary structure) to another structure (essentially nonlinear and the so-called non-linear energy sink (NES)) which is coupled with the primary structure. The principle of energy pumping has been analyzed theoretically and also validated experimentally. The aim of this paper is to study the energy pumping robustness considering the uncertainties of the parameters of a two DOF mass-spring-damper system composed of two subsystems: one linear subsystem, the primary structure, and one nonlinear subsystem, the NES. The two subsystems are coupled by a linear spring and the whole system corresponds to a grounded configuration. Three parameters of the system will be considered as uncertain: the coupling linear spring, the damper from the nonlinear system and the damper from the linear subsystem. Probability density functions are constructed for the random variables associated to the uncertain parameters applying the Maximum Entropy Principle. A sensitivity analysis is then performed. Depending on the dispersion, the pumping energy can be highly influenced.