Mitigation of Nonlinear Structural Vibrations by Duffing-Type Oscillators Using Real-Time Hybrid Simulation

Abstract

This work addresses the vibration reduction of nonlinear host structures by dynamic absorbers of Duffing type. For deriving the equations of motion, both host structure and absorber are modeled as nonlinear SDOF oscillators. The method of harmonic balance is applied to obtain an approximate analytical steady-state solution, which is used for parameter identification. Therefore, the frequency response function of either host structure or absorber is determined experimentally, and the dynamic system parameters are identified by a nonlinear least squares method. Since the focus of the work is on the absorber design, a generalization of Den Hartog’s equal-peak method renders the optimal parameters. These are strongly dependent on the operating point’s amplitude, and consequently, the optimization must be often repeated. To keep this effort minimal, DOE methods are applied in the test and design phase. After confirming a proper absorber design by numerical simulations, a physical model of the absorber is tested in a real-time hybrid simulation setup. Hence, the behavior of the nonlinear host structure is reproduced by a virtual simulation model coupled to the physical absorber using a transfer system. This method allows to focus on the physical absorber without the need to construct an expensive laboratory host structure model. Furthermore, all host structure parameters can be changed in the virtual model, without modifying the real-time hybrid simulation setup. Furthermore, the virtual host structure cannot be damaged or destroyed, and thus, all experiments can be repeated and optimized straight away. So far, all real-time hybrid simulation experiments are in good accordance with the theoretical predictions of this work and corresponding results already published in literature.