Active nonlinear energy sink using force feedback under transient regime
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ORIGINAL PAPER
Active nonlinear energy sink using force feedback under transient regime G. Zhao . G. Raze . A. Paknejad . A. Deraemaeker . G. Kerschen . C. Collette
Received: 27 May 2020 / Accepted: 3 October 2020 Ó Springer Nature B.V. 2020
Abstract In this paper, an active nonlinear energy sink (ANES) based on force feedback is investigated. The proposed device is composed of a pair of collocated actuator and force sensor. The control law is implemented by feeding back the output of the force sensor, through one single integrator and one double integrator of its cube. Its working principle can be understood by an equivalent mechanical network which consists of a linear dashpot, linear spring and a cube root inerter. Although the nonlinear assignment between the spring and mass or inerter quantities is different from that of traditional nonlinear energy sinks (NESs), it is found that ANES and NES behave similarly in terms of their slow-scale dynamics and the vibration mitigation effectiveness. Closed-form expressions for properly tuning the feedback gains are derived. Numerical simulations are performed to validate the analytical analysis. The damping G. Zhao (&) A. Paknejad C. Collette Precision Mechatronics Laboratory, Beams Department, Universite´ Libre de Bruxelles, F.D. Roosevelt Av 50, 1050 Brussels, Belgium e-mail: [email protected] G. Raze G. Kerschen C. Collette Department of Aerospace and Mechanical Engineering, University of Lie`ge, Alle´e de la De´couverte 9, 4000 Lie`ge, Belgium A. Deraemaeker BATir Department, Universite´ Libre de Bruxelles, F.D. Roosevelt Av 50, 1050 Brussels, Belgium
mechanism of ANES through targeted energy transfer and resonance capture cascade is demonstrated. Keywords Inerter Force feedback Nonlinear energy sink Targeted energy transfer Resonance capture cascade
1 Introduction Lightweight materials have been more and more used for system constructions in many engineering applications for the sake of fuel efficiency and reduction of environmental pollution [1, 2]. However, this will often make these structures lightly damped and responses could be unacceptably amplified around the resonance, causing many problems such as reduction in structural integrity, compromise of instrument functionality and even threat to human lives. In this sense, proper damping techniques need to be considered in parallel with the future design of lightweight structures. A tuned mass damper (TMD) [3] which typically consists of a proof mass and a spring-dashpot pair is often employed for such purpose. It acts as an auxiliary system to the host structures where additional damping is needed. The natural frequency of the added TMD is often suggested to be roughly equal to one of the resonance frequencies of the host structure [4]. In this way, the vibration energy associated with the considered mode can be quickly transferred and
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localised in the TMD where it is eventually dissipated. Due to this nature, TMDs a
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