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Analytical and numerical investigations on inerter-based NES absorber system with nonlinear damping

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Abstract

Two major concerns with the nonlinear energy sink (NES) when used as a passive vibration absorber are the mass of the NES and the threshold of external excitation to initiate the targeted energy transfer (TET). This work proposes an inertial NES with nonlinear damping to address the aforementioned concerns. An inerter replaces the conventional NES’s mass to reduce the absorber system’s effective mass. The addition of nonlinear damping created instability and therefore initiated the strongly modulated response (SMR) even for lower excitation amplitude which is the most favorable condition for TET. A base excited linear primary system appended with the proposed NES is used to demonstrate the claims. Multi-harmonic balance method (MHBM) combined with arc-length continuation and Floquet theory generates the frequency response plots and identifies the stable and unstable periodic solution branches. Numerical studies at the unstable periodic solution obtained by MHBM revealed the existence of SMR. The slow flow dynamics and the slow invariant manifold (SIM) associated with the SMR are derived using the complexification averaging (CX-A) method combined with the singular perturbation theory. The SIM topology is investigated for variations in the strength of nonlinearity, nonlinear damping factor, and mass ratio. The performance of the proposed inertial NES with nonlinear damping is compared with that of a conventional NES with viscous damping, and the merits are highlighted. It is observed that with the addition of nonlinear damping in the inertial NES, the SMR is initiated even at low excitation amplitude, and efficient energy transfer takes place from the linear oscillator to NES. The combined approach using MHBM and CX-A provided better insight into the analysis of NES-based vibration absorber systems.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, India

    Rony Philip, B. Santhosh & Bipin Balaram

  2. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Stefanowskiego Str. 1/15, 90-924, Łódź, Poland

    Bipin Balaram

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  1. Rony Philip
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Correspondence to B. Santhosh.

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Philip, R., Santhosh, B. & Balaram, B. Analytical and numerical investigations on inerter-based NES absorber system with nonlinear damping. Acta Mech 233, 4365–4383 (2022). https://doi.org/10.1007/s00707-022-03333-0

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