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Acta Mechanica

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18-11-2023 | Original Paper

Vibration suppression and stability analysis of a beam at large amplitude excitation using a two-degree-of-freedom nonlinear energy sink

Authors: Rajni Kant Kumar, Anil Kumar

Published in: Acta Mechanica | Issue 2/2024

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Abstract

A two-degree-of-freedom (TDOF) nonlinear energy sink (NES) is proposed to suppress the vibration of a simply supported beam subjected to a large amplitude excitation corresponding to its fundamental frequency. The Euler–Bernoulli beam theory along with the Euler–Lagrange equation is utilized for the dynamical modeling of the beam-NES system. The numerical solutions are compared with an approximate analytical solution based on the complexification-averaging method. As the beam response significantly depends on the values of the NES parameters, the optimal values are obtained by employing the particle swarm optimization. After comparison with a single-degree-of-freedom (SDOF) NES, it is found that at lower excitation amplitude SDOF NES is more effective than TDOF NES, however, as the excitation amplitude increases, the TDOF NES gets more effective in terms of resonant peak suppression and energy dissipation. The TDOF NES reduces the first peak amplitude of about 95% as well as dissipates the vibration energy of about 90–98.98%. The chaotic response of the beam is examined using the largest Lyapunov exponents with different parameters. The higher values of the NES stiffness, mass and the excitation amplitude make the system chaotic. Moreover, the analysis of steady-state response shows that a higher value of NES damping reduces the unstable band and thus provides stable response.

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Title: Vibration suppression and stability analysis of a beam at large amplitude excitation using a two-degree-of-freedom nonlinear energy sink
Authors: Rajni Kant Kumar
Anil Kumar
Publication date: 18-11-2023
Publisher: Springer Vienna
Published in: Acta Mechanica / Issue 2/2024
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI: https://doi.org/10.1007/s00707-023-03765-2

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Vibration suppression and stability analysis of a beam at large amplitude excitation using a two-degree-of-freedom nonlinear energy sink

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