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Vibration Suppression for an Elastically Supported Nonlinear Beam Coupled to an Inertial Nonlinear Energy Sink

Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, Beijing 100124, P. R. China

E-mail Address: zychang@emails.bjut.edu.cn

Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, Beijing 100124, P. R. China

Architecture and Civil Engineering Research Center, City University of Hong Kong Shenzhen Research Institute, Shenzhen 518057, P. R. China

E-mail Address: jchen@bjut.edu.cn

Corresponding author.

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Qiu-Sheng Li

Architecture and Civil Engineering Research Center, City University of Hong Kong Shenzhen Research Institute, Shenzhen 518057, P. R. China

Department of Architecture and Civil Engineering, City University of Hong Kong Kowloon, Hong Kong

E-mail Address: bcqsli@cityu.edu.hk

Corresponding author.

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https://doi.org/10.1142/S0219455423400175Cited by:11 (Source: Crossref)

This article is part of the issue:

Special Issue on Structural Engineering Dedicated to the 70th Birthday of Professor Y. B. Yang
Guest Editors: Weiyong Wang, C. W. Lim and Jie Yang

Abstract

This paper investigates the vibration suppression of an elastically supported nonlinear cantilever beam attached to an inertial nonlinear energy sink (NES). The nonlinear terms introduced by the NES are transferred as the external excitations acting on the beam. The governing equations of the nonlinear beam with an inertial NES are derived according to the Lagrange equations and the assumed mode method. The linear and nonlinear frequencies of the beam are numerically obtained by the Rayleigh–Ritz method and the direct iteration method, respectively. The frequencies are verified by the results of the finite element analysis and literature. The responses of the beam under shock excitations and harmonic excitations are numerically solved by the fourth-order Runge–Kutta method. The suppression effect of the inertial NES on the transverse vibration of the beam is evaluated through the values of amplitude reduction and energy dissipation. In addition, a parametric analysis of the inertial NES is conducted to improve the vibration reduction effect of the NES on the beam.

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