Authors: Karličić, Danilo 
Cajić, Milan 
Paunović, Stepa 
Adhikari, Sondipon
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Periodic response of a nonlinear axially moving beam with a nonlinear energy sink and piezoelectric attachment
Journal: International Journal of Mechanical Sciences
Issue Date: 1-Apr-2021
Rank: ~M21a
ISSN: 0020-7403
DOI: 10.1016/j.ijmecsci.2020.106230
An efficient semi-numerical framework is used in this paper to analyze the dynamic model of an axially moving beam with a nonlinear attachment composed of a nonlinear energy sink and a piezoelectric device. The governing equations of motion of the system are derived by using the Hamilton's principle with von Karman strain-displacement relation and Euler - Bernoulli beam theory. The nonlinear energy sink is modeled as a lumped - mass system composed of a point mass, a spring with nonlinear cubic stiffness and a linear viscous damping element. The piezoelectric device is placed in the ground configuration. Frequency response curves of the presented nonlinear system are determined by introducing the incremental harmonic balance and continuation method for different values of material parameters. Based on the Floquet theory, the stability of periodic solutions was determined. Moreover, the presented results are validated with the results obtained by a numerical method as well as the results from the literature. Numerical examples show a significant effect of the nonlinear attachment on frequency response diagrams and vibration amplitude reduction of the primary beam structure.
Keywords: Axially moving beam | Frequency response | Incremental harmonic balance | Nonlinear energy sink | Vibration attenuation
Publisher: Elsevier

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