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Research Papers

Nonlinear Resonances of Chains of Thin Elastic Beams With Intermittent Contact

[+] Author and Article Information
Akira Saito

Department of Mechanical Engineering,
Meiji University,
Kawasaki 214-8571,
Kanagawa, Japan
e-mail: asaito@meiji.ac.jp

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 23, 2017; final manuscript received June 7, 2018; published online July 2, 2018. Assoc. Editor: Eihab Abdel-Rahman.

J. Comput. Nonlinear Dynam 13(8), 081005 (Jul 02, 2018) (10 pages) Paper No: CND-17-1576; doi: 10.1115/1.4040540 History: Received December 23, 2017; Revised June 07, 2018

This paper deals with the forced response analysis of chains of thin elastic beams that are subject to periodic external loading and frictionless intermittent contact between the beams. Our study shows that the beams show nonlinear resonances whose frequencies are the same as the linear resonant frequencies if all the beams have the same stiffness. Furthermore, it is also shown that small gaps between the beams and small deviation or mistuning in the stiffness of each beam can cause drastic changes in the nonlinear resonant frequencies of the system dynamics. The system is modeled as a semidiscrete system of piecewise-linear oscillators with multiple degrees-of-freedom (DOF) that are subject to unilateral constraints, which is derived from a finite element discretization of the beams. The resulting equations of motions are solved by a second-order numerical integration scheme, and steady-state solutions are sought for various driving frequencies. Results of parametric studies with respect to the gaps between the beams and the number of beams are presented to discuss how these parameters affect the resonant behavior of the system.

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Figures

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Fig. 1

Schematics of the chain of beams with unilateral constraints

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Fig. 2

Convergence study with respct to time-step size

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Fig. 3

Forced response of the chain of tuned beams without contact nonlinearities: (a) nb = 2 and (b) nb = 6

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Fig. 4

Forced response of the chain of tuned beams with contact nonlinearities: (a) nb = 2 and (b) nb = 6

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Fig. 5

Spectral distribution of the tip displacement (i = 1) for the chain of tuned beams with contact nonlinearities: (a) nb = 2 and (b) nb = 6

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Fig. 6

Time histories of gap functions for the chain of tuned beams with contact nonlinearities: (a) nb = 2 and (b) nb = 6

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Fig. 7

Forced response of the chain of mistuned beams without contact nonlinearities: (a) nb = 2 and (b) nb = 6

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Fig. 8

Forced response for mistuned beams with contact nonlinearities: (a) nb = 2 and (b) nb = 6

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Fig. 9

Spectral distribution of the tip displacement (i = 1) for mistuned beams with contact nonlinearities: (a) nb = 2 and (b) nb = 6

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Fig. 10

Time histories of gap functions for the chain of mistuned beams with contact nonlinearities: (a) nb = 2 and (b) nb = 6

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Fig. 11

Forced response for tuned beams with contact nonlinearities and gaps: (a) nb = 2 and (b) nb = 6

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Fig. 12

Spectral distribution of the tip displacement (i = 1) for tuned beams with contact nonlinearities and gaps: (a) nb = 2 and (b) nb = 6

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Fig. 13

Time histories of gap functions for the chain of tuned beams with contact nonlinearities and gaps: (a) nb = 2 and (b) nb = 6

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Fig. 14

Forced response of the chain of mistuned beams with contact nonlinearities and gaps: (a) nb = 2 and (b) nb = 6

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Fig. 15

Spectral distribution of the tip displacement (i = 1) for mistuned beams with contact nonlinearities and gaps: (a) nb = 2 and (b) nb = 6

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Fig. 16

Time histories of gap functions for the chain of mistuned beams with contact nonlinearities and gaps: (a) nb = 2 and (b) nb = 6

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Fig. 17

Forced responses of the chains of mistuned beams for various forcing levels

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