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Article

Nonlinear Dynamic Response of Ropeway Roller Batteries via an Asymptotic Approach

Department of Structural and Geotechnical Engineering, Sapienza University of Rome, 00184 Rome, Italy
Academic Editor: Angelo Luongo
Appl. Sci. 2021, 11(20), 9486; https://doi.org/10.3390/app11209486
Received: 17 September 2021 / Revised: 5 October 2021 / Accepted: 7 October 2021 / Published: 13 October 2021
The nonlinear dynamic features of compression roller batteries were investigated together with their nonlinear response to primary resonance excitation and to internal interactions between modes. Starting from a parametric nonlinear model based on a previously developed Lagrangian formulation, asymptotic treatment of the equations of motion was first performed to characterize the nonlinearity of the lowest nonlinear normal modes of the system. They were found to be characterized by a softening nonlinearity associated with the stiffness terms. Subsequently, a direct time integration of the equations of motion was performed to compute the frequency response curves (FRCs) when the system is subjected to direct harmonic excitations causing the primary resonance of the lowest skew-symmetric mode shape. The method of multiple scales was then employed to study the bifurcation behavior and deliver closed-form expressions of the FRCs and of the loci of the fold bifurcation points, which provide the stability regions of the system. Furthermore, conditions for the onset of internal resonances between the lowest roller battery modes were found, and a 2:1 resonance between the third and first modes of the system was investigated in the case of harmonic excitation having a frequency close to the first mode and the third mode, respectively. View Full-Text
Keywords: ropeways; nonlinear dynamics; asymptotic analysis; primary resonances; internal resonances ropeways; nonlinear dynamics; asymptotic analysis; primary resonances; internal resonances
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MDPI and ACS Style

Arena, A. Nonlinear Dynamic Response of Ropeway Roller Batteries via an Asymptotic Approach. Appl. Sci. 2021, 11, 9486. https://doi.org/10.3390/app11209486

AMA Style

Arena A. Nonlinear Dynamic Response of Ropeway Roller Batteries via an Asymptotic Approach. Applied Sciences. 2021; 11(20):9486. https://doi.org/10.3390/app11209486

Chicago/Turabian Style

Arena, Andrea. 2021. "Nonlinear Dynamic Response of Ropeway Roller Batteries via an Asymptotic Approach" Applied Sciences 11, no. 20: 9486. https://doi.org/10.3390/app11209486

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