Next Article in Journal
Bonded-Particle Model with Nonlinear Elastic Tensile Stiffness for Rock-Like Materials
Next Article in Special Issue
Member Discrete Element Method for Static and Dynamic Responses Analysis of Steel Frames with Semi-Rigid Joints
Previous Article in Journal
A 3D Human Skeletonization Algorithm for a Single Monocular Camera Based on Spatial–Temporal Discrete Shadow Integration
Previous Article in Special Issue
Vibration Control of a Power Transmission Tower with Pounding Tuned Mass Damper under Multi-Component Seismic Excitations
Article Menu
Issue 7 (July) cover image

Export Article

Open AccessArticle
Appl. Sci. 2017, 7(7), 684; doi:10.3390/app7070684

Robustness Analysis of the Collective Nonlinear Dynamics of a Periodic Coupled Pendulums Chain

Department of Applied Mechanics, FEMTO-ST Institute, CNRS/UFC/ENSMM/UTBM, Univ. Bourgogne Franche-Comté, 25000 Besançon, France
*
Author to whom correspondence should be addressed.
Received: 2 June 2017 / Revised: 23 June 2017 / Accepted: 28 June 2017 / Published: 3 July 2017

Abstract

Perfect structural periodicity is disturbed in presence of imperfections. The present paper is based on a realistic modeling of imperfections, using uncertainties, to investigate the robustness of the collective nonlinear dynamics of a periodic coupled pendulums chain. A generic discrete analytical model combining multiple scales method and standing-wave decomposition is proposed. To propagate uncertainties through the established model, the generalized Polynomial Chaos Expansion is used and compared to the Latin Hypercube Sampling method. Effects of uncertainties are investigated on the stability and nonlinearity of two and three coupled pendulums chains. Results prove the satisfying approximation given by the generalized Polynomial Chaos Expansion for a significantly reduced computational time, with respect to the Latin Hypercube Sampling method. Dispersion analysis of the frequency responses show that the nonlinear aspect of the structure is strengthened, the multistability domain is wider, more stable branches are obtained and thus multimode solutions are enhanced. More fine analysis is allowed by the quantification of the variability of the attractors’ contributions in the basins of attraction. Results demonstrate benefits of presence of imperfections in such periodic structure. In practice, imperfections can be functionalized to generate energy localization suitable for several engineering applications such as vibration energy harvesting. View Full-Text
Keywords: nonlinear coupled pendulums; collective dynamics; robustness analysis; polynomial chaos expansion nonlinear coupled pendulums; collective dynamics; robustness analysis; polynomial chaos expansion
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Chikhaoui, K.; Bitar, D.; Kacem, N.; Bouhaddi, N. Robustness Analysis of the Collective Nonlinear Dynamics of a Periodic Coupled Pendulums Chain. Appl. Sci. 2017, 7, 684.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Appl. Sci. EISSN 2076-3417 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top