Collective dynamics of periodic nonlinear oscillators under simultaneous parametric and external excitations

被引：21

作者：

Bitar, Diala ^{[1
]}

Kacem, Najib ^{[1
]}

Bouhaddi, Noureddine ^{[1
]}

Collet, Manuel ^{[2
]}

机构：

[1] Univ Franche Comte, FEMTO ST Inst, Dept Appl Mech, UMR 6174, F-25000 Besancon, France

[2] Ecole Cent Lyon, UMR 5513, LTDS, F-69134 Ecully, France

来源：

NONLINEAR DYNAMICS | 2015年 / 82卷 / 1-2期

关键词：

Collective dynamics; Nonlinear oscillators; Periodic structures; Asymptotic numerical method; Basins of attraction; WAVE-PROPAGATION; SIMULTANEOUS RESONANCES; INTEGRITY MEASURES; BAND-GAPS; SYSTEMS; CHAINS; VIBRATIONS; LATTICES; SOLITONS;

D O I：

10.1007/s11071-015-2194-y

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

The collective dynamics of a periodic structure of coupled Duffing-Van Der Pol oscillators is investigated under simultaneous external and parametric excitations. An analytico-computational model based on a perturbation technique, combined with standing wave decomposition and the asymptotic numerical method is developed for a finite number of coupled oscillators. The frequency responses and the basins of attraction are analyzed for the case of small arrays, demonstrating the importance of the multi-mode solutions and the robustness of their attractors. This model can be exploited to design periodic structure-based smart systems with high performance, by taking advantage of the multi-modes induced by the collective dynamics.

引用

页码：749 / 766

页数：18

共 48 条

[1] Nonlinear 2-DOFs Vibration Energy Harvester Based on Magnetic Levitation [J].

Abed, I. ;

Kacem, N. ;

Bouazizi, M. L. ;

Bouhaddi, N. .

SHOCK & VIBRATION, AIRCRAFT/AEROSPACE, AND ENERGY HARVESTING, VOL 9, 2015, :39-45

[2] Asymmetric vortex solitons in nonlinear periodic lattices [J].

Alexander, TJ ;

Sukhorukov, AA ;

Kivshar, YS .

PHYSICAL REVIEW LETTERS, 2004, 93 (06) :063901-1

[3]

[Anonymous], SPRINGER SERIES SOLI

[4] Analytical and Experimental Analysis of Bandgaps in Nonlinear one Dimensional Periodic Structures [J].

Boechler, Nicholas ;

Daraio, Chiara ;

Narisetti, Raj K. ;

Ruzzene, M. ;

Leamy, M. J. .

IUTAM SYMPOSIUM ON RECENT ADVANCES OF ACOUSTIC WAVES IN SOLIDS, 2010, 26 :209-+

[5]

Brillouin L., 1953, Wave Propagation in Periodic Structures: Electric Filters and Crystal Lattices, V2

[6] Electrically tunable collective response in a coupled micromechanical array [J].

Buks, E ;

Roukes, ML .

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, 2002, 11 (06) :802-807

[7] Dynamics of a weakly non-linear periodic chain [J].

Chakraborty, G ;

Mallik, AK .

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2001, 36 (02) :375-389

[8] A PATH-FOLLOWING TECHNIQUE VIA AN ASYMPTOTIC-NUMERICAL METHOD [J].

COCHELIN, B .

COMPUTERS & STRUCTURES, 1994, 53 (05) :1181-1192

[9] Floquet-Bloch decomposition for the computation of dispersion of two-dimensional periodic, damped mechanical systems [J].

Collet, M. ;

Ouisse, M. ;

Ruzzene, M. ;

Ichchou, M. N. .

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2011, 48 (20) :2837-2848

[10] Wave Motion Optimization in Periodically Distributed Shunted Piezocomposite Beam Structures [J].

Collet, M. ;

Cunefare, K. A. ;

Ichchou, M. N. .

JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES, 2009, 20 (07) :787-808

← 1 2 3 4 5 →