Global bifurcations and chaotic dynamics for a string-beam coupled system

Cao, Dongxing; Zhang, W.

doi:10.1016/j.chaos.2006.09.072

Cited by 40 publications

(22 citation statements)

References 26 publications

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“…[ [27][28][29] regarding the behavior of vibrations and occurrence of jump phenomena and multi-valued amplitudes. (7) From the force response curve we concluded that, the region of multi-valued amplitude is increased for increasing values of ω 1 , ω 2 , α 14 , α 21 , σ and disappear for increasing μ 1 , μ 2 .…”

Section: Discussionmentioning

confidence: 99%

“…[27,28], we can obtain the following nonlinear ordinary differential governing equations (ODE) of motion for the string-beam coupled system under external, parametric and tuned excitation forces with two degrees of freedom…”

Section: Equations Of Motions and Perturbation Analysismentioning

confidence: 99%

“…(6) and (7) and more details can be found in Refs. [27,28]. The damping coefficients, nonlinear parameters and the forcing amplitudes are assumed to be 11 , εα 13 , εα 14 , εα 21 , εα 22 , εα 23 , εα 24 , εβ 21 , εβ 22 , εβ 23 , εf 2 , εf 11 , εf 12 , εf 3 }, (8) where ε is a small perturbation parameter and 0 < ε ≤ 1.…”

Section: Equations Of Motions and Perturbation Analysismentioning

confidence: 99%

“…Zhang et al [26] investigated the global bifurcations and chaotic dynamics in a rotoractive magnetic bearings system with time-varying stiffness using a global perturbation method. Zhang and Cao [27,28] investigated the global bifurcations and chaotic dynamics of a string-beam coupled system subjected to parametric and external excitations. Phase portrait, waveform, and Poincare map were applied to study the periodic and chaotic motions.…”

Section: Introductionmentioning

confidence: 99%

“…In comparison with the previous works of a stringbeam [27,28], the global bifurcations and chaotic dynamics of a string-beam coupled system subjected to parametric and external excitations are investigated with 1 : 2 internal resonances. The bifurcation analysis indicates that the string-beam coupled system can undergo pitchfork bifurcation, homoclinic bifurcations and the Silnikov type singlepulse homoclinic orbit.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear study of the dynamic behavior of a string-beam coupled system under combined excitations

et al. 2011

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In this paper, the nonlinear dynamic behavior of a string-beam coupled system subjected to external, parametric and tuned excitations is presented. The governing equations of motion are obtained for the nonlinear transverse vibrations of the string-beam coupled system which are described by a set of ordinary differential equations with two degrees of freedom. The case of 1:1 internal resonance between the modes of the beam and string, and the primary and combined resonance for the beam is considered. The method of multiple scales is utilized to analyze the nonlinear responses of the string-beam coupled system and obtain approximate solutions up to and including the second-order approximations. All resonance cases are extracted and investigated. Stability of the system is studied using frequency response equations and the phase-plane method. Numerical solutions are carried out and the results are presented graphically and discussed. The effects of the different parameters on both response and stability of the system are investigated. The reported results are compared to the available published work.

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Section: Discussionmentioning

confidence: 99%

Section: Equations Of Motions and Perturbation Analysismentioning

confidence: 99%

Section: Equations Of Motions and Perturbation Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear study of the dynamic behavior of a string-beam coupled system under combined excitations

et al. 2011

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Global bifurcations and single‐pulse homoclinic orbits of a plate subjected to the transverse and in‐plane excitations

Zhang

Chen

2017

Math Methods in App Sciences

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Communicated by T. WannerThe Shilnikov-type single-pulse homoclinic orbits and chaotic dynamics of a simply supported truss core sandwich plate subjected to the transverse and the in-plane excitations are investigated in detail. The resonant case considered here is principal parametric resonance and 1:2 internal resonance. Based on the normal form theory, the desired form for the global perturbation method is obtained. By using the global perturbation method developed by Kovacic and Wiggins, explicit sufficient conditions for the existence of a Shilnikov-type homoclinic orbit are obtained, which implies that chaotic motions may occur for this class of truss core sandwich plate in the sense of Smale horseshoes. Numerical results obtained by using the fourth-order Runge-Kutta method agree with theoretical analysis at least qualitatively.It is not difficult to show that, when the condition 3 2ˇ2 4 fI r cos c > 0 is satisfied, the fixed point p 0 is a center, and when the condition 3 2ˇ2 4 fI r cos s < 0 is satisfied, the fixed point q 0 is a saddle, which is connected to itself by a homoclinic orbit. The phase portrait of system (37) is given in Figure 3(a). Following the analysis presented by Kovacic and Wiggins, it is found that for sufficiently small , the

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Numerical and Experimental Modal Analysis of a Cantilever Beam Axially Loaded by a Tendon Which Is Attached in a Single Spanwise Location

Ondra

Titurus

2019

Topics in Modal Analysis &Amp; Testing, Volume 8

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Global bifurcations and chaotic dynamics for a string-beam coupled system

Cited by 40 publications

References 26 publications

Nonlinear study of the dynamic behavior of a string-beam coupled system under combined excitations

Nonlinear study of the dynamic behavior of a string-beam coupled system under combined excitations

Global bifurcations and single‐pulse homoclinic orbits of a plate subjected to the transverse and in‐plane excitations

Numerical and Experimental Modal Analysis of a Cantilever Beam Axially Loaded by a Tendon Which Is Attached in a Single Spanwise Location

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