Bifurcation analysis of an arch structure with parametric and forced excitation

Chen, Fangqi; Liang, Jianshu; Chen, Yushu; Liu, Xijun; Ma, Huili

doi:10.1016/j.mechrescom.2005.09.008

Cited by 14 publications

(8 citation statements)

References 2 publications

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“…where 1 and 2 are the phase angles. Substituting (12) into (11a) and (11b) and separating the real and imaginary part, the four-dimensional averaged equation in polar form is obtained aṡ1…”

Section: The Motion Equations and Perturbation Analysismentioning

confidence: 99%

“…Jin and Zou [11] applied singularity theory to a restrained pipe conveying fluid and obtained the dynamical behavior in different persistent regions. Chen et al [12] gave bifurcation analysis of an arch structure of parametric and forced excitation with codimension 5. Li et al [13] extended Lyapunov-Schmidt 2 Mathematical Problems in Engineering reduction to fractional ordinary differential systems (FODSs) with Caputo derivatives.…”

Section: Introductionmentioning

confidence: 99%

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Bifurcation Analysis of Composite Laminated Piezoelectric Rectangular Plate Structure in the Case of 1:2 Internal Resonance

Guo

Zhang

2019

Mathematical Problems in Engineering

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In this paper, the authors study the bifurcation problems of the composite laminated piezoelectric rectangular plate structure with three bifurcation parameters by singularity theory in the case of 1:2 internal resonance. The sign function is employed to the universal unfolding of bifurcation equations in this system. The proposed approach can ensure the nondegenerate conditions of the universal unfolding of bifurcation equations in this system to be satisfied. The study presents that the proposed system with three bifurcation parameters is a high codimensional bifurcation problem with codimension 4, and 6 forms of universal unfolding are given. Numerical results show that the whole parametric plane can be divided into several persistent regions by the transition set, and the bifurcation diagrams in different persistent regions are obtained.

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Section: The Motion Equations and Perturbation Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis of Composite Laminated Piezoelectric Rectangular Plate Structure in the Case of 1:2 Internal Resonance

Guo

Zhang

2019

Mathematical Problems in Engineering

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“…(34), we obtain [25] and [26], we can know that the codimension of the germ gða; fÞ ¼ a 4 þ f 2 is 5 and its universal unfolding is unique.…”

Section: Subharmonic Resonance Singularity Theory Analysis Of Axiallymentioning

confidence: 99%

Strongly Nonlinear Subharmonic Resonance and Chaotic Motion of Axially Moving Thin Plate in Magnetic Field

Jinzhi

2015

Journal of Computational and Nonlinear Dynamics

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In this paper, the nonlinear vibration and chaotic motion of the axially moving currentconducting thin plate under external harmonic force in magnetic field is studied. Improved multiple-scale method is employed to derive the strongly nonlinear subharmonic resonance bifurcation-response equation of the strip thin plate in transverse magnetic field. By using the singularity theory, the corresponding transition variety and bifurcation, which contain two parameters of the universal unfolding for this nonlinear system, are obtained. Numerical simulations are carried out to plot the bifurcation diagrams, corresponding maximum Lyapunov exponent diagrams, and dynamical response diagrams with respect to the bifurcation parameters such as magnetic induction intensity, axial tension, external load, external excited frequency, and axial speed. The influences of different bifurcation parameters on period motion, period times motion, and chaotic motion behaviors of subharmonic resonance system are analyzed. The results show that the complex dynamic behaviors of resonance system can be controlled by changing the corresponding parameters.

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“…Taking the germ that g 0 (a, ζ ) = a 4 + ζ 2 , where its codimension is 5, we have the universal unfolding [37,38] G(a, ζ, α 1 , α 2 , α 3 , α 4 , α 5 ) = a 4 + ζ 2 + α 1 a 2 ζ + α 2 aζ + α 3 a 2 + α 4 a + α 5 (21) where α 1 , α 2 , α 3 , α 4 , and α 5 are unfolding parameters. It is very difficult to discuss the bifurcation behavior of (21) in full detail.…”

Section: Local Bifurcationmentioning

confidence: 99%

The bifurcation analysis on the circular functionally graded plate with combination resonances

Zhang

2011

Nonlinear Dyn

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The bifurcation and chaos of a clamped circular functionally graded plate is investigated. Considered the geometrically nonlinear relations and the temperature-dependent properties of the materials, the nonlinear partial differential equations of FGM plate subjected to transverse harmonic excitation and thermal load are derived. The Duffing nonlinear forced vibration equation is deduced by using Galerkin method and a multiscale method is used to obtain the bifurcation equation. According to singularity theory, the universal unfolding problem of the bifurcation equation is studied and the bifurcation diagrams are plotted under some conditions for unfolding parameters. Numerical simulation of the dynamic bifurcations of the FGM plate is carried out. The influence of the period doubling bifurcation and chaotic motion with the change of an external excitation are discussed.

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Bifurcation analysis of an arch structure with parametric and forced excitation

Cited by 14 publications

References 2 publications

Bifurcation Analysis of Composite Laminated Piezoelectric Rectangular Plate Structure in the Case of 1:2 Internal Resonance

Bifurcation Analysis of Composite Laminated Piezoelectric Rectangular Plate Structure in the Case of 1:2 Internal Resonance

Strongly Nonlinear Subharmonic Resonance and Chaotic Motion of Axially Moving Thin Plate in Magnetic Field

The bifurcation analysis on the circular functionally graded plate with combination resonances

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