Homoclinic bifurcations and chaotic dynamics of non-planar waves in axially moving beam subjected to thermal load

Wu, Qiliang; Qi, Guoyuan

doi:10.1016/j.apm.2020.03.013

Cited by 28 publications

(13 citation statements)

References 30 publications

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“…e first and second measurements are then applied to explore the homoclinic chaos and the chaotic threshold for the wave equation. Afterward, numerical examples are also carried out using the differential quadrature method [27][28][29]. e simulating results confirm the validity of the theoretical prediction and illustrate larger damping coefficient resulting in the more complicated dynamical behaviors of the GBE.…”

Section: Introductionsupporting

confidence: 55%

“…According to [27][28][29][30], the second measurement, called as the geometric analysis (Figure 3(b)), is described as…”

Section: Second Measurementmentioning

confidence: 99%

“…To test the aforementioned chaotic threshold (25), the differential quadrature method [27][28][29] in MATLAB is employed using equation (1) to study the influence of the damping coefficient μ on the nonlinear dynamical behaviors Figure 2: e exact form of the heteroclinic orbit for equation (17).…”

Section: Numerical Simulationmentioning

confidence: 99%

“…e persistent homoclinic orbits of nonlinear Schrödinger (NLS) and sine-Gordon (SG) equations were constructed by using invariant manifolds, foliations, and Melnikov analysis. Furthermore, Zhang et al [27], Wu and Qi [28,29], and Li et al [30] improved the analytic theory for infinite-dimensional systems [23][24][25][26] to obtain the chaotic threshold of mechanical systems such as truss core sandwich plates, pipes conveying fluid, axial moving beams, and carbon nanotubes. e aforementioned literature focused on solid structure systems; however, analysis on global dynamics for fluid systems, e.g., GBE, remains lacking.…”

Section: Introductionmentioning

confidence: 99%

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Analytical and Numerical Results on Global Dynamics of the Generalized Boussinesq Equation with Cubic Nonlinearity and External Excitation

Zhang

2021

Mathematical Problems in Engineering

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This paper analytically and numerically presents global dynamics of the generalized Boussinesq equation (GBE) with cubic nonlinearity and harmonic excitation. The effect of the damping coefficient on the dynamical responses of the generalized Boussinesq equation is clearly revealed. Using the reductive perturbation method, an equivalent wave equation is then derived from the complex nonlinear equation of the GBE. The persistent homoclinic orbit for the perturbed equation is located through the first and second measurements, and the breaking of the homoclinic structure will generate chaos in a Smale horseshoe sense for the GBE. Numerical examples are used to test the validity of the theoretical prediction. Both theoretical prediction and numerical simulations demonstrate the homoclinic chaos for the GBE.

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Section: Introductionsupporting

confidence: 55%

“…According to [27][28][29][30], the second measurement, called as the geometric analysis (Figure 3(b)), is described as…”

Section: Second Measurementmentioning

confidence: 99%

Section: Numerical Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analytical and Numerical Results on Global Dynamics of the Generalized Boussinesq Equation with Cubic Nonlinearity and External Excitation

Zhang

2021

Mathematical Problems in Engineering

Self Cite

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“…The latter can be addressed by the so-called Melnikov function and Poincaré portrait analysis. [54][55][56][57][58] In the driven system, the unstable equilibrium turns into an unstable periodic orbit. To calculate the Melnikov function, the heteroclinic and homoclinic solutions are necessary inputs.…”

Section: Chaosmentioning

confidence: 99%

Chaotic motion due to lateral Casimir forces during nonlinear actuation dynamics

Tajik

Masoudi

Sedighi

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Nonlinear dynamic and stability of a small size moving beam under thermal conditions

Ali

2023

Math Methods in App Sciences

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Nonlinear transverse vibration of a micro‐size moving beam like structure under the influence of thermal conditions is studied. Hamilton principle is used to derive the nonlinear equation of motion. The derived equation of transverse motion is discretized using the Galerkin technique. The vibration attributes of the moving beam, such as frequencies of the transverse response, time response, and stability analysis, are investigated at different temperatures. For stability analysis, bifurcation diagrams are presented under the influence of temperature, length‐scale parameter, and excitation frequencies at various axial speeds of the beam.

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Homoclinic bifurcations and chaotic dynamics of non-planar waves in axially moving beam subjected to thermal load

Cited by 28 publications

References 30 publications

Analytical and Numerical Results on Global Dynamics of the Generalized Boussinesq Equation with Cubic Nonlinearity and External Excitation

Analytical and Numerical Results on Global Dynamics of the Generalized Boussinesq Equation with Cubic Nonlinearity and External Excitation

Chaotic motion due to lateral Casimir forces during nonlinear actuation dynamics

Nonlinear dynamic and stability of a small size moving beam under thermal conditions

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