Global dynamics of a pipe conveying pulsating fluid in primary parametrical resonance: Analytical and numerical results from the nonlinear wave equation

Wu, Qiliang; Qi, Guoyuan

doi:10.1016/j.physleta.2019.02.019

Cited by 24 publications

(12 citation statements)

References 41 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

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“…Faramin and Ataei [20] analyzed the chaos of the satellite attitude via the Lyapunov exponents (LEs), designed a nonlinear robust control to suppress chaos, and confirmed its suppression using Melnikov's analysis. Generally, the Melnikov method affords the necessary conditions for the existence of chaotic motion [31][32][33][34]. In dynamic research, a typical rigid body is the gyrostat.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Analysis of Chaos and Bifurcations for the Attitude System of a Quadrotor Unmanned Aerial Vehicle

2019

Complexity

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A model of the attitude system for a quadrotor unmanned aerial vehicle (QUAV), assumed to be a rigid body, is developed. For specific parameter configurations, a chaotic region with a saddle and two stable node-focus equilibrium points is identified. The chaotic model provides an important reference for dynamic analysis and a challengeable task of controller design once the flight enters the chaotic region of parameters. The pitchfork bifurcation of the equilibrium points is provided. Rich dynamics of the system are revealed by two bifurcation regions, which demonstrates the diversity of the flight behaviors as the parameters vary. One bifurcation analysis is with respect to the speed of the front propeller and the speed difference of the front and left propellers, and another one is with respect to the speed of the front propeller and moment of inertia. The dynamic characteristics of the QUAV are further verified by the Casimir power bifurcations. The trajectories of three settings with different structural parameters are analyzed in detail. The stability of the QUAV is found to be enhanced for certain optimized values of the structural parameters. Finally, using the Casimir power and Lagrange multiplier method, a supremum bound of the chaotic attractor is presented.

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Stability and Nonlinear Response Analysis of Parametric Vibration for Elastically Constrained Pipes Conveying Pulsating Fluid

Hao

Ding

Mao

et al. 2022

Acta Mech. Solida Sin.

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Global dynamics of a pipe conveying pulsating fluid in primary parametrical resonance: Analytical and numerical results from the nonlinear wave equation

Cited by 24 publications

References 41 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

Modeling and Analysis of Chaos and Bifurcations for the Attitude System of a Quadrotor Unmanned Aerial Vehicle

Stability and Nonlinear Response Analysis of Parametric Vibration for Elastically Constrained Pipes Conveying Pulsating Fluid

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