scholarly journals Temperature Effects on Dynamic Properties of Suspended Cables Subjected to Dual Harmonic Excitations

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Yaobing Zhao ◽  
Panpan Zheng ◽  
Henghui Lin ◽  
Chaohui Huang
Keyword(s):  
Thermal Effects ◽  
Dynamic Properties ◽  
Time History ◽  
Excitation Amplitude ◽  
Phase Portraits ◽  
Temperature Variations ◽  
Thermal Environments ◽  
Dynamical Behaviors ◽  
Harmonic Excitations ◽  
Suspended Cables

The paper aims at studying the influences of temperature on the suspended cables’ dynamical behaviors subjected to dual harmonic excitations in thermal environments. Significantly, the quadratic nonlinearity and the corresponding secondary resonances are considered. By introducing a tension variation factor, the nonlinear vibration equations of motion could be obtained based on the condensation model. By using Galerkin’s procedure, the continuous model of the nonlinear system is reduced to a set of infinite models with quadratic and cubic nonlinearities. By using the multiple scales method, the resultant reduced model is solved and the stability analysis is also presented in two simultaneous resonance cases. Nonlinear dynamical behaviors with thermal effects are presented using bifurcation diagrams, time-history curves, phase portraits, frequency spectrums, and Poincaré sections. The numerical results show that thermal effects induce different scenarios. The sensitivities of linear (natural frequency) and nonlinear (quadratic and cubic) coefficients to temperature variations are different. The temperature may increase or decrease the response amplitudes depending on the excitation amplitude and the sag-to-span ratio. The inflection point is shifted and exhibited at a smaller or larger excitation amplitude in thermal environments. The resonant range between two Pitchfork bifurcations seems to be reduced when the temperature is decreasing. The response amplitude is very sensitive to temperature, and even an opposite spring behavior may be exhibited due to warming/cooling conditions. However, the periodic motions seem independent of temperature variations.

Nonlinear Dynamics of Suspended Cables under Periodic Excitation in Thermal Environments: Two-to-One Internal Resonance

2021 ◽  
Vol 31 (10) ◽  
pp. 2150153
Author(s):  
Yaobing Zhao ◽  
Henghui Lin
Keyword(s):  
Thermal Effects ◽  
Numerical Solutions ◽  
Time History ◽  
Phase Portraits ◽  
Periodic Excitation ◽  
Internal Resonances ◽  
Chaotic Motions ◽  
Temperature Changes ◽  
Thermal Environments ◽  
Suspended Cables

The temperature change is a non-negligible factor in examining the vibration behaviors of the cable structures. For this reason, the paper aims at investigating the thermal effects on suspended cables’ resonant responses considering two-to-one internal resonances. Firstly, a nonlinear continuous condensed model of the suspended cable under periodic excitation in thermal environments is adopted. Then, a multidimensional discretized model is constructed via the Galerkin method. Following the multiple scaling procedure, the modulation equations with both polar and Cartesian forms are obtained, which are solved numerically. A complete dynamic scenario is presented through bifurcation diagrams, phase portraits, time history curves, Fourier spectra, and Poincaré sections in three internal resonant cases. Numerical examples show that a small change in the static configuration due to thermal effects induces some noticeable changes in dynamic behaviors. The response amplitude, the nonlinear spring behavior, the resonant and stability region, the multi-periodic and chaotic motions are all dependent on temperature changes. Additional Hopf bifurcations might be found due to temperature changes, and it may lead to some more complicated dynamic characteristics. A good agreement between the perturbation and numerical solutions is observed to confirm the results’ correctness and accuracy.

scholarly journals Parametric and Internal Resonances of an Axially Moving Beam with Time-Dependent Velocity

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Bamadev Sahoo ◽  
L. N. Panda ◽  
G. Pohit
Keyword(s):  
Internal Resonance ◽  
Multiple Scales ◽  
Time History ◽  
Mean Value ◽  
Phase Portraits ◽  
Axially Moving Beam ◽  
Internal Resonances ◽  
Moving Beam ◽  
Axially Moving ◽  
The Stability

The nonlinear vibration of a travelling beam subjected to principal parametric resonance in presence of internal resonance is investigated. The beam velocity is assumed to be comprised of a constant mean value along with a harmonically varying component. The stretching of neutral axis introduces geometric cubic nonlinearity in the equation of motion of the beam. The natural frequency of second mode is approximately three times that of first mode; a three-to-one internal resonance is possible. The method of multiple scales (MMS) is directly applied to the governing nonlinear equations and the associated boundary conditions. The nonlinear steady state response along with the stability and bifurcation of the beam is investigated. The system exhibits pitchfork, Hopf, and saddle node bifurcations under different control parameters. The dynamic solutions in the periodic, quasiperiodic, and chaotic forms are captured with the help of time history, phase portraits, and Poincare maps showing the influence of internal resonance.

scholarly journals Nonlinear Dynamics and Chaos in Fractional-Order Hopfield Neural Networks with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xia Huang ◽  
Zhen Wang ◽  
Yuxia Li
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Fractional Order ◽  
Hopfield Neural Network ◽  
Hopfield Neural Networks ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Chaotic Motions ◽  
Dynamical Behaviors ◽  
Nonlinear Dynamics And Chaos

A fractional-order two-neuron Hopfield neural network with delay is proposed based on the classic well-known Hopfield neural networks, and further, the complex dynamical behaviors of such a network are investigated. A great variety of interesting dynamical phenomena, including single-periodic, multiple-periodic, and chaotic motions, are found to exist. The existence of chaotic attractors is verified by the bifurcation diagram and phase portraits as well.

Random Disordered Periodical Input Induced Chaos in Discontinuous Systems

2019 ◽  
Vol 29 (01) ◽  
pp. 1950002 ◽  
Author(s):  
Di Liu ◽  
Yong Xu
Keyword(s):  
Noise Intensity ◽  
Stochastic Systems ◽  
Time History ◽  
Phase Portraits ◽  
System Response ◽  
Unperturbed System ◽  
Discontinuous Systems ◽  
Stable And Unstable Manifolds ◽  
Stochastic Force ◽  
Onset Of Chaos

In this paper, we extend the random Melnikov method from stochastic systems with a continuous vector field to discontinuous systems driven by a random disordered periodic input under the assumption that the unperturbed system is a piecewise Hamiltonian system. By measuring the distance of the perturbed stable and unstable manifolds, the nonsmooth random Melnikov process can be derived in detail, and then the mean square criterion for the onset of chaos is established in the statistical sense. It is shown that the threshold for the onset of chaos depends on the stochastic force and a scalar function of hypersurface. Finally, an example is given to analyze the chaotic dynamics using this extended approach, and discuss the effects of noise intensity on the dynamical behaviors of the system. The results indicate that the increase of the noise intensity will result in a chaotic motion of the discontinuous stochastic system and the changes of possible chaotic degree in the phase space. At the same time, the effects of noise intensity on chaos are further investigated through the system response including time history and phase portraits, Poincaré maps and [Formula: see text]-[Formula: see text] test.

Effects of temperature variations on the dynamics of microtubules

2019 ◽  
Vol 33 (34) ◽  
pp. 1950433
Author(s):  
M. C. Ekosso ◽  
A. J. Fotue ◽  
S. C. Kenfack ◽  
H. Fotsin ◽  
L. C. Fai
Keyword(s):  
Wave Function ◽  
Biological Activity ◽  
Environmental Temperature ◽  
Hybrid Structures ◽  
Self Organization ◽  
Intrinsic Parameter ◽  
Temperature Variations ◽  
Dynamical Behaviors ◽  
Effects Of Temperature ◽  
Increasing Functions

Cells actively modify their behavior in on account of changes in their environment. The most important intrinsic parameter related to the intracellular environment is the temperature, the variations of which modify the dynamical behaviors of biomolecules. Indeed, an increase in temperature leads to an increase in fluidity which can damage the proteinous membrane and induce cellular death. If the temperature is extremely high, the proteins can be broken down or denatured as a consequence. However, concerning microtubules (MTs), we show that by their intrinsic behavior of self-organization, they are able to modulate temperature variations in order to avoid denaturation for values of temperature up to [Formula: see text]. Above this temperature, there is a critical point at [Formula: see text] where the wave function completely disappears which is indicative of denaturation as the biological activity of the neuronal MTs is lost. We show that temperature variations change the viscosity of the cytosol which modifies the wave function and give rise to hybrid soliton structures. These hybrid solitons come from the collision of waves propagating along MTs. We also show that the supersonic velocity of these hybrid structures can be decreasing or increasing functions of environmental temperature.

Various Attractors, Coexisting Attractors and Antimonotonicity in a Simple Fourth-Order Memristive Twin-T Oscillator

2018 ◽  
Vol 28 (04) ◽  
pp. 1850050 ◽  
Author(s):  
Ling Zhou ◽  
Chunhua Wang ◽  
Xin Zhang ◽  
Wei Yao
Keyword(s):  
Fourth Order ◽  
Chaotic Systems ◽  
Basin Of Attraction ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Coexisting Attractors ◽  
Dynamical Behaviors ◽  
Random Bit Generator ◽  
In Series ◽  
Dynamical Features

By replacing the resistor in a Twin-T network with a generalized flux-controlled memristor, this paper proposes a simple fourth-order memristive Twin-T oscillator. Rich dynamical behaviors can be observed in the dynamical system. The most striking feature is that this system has various periodic orbits and various chaotic attractors generated by adjusting parameter [Formula: see text]. At the same time, coexisting attractors and antimonotonicity are also detected (especially, two full Feigenbaum remerging trees in series are observed in such autonomous chaotic systems). Their dynamical features are analyzed by phase portraits, Lyapunov exponents, bifurcation diagrams and basin of attraction. Moreover, hardware experiments on a breadboard are carried out. Experimental measurements are in accordance with the simulation results. Finally, a multi-channel random bit generator is designed for encryption applications. Numerical results illustrate the usefulness of the random bit generator.

Simultaneous Resonances of Suspended Cables Subjected to Primary and Super-Harmonic Excitations in Thermal Environments

2019 ◽  
Vol 19 (12) ◽  
pp. 1950155
Author(s):  
Yaobing Zhao ◽  
Henghui Lin ◽  
Lincong Chen ◽  
Chenfei Wang
Keyword(s):  
Perturbation Method ◽  
Multiple Scales ◽  
Effect Of Temperature ◽  
Response Curves ◽  
Temperature Changes ◽  
Poincaré Sections ◽  
Thermal Environments ◽  
Direct Integration Method ◽  
Harmonic Excitations ◽  
Poincare Sections

This paper concerns with a suspended cable in thermal environments under bi-frequency harmonic excitations, with a focus placed on the effect of temperature changes on one type of simultaneous resonance. First, the nonlinear equation of motion in thermal environments is obtained for the in-plane displacement of the cable. Then, the Galerkin method is employed to reduce the partial differential equation to an ordinary one. Second, based on the discretized form of the governing equation, the method of multiple scales is employed to obtain the second-order approximate solutions, with the stability characteristics determined. Third, numerical results are presented by using the perturbation method, together with numerical integration by the following means: frequency-response curves, time-displacement curves, phase-plane diagrams, and Poincare sections. The direct integration method is utilized to verify the results obtained by the perturbation method, while revealing more nonlinear dynamic behaviors induced by temperature changes. Both the softening and/or hardening behaviors, and the switching between them are observed for the cable in thermal environments. The response amplitude of the cable is very sensitive to temperature changes, but the number of circles in the phase diagrams and the number of cluster points in Poincaré sections is independent of the thermal effects in most cases. Finally, the vibration characteristics of the cable for different thermal expansion coefficients and temperature-dependent Young’s moduli are also investigated.

Nonlinear planar secondary resonance analyses of suspended cables with thermal effects

2019 ◽  
Vol 42 (12) ◽  
pp. 1515-1534 ◽  
Author(s):  
Yaobing Zhao ◽  
Chaohui Huang ◽  
Lincong Chen
Keyword(s):  
Thermal Effects ◽  
Secondary Resonance ◽  
Suspended Cables

Aseismic Structural Systems for Buildings

2006 ◽  
Vol 1 (3) ◽  
pp. 358-377 ◽  
Author(s):  
Makoto Watabe ◽  
Keyword(s):  
Simple Structure ◽  
Dynamic Properties ◽  
Time History ◽  
Structural Systems ◽  
Initial Displacement ◽  
Single Degree Of Freedom ◽  
Principal Factors ◽  
History Of ◽  
Circular Frequency ◽  
General Dynamic

When structures are subjected to earthquake motions, the principal factors controlling their behavior are i) dynamic characteristics of the structure ii) characteristics of the input earthquake motions. In this sense, it is essential, first of all, to be acquainted with general dynamic properties. Let the simple structure – single degree of freedom system – as illustrated in Fig. 1 be considered. Spring, mass, and damper are the three elements which characterize the system. If to this system, an initial displacement is applied, then set it free, the time history of the displacement, velocity and acceleration will be as shown in Fig. 2. In Fig. 2 the basic concepts of period, frequency and circular frequency of the system are also explained.

Subharmonic Bifurcations and Transition to Chaos in a Pipe Conveying Fluid under Harmonic Excitation

2013 ◽  
Vol 444-445 ◽  
pp. 791-795
Author(s):  
Yi Xiang Geng ◽  
Han Ze Liu
Keyword(s):  
Chaotic Behavior ◽  
Melnikov Method ◽  
Harmonic Excitation ◽  
Phase Portraits ◽  
Pipe Conveying Fluid ◽  
Bifurcation Diagrams ◽  
Dynamical Behaviors ◽  
Transition To Chaos ◽  
Subharmonic Bifurcations ◽  
Conveying Fluid

The subharmonic and chaotic behavior of a two end-fixed fluid conveying pipe whose base is subjected to a harmonic excitation are investigated. Melnikov method is applied for the system, and Melnikov criterions for subharmonic and homoclinic bifurcations are obtained analytically. The numerical simulations (including bifurcation diagrams, maximal Lyapunov exponents, phase portraits and Poincare map) confirm the analytical predictions and exhibit the complicated dynamical behaviors.

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