Nonlinear vibration behaviors of suspended cables under two-frequency excitation with temperature effects

Zhao, Yaobing; Huang, Chaohui; Chen, Lincong; Jian, Peng

doi:10.1016/j.jsv.2017.11.035

Cited by 38 publications

(15 citation statements)

References 30 publications

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“…Recently, based on Hamilton's principle, temperature effects on the vibration behaviors of the cable-stayed-beam by introducing two nondimensional factors were investigated by Zhao et al [33]. The nonlinear free and forced vibration characteristics of the suspended cable were studied by Zhao et al [34,35].…”

Section: Introductionmentioning

confidence: 99%

Temperature Effects on Nonlinear Vibration Behaviors of Euler‐Bernoulli Beams with Different Boundary Conditions

Zhao

Huang

2018

Shock and Vibration

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This paper is concerned with temperature effects on the modeling and vibration characteristics of Euler-Bernoulli beams with symmetric and nonsymmetric boundary conditions. It is assumed that in the considered model the temperature increases/decreases instantly, and the temperature variation is uniformly distributed along the length and the cross-section. By using the extended Hamilton’s principle, the mathematical model which takes into account thermal and mechanical loadings, represented by partial differential equations (PDEs), is established. The PDEs of the planar motion are discretized to a set of second-order ordinary differential equations by using the Galerkin method. As to three different boundary conditions, eigenvalue analyses are performed to obtain the close-form eigenvalue solutions. First four natural frequencies with thermal effects are investigated. By using the Lindstedt-Poincaré method and multiple scales method, the approximate solutions of the nonlinear free and forced vibrations (primary, super, and subharmonic resonances) are obtained. The influences of temperature variations on response amplitudes, the localisation of the resonance zones, and the stability of the steady-state solutions are investigated, through examining frequency response curves and excitation response curves. Numerical results show that response amplitudes, the number and the stability of nontrivial solutions, and the hardening-spring characteristics are all closely related to temperature changes. As to temperature effects on vibration behaviors of structures, different boundary conditions should be paid more attention.

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Section: Introductionmentioning

confidence: 99%

Temperature Effects on Nonlinear Vibration Behaviors of Euler‐Bernoulli Beams with Different Boundary Conditions

Zhao

Huang

2018

Shock and Vibration

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“…Rega investigated the super harmonic resonances and subharmonic resonances of an elastic cable; Warnitchai et al proposed a nonlinear dynamic model with quadratic and cubic nonlinear couplings for a cable under small support motion. Rega et al studied the nonlinear dynamic behavior of a stay cable by experiment, which was confirmed by theoretical results of 1‐ to 2‐degree of freedom (DOF) and 4‐DOF models; Kang et al studied the in‐plane nonlinear dynamics of a stay cable considering the effect of support motion; Zhao et al studied the nonlinear vibration behaviors of suspended cables under two‐frequency excitation with temperature effects.…”

Section: Introductionmentioning

confidence: 82%

Unified modal analysis of complex cable systems via extended dynamic stiffness method and enhanced computation

Dan

Han

Cheng

et al. 2019

Struct Control Health Monit

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Summary With the increase of the span and height of modern engineering structures, the design length and complexity of the cable structure are constantly increasing, whose dynamic problem has become the key to structural design, performance monitoring and maintenance, and vibration control. Therefore, it is necessary to study and develop a unified dynamic analysis theory for complex cable system to meet the requirements of calculation accuracy and efficiency. In view of this, a unified dynamic analysis method for dynamic analysis of complex cable system is proposed in this paper on the basis of the classical dynamic stiffness method. In this paper, the dynamic stiffness method has been enhanced in multiple aspects, which not only retains the advantages of high computational efficiency and wide application range but also overcomes its technical bottlenecks in analysis of shallow‐sag cable system considering the damping effect, composite cable systems, and multisegment cable systems. The proposed method can not only be used to the structural design of the complex cable system but also be extended to the vibration control of the system during the service period.

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“…en, the temperature-dependent materials were illustrated in [23]. e influences of temperature on suspended cables' nonlinear vibration behaviors subjected to multifrequency excitations were also discussed by Zhao et al [24].…”

Section: Introductionmentioning

confidence: 96%

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

Zhao

Zheng

Lin

et al. 2021

Shock and Vibration

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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.

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Nonlinear vibration behaviors of suspended cables under two-frequency excitation with temperature effects

Cited by 38 publications

References 30 publications

Temperature Effects on Nonlinear Vibration Behaviors of Euler‐Bernoulli Beams with Different Boundary Conditions

Temperature Effects on Nonlinear Vibration Behaviors of Euler‐Bernoulli Beams with Different Boundary Conditions

Unified modal analysis of complex cable systems via extended dynamic stiffness method and enhanced computation

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

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