Approximate Series Solutions for Nonlinear Free Vibration of Suspended Cables

Zhao, Yaobing; Sun, Ceshi; Wang, Zhiqian; Wang, Lianhua

doi:10.1155/2014/795708

Cited by 5 publications

(3 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Nonlinear Free Vibration. This section begins with the approximate series solutions for the nonlinear free vibrations obtained with the Lindstedt-Poincaré method [42]. Firstly, a new independent variablẽis introduced, which is̃= ,…”

Section: Perturbation Analysismentioning

confidence: 99%

See 1 more Smart Citation

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

Zhao

Huang

2018

Shock and Vibration

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Perturbation Analysismentioning

confidence: 99%

“…Substituting (43)-(44) into (42) and equating the coefficients on both sides, the nonlinear ordinary equations are reduced to a set of linearized equations. Then, the polar form is introduced and the secular terms are set to zero.…”

Section: Perturbation Analysismentioning

confidence: 99%

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

Zhao

Huang

2018

Shock and Vibration

Self Cite

View full text Add to dashboard Cite

show abstract

“…Ouni and Kahla [19] investigated the nonlinear dynamics of a cable under first-and second-order parametric excitations. Zhao et al [20,21] investigated the approximate series solutions of nonlinear free vibrations of suspended cables via the Lindstedt-Poincaré method and the homotopy analysis method.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration of iced cable under wind excitation using three-degree-of-freedom model*

Zhang¹,

Li²,

Wu³

et al. 2021

Chinese Phys. B

View full text Add to dashboard Cite

High-voltage transmission line possesses a typical suspended cable structure that produces ice in harsh weather. Moreover, transversely galloping will be excited due to the irregular structure resulting from the alternation of lift force and drag force. In this paper, the nonlinear dynamics and internal resonance of an iced cable under wind excitation are investigated. Considering the excitation caused by pulsed wind and the movement of the support, the nonlinear governing equations of motion of the iced cable are established using a three-degree-of-freedom model based on Hamilton’s principle. By the Galerkin method, the partial differential equations are then discretized into ordinary differential equations. The method of multiple scales is then used to obtain the averaged equations of the iced cable, and the principal parametric resonance-1/2 subharmonic resonance and the 2:1 internal resonance are considered. The numerical simulations are performed to investigate the dynamic response of the iced cable. It is found that there exist periodic, multi-periodic, and chaotic motions of the iced cable subjected to wind excitation.

show abstract

Analytical solution of the eigenvalue problem for the elastic cable loaded with a mass point

Wenin

2022

Arch Appl Mech

View full text Add to dashboard Cite

Approximate Series Solutions for Nonlinear Free Vibration of Suspended Cables

Cited by 5 publications

References 22 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

Nonlinear vibration of iced cable under wind excitation using three-degree-of-freedom model*

Analytical solution of the eigenvalue problem for the elastic cable loaded with a mass point

Contact Info

Product

Resources

About