Features of the behavior of solutions to a nonlinear dynamical system in the case of two-frequency parametric resonance

Koverga, A. Yu.; Kubyshkin, E. P.

doi:10.1134/s0965542513050060

Cited by 2 publications

(2 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Formulas (16) and (21) are brought into formula (12) by the Galerkin method, on both sides multiplied by sin( ) and at the same time, and integral on [0, 1]; it can be obtained by using the mode orthogonality principle:…”

Section: Theoretical Model Of Parametric Resonancementioning

confidence: 99%

Theoretical and Numerical Analysis of 1 : 1 Main Parametric Resonance of Stayed Cable Considering Cable-Beam Coupling

Zhang

Wang

et al. 2017

Advances in Materials Science and Engineering

View full text Add to dashboard Cite

For the 1 : 1 main parametric resonances problems of cable-bridge coupling vibration, a main parametric resonances model considering cable-beam coupling is developed and dimensionless parametric resonances differential equations are derived. The main parametric resonances characteristics are discussed by means of multiscale approximation solution methods. Using an actual cable of cable-stayed bridge project for research object, numerical simulation analysis under a variety of conditions is illustrated. The results show that when the coupling system causes 1 : 1 parametric resonance, nonlinear main parametric resonances in response are unrelated to initial displacement of the cable, but with the increase of deck beam end vertical initial displacement increases, accompanied with a considerable “beat” vibration. When the vertical initial displacement of deck beam end is 10−6 m order of magnitude or even smaller, “beat” vibration phenomenon of cable and beam appears. Displacement amplitude of the cable is small and considerable amplitude vibration may not occur at this time, only making a slight stable “beat” vibration in the vicinity of the equilibrium position, which is different from 2 : 1 parametric resonance condition of cable-bridge coupling system. Therefore, it is necessary to limit the initial displacement excitation amplitude of beam end and prevent the occurrence of amplitude main parametric excitation resonances.

show abstract

Section: Theoretical Model Of Parametric Resonancementioning

confidence: 99%

Theoretical and Numerical Analysis of 1 : 1 Main Parametric Resonance of Stayed Cable Considering Cable-Beam Coupling

Zhang

Wang

et al. 2017

Advances in Materials Science and Engineering

View full text Add to dashboard Cite

show abstract

“…Parametric vibration system means the excitation depends on time and is used as a parameter in the governing equation; one of the characteristics of the vibration system is that the parameters of the system are changed with time. Different from the external incentive system, in the parametric excitation system, when the frequency of the excitation is equal to multiple system natural frequency of a certain order, small incentives can also stimulate a large system response [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

Experimental Research on 2 : 1 Parametric Vibration of Stay Cable Model under Support Excitation

Zhang¹,

Li²,

Yu³

et al. 2016

Advances in Materials Science and Engineering

View full text Add to dashboard Cite

For 2 : 1 parametric vibration problem of stay cable under support excitation, a sliding support only in the vertical moving is designed to simulate the bridge stay cable’s vibration test model. Meanwhile, using numerical simulation of cable free vibration and dynamic characteristic test analysis, the experimental research under various conditions is implemented in the actual cable-stayed bridge as the research object, which is compared with the corresponding numerical simulation results. According to the analysis results, it shows that as the vibration test model has 2 : 1 parametric vibration under the support excitation the results of maximum cable displacement from experimental analysis and numerical simulation are basically consistent which revealed that the parametric vibration of stay cable exists and is easy to occur. Additionally, when the bridge bearing excitation frequency is similar to the 2 : 1 frequency ratio, small excitation can indeed lead to the sharp “beat” vibration of cable; therefore it is very necessary to limit the amplitude of support excitation to prevent the occurrence of a large main parametric resonance.

show abstract

Features of the behavior of solutions to a nonlinear dynamical system in the case of two-frequency parametric resonance

Cited by 2 publications

References 2 publications

Theoretical and Numerical Analysis of 1 : 1 Main Parametric Resonance of Stayed Cable Considering Cable-Beam Coupling

Theoretical and Numerical Analysis of 1 : 1 Main Parametric Resonance of Stayed Cable Considering Cable-Beam Coupling

Experimental Research on 2 : 1 Parametric Vibration of Stay Cable Model under Support Excitation

Contact Info

Product

Resources

About