Nonlinear primary resonance in vibration control of cable-stayed beam with time delay feedback

Jian, Peng; Xiang, Mingjiao; Wang, Lianhua; Xie, Xianzhong; Sun, Hongxin; Yu, Jiguo

doi:10.1016/j.ymssp.2019.106488

Cited by 49 publications

(15 citation statements)

References 66 publications

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“…Substituting Eqs. ( 14) and (15) into Eqs. ( 9) and (10) and using the Galerkin's method, the following ODEs can be obtained…”

Section: Governing Equations and Perturbation Techniquementioning

confidence: 99%

“…Although a single-cable model can reveal some characteristics of the cable-stayed bridge, however, it cannot consider the coupling interaction between the cable and bridge deck. Therefore, the attention is paid to cablestayed beam and quite a few studies are carried out [14,15]. Fujino et al [16] established a cable-beam model considering three degrees of freedom (DOFs) and proposed the concepts of global mode and local mode.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Internal resonance and energy transfer of a cable-stayed beam with a tuned mass damper

Kang

Guo

et al. 2022

Nonlinear Dyn

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This study considers a novel nonlinear system, namely, a cable-stayed beam with a tuned mass damper (cablebeam-TMD model), allowing the description of energy transfer among the beam, cable and TMD. In this system, the vibration of the TMD is involved and one-to-one-to-one internal resonance among the modes of the beam, cable and TMD is investigated when external primary resonance of the beam occurs. Galerkin's method is utilized to discretize the equations of motion of the beam and cable. In this way, a set of ordinary differential equations (ODEs) are derived, which are solved by the method of multiple time scales (MTS). Then the steady state solutions of the system are obtained by suing Newton-Raphson method and continued by pseudo arclength algorithm. The response curves, time histories and phase portraits are provided to explore the effect of the TMD on the nonlinear behaviours of the model. Meanwhile, a partially coupled system, namely, a cable-beam-TMD model ignoring the vibration of the TMD, is also studied. The nonlinear characteristics of the two cases are compared with each other. The results reveal the occurrence of energy transfer among the beam, cable and TMD.

show abstract

“…Substituting Eqs. ( 14) and (15) into Eqs. ( 9) and (10) and using the Galerkin's method, the following ODEs can be obtained…”

Section: Governing Equations and Perturbation Techniquementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Internal resonance and energy transfer of a cable-stayed beam with a tuned mass damper

Kang

Guo

et al. 2022

Nonlinear Dyn

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show abstract

“…Xiang et al [9] studied seismic vibration control of building structures with multiple tuned mass dampers. Peng et al [10] studied the large-scale vibration control of a long-span cable-stayed beam under time-delay technology. Zhou et al [11] investigated the optimum problem on windinduced vibration control of high-rise buildings with viscous dampers.…”

Section: Introductionmentioning

confidence: 99%

Wind‐Induced Vibration Control of High‐Rise Structures Using Compound Damping Cables

Duan

Zhang

et al. 2021

Shock and Vibration

Self Cite

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Based on the vibration reduction mechanism of compound damping cables, this study focuses on the wind-induced vibration control of high-rise structures with additional mass at the top. The differential equation of motion of the system under the action of the composite damping cable is established, and the analytical solution of the additional damping ratio of the structure is deduced, which is verified by model tests. The vibration response of the structure under the action of simple harmonic vortex excitation and randomly fluctuating wind loads is studied, and the effect of different viscous coefficients of the dampers in the composite damping cable and different installation heights of the damping cable on the vibration control is analyzed. The results show that a small vortex excitation force will cause large vibrations of low-dampened towering structures, and the structure will undergo buffeting under the action of wind load pulse force. The damping cable can greatly reduce the amplitude of structural vibration. The root means square of structural vibration displacement varies with damping. The viscosity coefficient of the device and the installation height of the main cable of the damping cable are greatly reduced.

show abstract

Section: Introductionmentioning

confidence: 99%

Internal Resonance and Energy Transfer of a Cable-stayed Beam With a Tuned Mass Damper

Kang

Guo

et al. 2021

Preprint

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This study considers a novel nonlinear system, namely, a cable-stayed beam with a tuned mass damper (cable-beam-TMD model), allowing the description of energy transfer among the beam, cable and TMD. In this system, the vibration of the TMD is involved and one-to-one-to-one internal resonance among the modes of the beam, cable and TMD is investigated when external primary resonance of the beam occurs. Galerkin’s method is utilized to discretize the equations of motion of the beam and cable. In this way, a set of ordinary differential equations (ODEs) are derived, which are solved by the method of multiple time scales (MTS). Then the steady state solutions of the system are obtained by suing Newton-Raphson method and continued by pseudo arclength algorithm. The response curves, time histories and phase portraits are provided to explore the effect of the TMD on the nonlinear behaviours of the model. Meanwhile, a partially coupled system, namely, a cable-beam-TMD model ignoring the vibration of the TMD, is also studied. The nonlinear characteristics of the two cases are compared with each other. The results reveal the occurrence of energy transfer among the beam, cable and TMD.

show abstract

Nonlinear primary resonance in vibration control of cable-stayed beam with time delay feedback

Cited by 49 publications

References 66 publications

Internal resonance and energy transfer of a cable-stayed beam with a tuned mass damper

Internal resonance and energy transfer of a cable-stayed beam with a tuned mass damper

Wind‐Induced Vibration Control of High‐Rise Structures Using Compound Damping Cables

Internal Resonance and Energy Transfer of a Cable-stayed Beam With a Tuned Mass Damper

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