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

Frequency locking in the internal resonance of two electrostatically coupled micro-resonators with frequency ratio 1:3

Based on a double cable-stayed shallow arch model of the cable-stayed bridge, the novel dynamic theory and analysis of nonlinear dynamic behavior of the system when cables' upper ends are subjected to harmonic excitation introduced by motion of tower are established and carried out. A set of partial differential equations governing the motion of present system are derived firstly according to the classic dynamic theories of cables and the shallow arch. Then, they are used to obtain the ordinary differential equations of the system by Galerkin's integral method. The corresponding modulation equations are derived by implementing the standard process of perturbation method of multiple scales when the 1:1:1 internal resonance among the lowest modes of cables and the shallow arch and external resonance of the system occur simultaneously. Frequency- and force-response curves are plotted to explore the rich dynamic behaviors of the system. The research shows the asymmetric harmonic excitations can cause the different jump phenomenon of cables, even the reverse jump is observed when the subharmonic resonance occurs.

Planar nonlinear dynamic behavior of a cable-stayed bridge under excitation of tower motion

The nonlinear dynamic behaviors of the cable-stayed bridge are considerably complicated and very interesting. In order to explore the nonlinear behaviors of a cable-stayed bridge, a scaled physical model with Xiangshangang Bridge as the prototype is established and the systematical experiments are carried out. Firstly, the physical parameters, especially initial tension forces, of cables are measured by free vibration test and the data is dealt with FFT and filtering technology. The corresponding modal analysis is conducted and the test results are in good agreement with those obtained by OECS model and MECS model, which shows the experimental effectivity. Then, the free vibrations of cables are analyzed and the 1:1 resonance between different cables is revealed. Thereafter, by applying a single excitation to the beam, the nonlinear resonance of the cable-stayed bridge is studied and the rich nonlinear phenomena are observed, such as the parametric vibration, harmonic resonance, multiple internal resonance, primary resonance and cable–cable coupling vibration. Finally, some interesting conclusions are drawn, for example, the large amplitude vibrations of cables can be induced when the nonlinear resonance conditions are matched under external excitation.

Experimental study on in-plane nonlinear vibrations of the cable-stayed bridge

Many civil structures and facilities can be modeled using cable-stayed cantilever beams. This study is to investigate the nonlinear dynamic response and dynamic behavior of a cable-stayed cantilever beam subjected to two different external excitations through theoretical analyses. First, the equations of motion of the cable and the beam are established. Then, based on the Galerkin method, dynamic structural responses are expressed into the superimposition of mode shapes, with the generalized time coordinates as unknown coefficients. To obtain the unknown coefficients, modulation equations governing the amplitude and phase are derived by using the method of multiple scales. Four representative cases of simultaneous resonances (four representative excitation cases) are considered. Based on the derived analytical solutions, for each case, the frequency response and amplitude response of the system are obtained through parametric studies and nonlinear dynamic behavior of the system are explored. The obtained results demonstrate: (1) both the beam and the cable can behave the harden spring properties and the soften spring property in the frequency response; and the cable experiences larger response than the beam although excitations are applied on the beam; (2) the effect of the amplitude variation of secondary resonance on the responses of the beam and the cable is smaller than the primary resonance; and (3) the addition of a secondary resonance, such as Order 1/2 and 1/3 sub-harmonic resonance and Order 2 and 3 super-harmonic resonance, to the primary resonance can suppress the response of the beam or the cable to a certain extent.

Investigation of Dynamic Behavior of a Cable-Stayed Cantilever Beam under Two-Frequency Excitations

Planar multimodal 1:2:2 internal resonance analysis of cable-stayed bridge

As a classic bridge type, cable-stayed bridge is widely used because of its superior spanning capacity. Based on the mechanical characteristics of stay cable supporting deck, we propose a novel mec...

Modeling and Parametric Analysis of In-Plane Free Vibration of a Floating Cable-Stayed Bridge with Transfer Matrix Method

Cable-stayed bridge is one of the most popular bridges in the world and is always the focus in engineering field. In this work, the in-plane free vibration of a multi-cable-stayed beam, which exists in cable-stayed bridge, has been studied. The general expressions are conducted for the multi-cable-stayed beam based on basic principle of the transfer matrix method. A double-cable-stayed beam is taken as an example and solved according to governing differential equations considering axial and transverse vibrations of cables and beam. Then, numerical analyses are implemented based on carbon fiber-reinforced polymer cables. The dynamic characteristics including natural frequencies and mode shapes are investigated and compared with those obtained by finite element model. Meanwhile, parametric analyses are carried out in detail aiming to explore the effects of parameters on natural frequencies of a two-cable-stayed beam. Finally, some interesting phenomena are revealed and a few interesting conclusions are also drawn.

Dynamic analysis of the in-plane free vibration of a multi-cable-stayed beam with transfer matrix method

The nonlinear dynamic behaviors of a double cable-stayed shallow arch model are investigated under the one-to-one-to-one internal resonance among the lowest modes of cables and the shallow arch and external primary resonance of cables. The in-plane governing equations of the system are obtained when the harmonic excitation is applied to cables. The excitation mechanism due to the angle-variation of cable tension during motion is newly introduced. Galerkin’s method and the multi-scale method are used to obtain ordinary differential equations (ODEs) of the system and their modulation equations, respectively. Frequency- and force-response curves are used to explore dynamic behaviors of the system when harmonic excitations are symmetrically and asymmetrically applied to cables. More importantly, comparisons of frequency-response curves of the system obtained by two types of trial functions, namely, a common sine function and an exact piecewise function, of the shallow arch in Galerkin’s integration are conducted. The analysis shows that the two results have a slight difference; however, they both have sufficient accuracy to solve the proposed dynamic system.

Yunyue Cong

Papers

Planar multimodal 1:2:2 internal resonance analysis of cable-stayed bridge

Modeling and Parametric Analysis of In-Plane Free Vibration of a Floating Cable-Stayed Bridge with Transfer Matrix Method

Dynamic analysis of the in-plane free vibration of a multi-cable-stayed beam with transfer matrix method

Analysis of in-plane 1:1:1 internal resonance of a double cable-stayed shallow arch model with cables’ external excitations

One-to-one internal resonance of a cable-beam structure subjected to a concentrated load