Showing papers by "Houjun Kang published in 2019"

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

Abstract: 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.

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

Abstract: 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.

An inclined cable excited by a non-ideal massive moving deck: an asymptotic formulation

Abstract: A moving deck is an important (kinematic) excitation source for the inclined cable in cable-stayed bridges. In ideal cases, the deck motion is assumed to be harmonic oscillation and cable’s dynamic effects on the deck are neglected. As a refined version, an inclined cable excited by a massive non-ideal moving deck, i.e., the deck’s oscillation, is slowly modulated by the cable and thus not exactly harmonic is investigated in an asymptotically coupled formulation for understanding cable–deck dynamic interactions. More explicitly, by ordering the deck/cable mass ratio as a large parameter, the coupled system is reduced using asymptotic approximations and multi-scale expansions. After neglecting the reduced model’s nonlinear terms, firstly, cable–deck linear coupled modes are obtained, leading to two different kinds of linear modal dynamics, i.e., the cable-dominated one and the deck-dominated one, whose asymptotic characteristics are also revealed. Then cable’s forced nonlinear vibrations, excited by the deck’s modulated oscillation (i.e., non-ideal moving deck), are fully investigated. Nonlinear frequency responses of the cable–deck coupled system are found, and the dynamic effects on the cable’s periodic and quasi-periodic behaviors, due to cable–deck coupling (characterized by the deck/cable mass ratio), cable’s inclinations, and boundary damping, are also presented.

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

Abstract: 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.

Nonlinear vibrations for double inclined cables-deck beam coupled system using asymptotic reductions

Abstract: For complex cable-stayed structures, dynamic coupling between cables and deck beam is important. In this work, an asymptotically reduced coupled model, consisting of two inclined cables and one deck beam, is established for understanding dynamic interactions inherent with the cable-stayed structures, after confining oneself to the simplified case that the beam’s motion is much weaker than the cables’ and the deck beam/cable mass ratio is a large parameter. More explicitly, through focusing on the cables–deck interfaces, the double cables–deck beam coupling is decomposed into deck-induced and cable-induced weak boundary/interior modulations on each other, which are analytically characterized by three boundary coupling coefficients. Based upon the asymptotic model, two different kinds of coupled dynamics are fully investigated, the first with only one of the two cables excited, and the second with the deck beam excited, leading to the coupled system’s different nonlinear forced responses. The steady solutions’ stabilities are determined and bifurcations, such as saddle–node bifurcation, Hopf bifurcation, and pitchfork bifurcation, are all detected. Special attentions are paid to the dynamic effects caused by the deck beam/cable mass ratio, cable’s inclinations.

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

Abstract: 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.