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• The dynamic model of long-span arch bridges conducted by the cantilever construction method is established. • The proposed method has excellent applicability for planner-free vibration of long-span arch bridges during construction. • The vibration of towers cannot be neglected unless it is sufficiently stiff. • The proposed model and method can be extended to the other multi-cable supported arch structures. The cantilever construction model, which consists of the arch, towers and cables, can be regarded as a cable-stayed system and is widely applied in constructing long-span arch bridges. The vibration induced by this temporary structure's unstable property has a safety risk and deserves to be concerned. Thus, a fully analytical beam-spring-arch model is presented for the cantilever and closure construction states of long-span arch bridges. Subsequently, based on the boundary and continuity conditions, the governing differential equations for in-plane free vibration are derived according to the Hamilton principle and solved using the transfer matrix method to determine frequencies and mode shapes of the system. Meanwhile, the results calculated by the proposed method are verified with the finite element method. Finally, the effects of structural parameter variations during construction on in-plane vibration properties are investigated. The results show that as the length of the erected arch rib gets longer, the system's first six-order frequencies and mode shapes are significantly affected. Moreover, the veering phenomenon is observed. The cables can increase the frequencies of the system to a certain extent. The model that neglects the tower's vibration would overestimate the stiffness of the erection system unless the tower's stiffness is much bigger than the arch. [ABSTRACT FROM AUTHOR]

Highlights • The suspension bridge with spatially inclined main cables is studied. • Nonlinear dynamics of a sectional model of suspension bridge is investigated. • The primary and secondary resonances of the first two modes are checked. • The effect of second and third order nonlinear stiffness of the system on the nonlinear dynamics are studied in details. Abstract The nonlinear dynamics of a suspended bridge deck with inclined main cables and its sensitivity to the nonlinear stiffness are investigated via a 6-DoFs sectional model in this study. Four configurations with different main cable inclination angles are investigated. Two higher order numerical models are analyzed to examine the effects of higher order nonlinear stiffnesses on the dynamic properties, with one considering the linear and quadratic stiffness terms and the other includes additionally the cubic stiffness term. Incremental harmonic balance method is adopted for the nonlinear dynamic analysis, and primary resonances at the first and second modes are studied in details. Results show that the nonlinearity introduced by the inclined main cables has only very minor effects on the first primary resonance modal response. However, the cubic stiffness term shows quite strong effect on the dynamic response of the second mode. If only the linear and quadratic stiffnesses are included in the model, the frequency-response curve from the first harmonic term shows weak softening features. The system, however, performs like a hard spring when the cubic stiffness is included which is totally different from existing published results. The observations on the super-harmonic resonance at the first two modes of the system also show great differences in the behavior of the two numerical models. Results from this study suggest that the cubic nonlinear stiffness should be included for better modeling of a sectional suspension bridge model. [ABSTRACT FROM AUTHOR]

This work studies the dynamic properties and non-linear responses of a sectional model of long-span cable-supported bridge deck under scenarios of resonance with vortex induced vibration or wind fluttering. The cable supported bridge with spatially inclined cables is modeled by a 6-degrees-of-freedom system. The equations of motion for an undamped system are formulated for the study of the effects of inclination angle of cable on the modal parameters. The inclination angle is found strongly affecting the torsional modal frequency of the deck. The equations of motion on the forced excitation of a damped system are also developed for the study of non-linear responses when in resonance. The response analysis is conducted with the Incremental Harmonic Balance method. The inclination angle does not have notable nonlinear effects on the primary resonance of deck heaving response with vertical excitation as the responses of the system are almost identical with those obtained through the linearized model. However, the primary resonance response due to periodic pitching moment indicates an increasing nonlinear effect with an increase in the cable inclination angle. The cables vibrate strongly in both the horizontal and vertical directions with multiple frequency components and non-zero stationary component. The super-harmonic resonance of deck heaving and rotation can only be observed when the damping ratio of system is extremely low. [ABSTRACT FROM AUTHOR]

A novel nonlinear dynamic double-cable-stayed shallow-arch model of cable-stayed bridge is established and the in-plane 1:1:1 internal resonance between three first modes of shallow arch and two cables under both external primary and subharmonic resonance is investigated, respectively. The Galerkin discretization and the method of multiple scales are applied to obtain the modulation equations of the dynamic system. The stable equilibrium solutions of the modulation equations are examined by Newton-Raphson method. Numerical simulations are carried out to investigate the dynamic behavior of the new dynamic system and Runge-kutta method is also used to solve the ordinary differential equations to verify the results. The results show the rich nonlinear phenomena and some new conclusions are also drawn. [ABSTRACT FROM AUTHOR]

Abstract This study investigated the internal resonance phenomenon of a suspended bridge structure with a 6-Degree-of-Freedom sectional model. The primary resonance of the second mode of the system under harmonic excitation is firstly studied. The one-to-two internal resonance between the second and third modes, and one-to-three internal resonance between the second and fourth modes may be induced if the corresponding natural frequency ratios are close to 2.0 and 3.0, respectively. Numerical analysis also shows that the two-to-one internal resonance between the third and second modes can be induced under different scenarios of excitation. The first one happens with the second mode being excited, resulting in two response peaks in the frequency response curves. The second one may occur when the third mode is excited with sufficient large excitation where most of the energy input will be transmitted to the second mode. Hopf bifurcation can also be found in the frequency response curve of the system. Lastly, the three-to-one internal resonance between the fourth and second modes is also found when the second mode is excited. The response of the second mode is slightly reduced with a distinct increase in the response of the fourth mode due to the internal resonance. All these behaviors of this dynamic system indicate the meaningful role played by a variety of internal resonances in the design of mega-scale cable-supported bridge structure. Highlights • The modal property of a 6-dof sectional model of suspension bridge is studied. • Primary resonance of the second mode is examined. • The one-to-two internal resonance between the second and third mode is studied. • The one-to-three internal resoance between the second and fourth mode is checked. [ABSTRACT FROM AUTHOR]