Cable-stayed Beam Research Articles

Nonlinear Dynamic Analysis for the Coupled Structure of Cable-stayed Beam Subject to Fully Parametric Excitation

The nonlinear dynamic analysis for the coupled structure of cable-stayed beam subject to fully parametric excitation is provided.The mechanical model of cable-stayed beam is established.The non-linear partial differential equations are derived for a coupled structure of cable-stayed beam subject to fully parametric excitation by using Hamilton principle.The Galerkin method is adopted to obtain ordinary differential equations of the coupling motion in stayed system.The non-linear vibration of coupled structure is analyzed with the help of multi-scale method.By means of Runge-Kutta method,the numerical solutions of differential equations are obtained which indicate that there is serious parametric resonance when the cable-stayed beam frequency ratio is 2:1.Through the analysis of relative response curves,the damping parameters are concluded which have significant influence on the coupling vibration of the cable-stayed beam.The conclusion having actual meaning to engineering is proposed.

Localization and veering in the dynamics of cable-stayed bridges

Cable-stayed systems are known to exhibit local modes that mainly involve the transversal cable dynamics. Their fan-shaped cable nets posses a dense spectrum of local frequencies, in which closeness with global ones commonly occurs. In these cases cable-stayed bridges present coupled cable–deck modes, whose interpretation presently remains incomplete. In this paper the solution of the eigenproblem of a simple cable-stayed beam model enables a synthetic description of the spectral properties of stayed-structures. The model shows the ability of a newly introduced localization factor to identify local modes and, especially, to reveal a veering phenomenon that occurs between local and global frequencies for particular parameter combinations. A small variation of the mechanical parameters is proved to produce a flipping between local/global (cable/beam) modal shapes within the veering region. Under these conditions, hybrid modes arise from the combination of the involved eigenfunctions. The occurrence of modal hybridization can be effectively predicted by the coincidence of the mode localization factors. These dynamical properties, which are further validated by a refined finite element model of a cable-stayed bridge, are proved to significantly affect the linear free and forced dynamics of cable-stayed structures.

One-to-two global-local interaction in a cable-stayed beam observed through analytical, finite element and experimental models

The mechanism of cable end angle-variation induced oscillations in the non-linear interactions between beams and cables in stayed-systems is first explained by a proposed analytical model. It is then verified by both experimental and finite element models. The non-linear interaction maximizes its effects for cable oscillations when inherent quadratic coupling between local and global modes produces energy transfer from low to high frequency vibrations by means of a one-to-two global–local autoparametric resonance. The response of the analytical model is fully described using a continuation method applied directly to the reduced two degree of freedom discrete model showing that, for a selected one-to-two global–local resonant system, primary harmonic excitation of the global mode produces large oscillations of the local mode at twice the excitation frequency. Detailed comparisons between the responses of the analytical model, experimental results and finite element simulations show excellent agreement both in the qualitative behaviour and in the calculated/measured response amplitudes.

Nonlinear interactions in the planar dynamics of cable-stayed beam

An analytical model is proposed to study the nonlinear interactions between beam and cable dynamics in stayed-systems. The integro-differential problem, describing the in-plane motion of a simple cable-stayed beam, presents quadratic and cubic nonlinearities both in the cable equation and at the boundary conditions. Mainly studied are the effects of quadratic interactions, appearing at relatively low oscillation amplitude. To this end an analysis of the sensitivity of modal properties to parameter variations, in intervals of technical interest, has evidenced the occurrence of one-to-two and two-to-one internal resonances between global and local modes. The interactions between the resonant modes evidences two different sources of oscillation in cables, illustrated by simple 2dof discrete models. In the one-to-two global–local resonance, a novel mechanism is analyzed, by which cable undergoes large periodic and chaotic oscillations due to an energy transfer from the low-global to high-local frequencies. In two-to-one global–local resonance, the well-known parametric-induced cable oscillation in stayed-systems is correctly reinterpreted through the autoparametric resonance between a global and a local mode. Increasing the load the saturation of the global oscillations evidences the energy transfer from high-global to low-local frequencies, producing large cable oscillations. In both cases, the effects of detuning from internal and external resonance are presented.

DYNAMIC MODELLING AND VIBRATION ANALYSIS OF A FLEXIBLE CABLE-STAYED BEAM STRUCTURE

In this paper, the non-linear vibration of a cable-stayed beam with time-varying length and tension in the cable is investigated. A set of non-linear, time-varying differential equations describing this coupling system is derived by Hamilton's principle and the finite element method. According to the results of numerical simulation, the tension of the cable is related to the cable length, which in turn is a function of the longitudinal and transverse displacements of the cable. Furthermore, it is shown that the tension and length of the cable can be considerably different by using linear and non-linear models.

A parametric analytical model for non‐linear dynamics in cable‐stayed beam

AbstractThe governing equations for dynamic transverse motion of a cable‐stayed beam are obtained by means of a classical variational formulation. The analytical model permits a parametric investigation of linear and non‐linear behaviour in a family of cable‐stayed beam systems. Analytical eigensolutions of the linearized equations are used to investigate how the mechanical characteristics influence the occurrence of global, local and coupled modes. The exact eigenfunctions are assumed to describe the forced harmonic motion in the neighbourhood of a selected frequency. The frequency–amplitude relationship, obtained by the use of the multiple scale method, permits the description of softening and hardening behaviour in the global, local and coupled classes of motion. Copyright © 2002 John Wiley & Sons, Ltd

Nonlinear Decentralized Control of a Flexible Cable-stayed Beam Structure

A decentralized controller that suppresses the vibrations of a flexible cable-stayed beam structure induced by an external random disturbance is presented. The controller is designed based on a lumped-mass model representation of the distributed parameter flexible beam structure. It contains a linear part and a nonlinear part. The linear part is used to introduce damping into the beam structure and the nonlinear part is used to further reduce the vibrations caused by the external disturbance. Its performance is assessed via digital computer simulation.

EXPERIMENTAL AND ANALYTICAL STUDY ON INTERNAL RESONANCES IN A CABLE-STAYED BEAM MODEL

EXPERIMENTAL AND ANALYTICAL STUDY ON INTERNAL RESONANCES IN A CABLE-STAYED BEAM MODEL