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

Abstract

SUMMARYThe 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 in uence 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.

Bifurcation and chaos of a cable–beam coupled system under simultaneous internal and external resonances

“…Based on research given by Cheng and Zu [16], the transverse displacements v 1 (x, t) and v 2 (x, t) are approximated by the vibration modes of the first order as follows: where φ 1 (x), φ 2 (x) are the mode shapes of the beam and the cable, respectively, and can be written as [17]:…”

Nonlinear Vibration Signal Tracking of Large Offshore Bridge Stayed Cable Based on Particle Filter

“…The article analyses cable vibration system and builds cable-beam coupling model of cable-stayed bridge [2,9]. Tagata [9] points out that the basic mode plays a major role in tightening string-end vibration.…”

“…Tagata [9] points out that the basic mode plays a major role in tightening string-end vibration. According to oscillatory differential equation [2] under beam-end excitation, combining with model boundary conditions, introducing viscous damping ratio ζ c , Galerkin method is used to get cable non-linear vibration equation of beam vertical excitation. In Fig.1, where d 1 is defined as span sag, l c is the length of cable.…”

Finite Element Analysis of Cable-Stayed Bridges with Appropriate Initial Shapes Under Seismic Excitations Focusing on Deck-Stay Interaction

“…In the previous literature, the deck-stay interaction is due to the linear coupling (primary resonance) [3][4][5][6][7][8]11] or the nonlinear coupling (secondary resonance), which can be further categorized into the subharmonic resonance of order 1/2 (two-to-one resonance) [3][4][5][6][7][8][9] and the superharmonic resonance of order 2 (one-to-two resonance) [6,9,10]. The primary, two-to-one and one-to-two resonances individually result in the fact that the global modes induce the direct, parametric and angle variation excitations of the local modes.…”

“…The primary, two-to-one and one-to-two resonances individually result in the fact that the global modes induce the direct, parametric and angle variation excitations of the local modes. Two types of simplified models: the single cable with moving anchorage [5][6][7] and the cable-supported cantilever beam [3,4,[8][9][10][11], have been presented to theoretically investigate the deck-stay interaction. To extend the results of the simplified models, the OECS and MECS models of full cable-stayed bridges based on the finite element method have been widely used to explore such coupled phenomena of real structures [1,[11][12][13][14][15][16].…”