Dynamic properties of cable-stayed system

It is well known that non-linear vibrations of long span cables present a considerable problem of lightweight structures like suspended roofs, cable stayed bridges and cable stayed masts. In the analysis of global structural behaviour, cables are often modelled as equivalent tendon elements. The importance of modelling coupled cable-structure dynamics has been demonstrated by a number of researchers. Dynamic response of non-linear systems can lead to internal or auto-parametric resonance in the case of integer frequency ratio. The analysis of cable-stayed system frequency spectra can show parameter values for which integer frequency ratio condition is fulfilled. In this paper an analytic model of simplified cable-stayed system is formulated. Parabolic cable is modelled using the assumption of quasi-static stretching, while the structure is modelled as Euler-Bernoulli beam. Equations of motions are derived by Hamilton’s principle and then linearized around a static equilibrium configuration. Differential equations of motion are solved by the method of variable separation. System deformation is described using analytical functions. Equations of motions together with boundary conditions are solved in closed form to obtain a characteristic equation. For chosen system parameters, the eigenvalue spectra are determined. Parametric analysis of dynamical properties is carried out and integer frequency ratios along with the associated modes are pointed out. Analytic solutions are verified with finite element modelling