engleski

Frequencies and modal shapes of cable-stayed system

Cables are highly nonlinear elements that are very often treated as equivalent tendon members in structures like cable stayed bridges, suspended roofs, cable stayed mast. Several authors highlighted the importance of cable-structure modelling that considers not only global structural behavior but also local cable and coupled cable-structure dynamics. It is also well known that nonlinear system could exhibit some kind of internal or auto-parametric resonance for integer ratio of system frequencies. So, in order to properly define nonlinear problem it is necessary to investigate system frequency spectra. In this paper mathematical model with analytical modelling of simplified cable-stayed structure is formulated. Cable is modeled using quasi-static elongation assumption and small sag to span ratio. Structure is modeled as Euler - Bernoulli beam neglecting its axial, torsion and shear stiffness. In order to simplify analytical model, other elastic structural components are modeled as equivalent elastic springs. Hamiltonian principle is used to obtain differential equations of motion which are linearized around the static equilibrium configuration. The eigenvalue problem is formulated assuming continuous functions for modal shapes. System of equations is solved in closed form to obtain characteristic equation which is then solved numerically. Analytic models for the static equilibrium of the system as well as the solutions of dynamic characteristics are verified with finite element modelling. Varying properties of cable-stayed system, parametric analysis of system frequencies and respondent mode shapes is carried out. Frequencies integer ratios and associated modes are pointed out.

analytic models; natural frequencies; cable-structure dynamics

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