Mixed Rayleigh-Ritz Method for the Dynamic Analysis
of Cables Subjected to Support Motions
Jong Hyuk Baek
Aerodynamic stabilizing cables have been introduced for reducing oscillation of erected cable-stayed bridges by wind loads because stiffness of the under-construction bridge constructed by a balanced cantilever method is less compared with that of completed one. The trembling girder in wind loads can apply large support motions to stabilizing cables. Thus precise dynamic analysis considering effect of support motions is required. This study was performed to develope a precise dynamic analysis method for cables subjected to support motions.
Previous method is displacement-based Rayleigh-Ritz method which uses solutions of initial equilibrium state by ECC(elastic catenary cable) analysis for initial values and using sine functions for discretizing dynamic displacement. This thesis proves that the previous method does not satisfy ¡°path independency in elastic problem¡± and does not give precise value of tension.
It is proposed that initial equilibrium state be analyzed by Rayleigh-Ritz method assuming cable position of the state using same function space with dynamic displacement to satisfy path independency. Mixed Rayleigh-Ritz method assuming displacement and strain respectively is also proposed to obtain precise value of tension. The equilibrium equations and strain-displacement relationship are imposed by weak form and combined together. Newmark-b method is applied to perform time domain analysis.
Dynamic analysis of a cable subjected to support motions is performed by mixed Rayleigh-Ritz method. It is also applied to a simple model of the stabilizing cable and the erected cable-stayed bridge. Its results are compared with the results of the displacement-based formulation using 100 sine function to demenstrate the validity and the effectiveness of the proposed method.
Cable, Support motion, Nonlinear analysis, Initial equilibrium state, Mixed Rayleigh-Ritz method, Weak form