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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 73
Edited by: B.H.V. Topping
Paper 35

A New Method for Dynamic Modelling of a Suspension Bridge for Aerodynamic Instability

C.P. Pagwiwoko+, M.A.M. Said+ and C.K. Keong*

+School of Aerospace Engineering, *School of Civil Engineering, University of Science Malaysia, Engineering Campus Transkrian, Pulau Pinang, Malaysia

Full Bibliographic Reference for this paper
C.P. Pagwiwoko, M.A.M. Said, C.K. Keong, "A New Method for Dynamic Modelling of a Suspension Bridge for Aerodynamic Instability", in B.H.V. Topping, (Editor), "Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 35, 2001. doi:10.4203/ccp.73.35
Keywords: aero-elasticity, structural dynamics, system dynamics, power bond graph method, dynamic modelling, simulation.

Suspension bridges are normally constructed in a low stiffness in bending as well as in torsion, therefore they are usually exposed to wind loadings of even fairly high speeds. These bridges are susceptible to the following flow induced vibration phenomena: von Karman Vortex, classical flutter and torsional divergence. The loss of aerodynamic instability can be explained as the absence of aerodynamic stiffness and damping in the aero-elastic system of the structure at a certain critical air speed. In the classical flutter phenomenon, the instability is manifested by the motions of coupled bending-torsional modes. Above the critical speed, there will be an unbalance of energy flowing into the structure compared with the energy that can be dissipated, subsequently the vibrations becomes diverge until it destructs the structure. The flutter calculation methode has been developed many years ago by some authors, for typical sectional bridge two degree of freedom movement. The analysis is conducted normally, in frequency domain using Theodorsen's unsteady aerodynamic theory.

In this paper, the aero-elasticity of the bridge is considered as a dynamic system. Power Bond Graph Technique is applied in simulation model construction. The dynamic system consists of several subsystems and components, which are bonded together by using the rules of flowing energy and the mechanism of interaction between components. The basic elements utilized in the modeling are: 1-port store energy component i.e. capacitor and inertia, energy dissipating component known as resistor, they can be related with the distribution of stiffness, mass and damping of the structure. The 2-port transformer elements are utilized for transforming the natural coordinate of multi degree of freedom problem to the modal coordinate which is needed to simplify the dynamic representation of the problem. The multi- port junctions explain the physical laws of the structure. The bond graph model is constructed using a certain established procedure.

In determining the unsteady aerodynamic loads, 2 dimensional attached flow is assumed to calculate the lift and pitching moment as a function of lifting surface response. To construct the aero-elastic model in the form of bond graph, the energy source element acting on structure, is considered as a filter having the structural response input signals. Thus the flutter phenomenon is represented in a closed loop system due to aero-structural interaction that explains the mechanism of flow induced vibration. To enable analysing in time domain, the aerodynamic force equation is transformed in Laplace variable using Padé rational function as an approximation. As the bond graph model can be converted directly into equivalent block diagram, consequently it can be simulated directly in time domain using system dynamic software as Simulink-Matlab.

Some results of the dynamic simulation showed a good accuracy comparing with the classical methods. The nature of flutter i.e. the interaction mechanismof flow induced vibration and the physical meaning of aero-structural coupling, can be observed clearly. Concerning to its simplicity and efficiency in flutter analysis, the power bond graph technique can be considered as a design tool in structure. Another advantage using time domain analysis is that it gives the facilities to take into account the non-linear terms accurately.

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