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CivilComp Proceedings
ISSN 17593433 CCP: 73
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING 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 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", CivilComp Press, Stirlingshire, UK, Paper 35, 2001. doi:10.4203/ccp.73.35
Keywords: aeroelasticity, structural dynamics, system dynamics, power bond graph method, dynamic modelling, simulation.
Summary
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 aeroelastic system of the structure at a certain critical air speed.
In the classical flutter phenomenon, the instability is manifested by the motions of
coupled bendingtorsional 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 aeroelasticity 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: 1port 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 2port 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 aeroelastic 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 aerostructural 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 SimulinkMatlab. 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 aerostructural 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 nonlinear terms accurately.
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