## 3 Aeroelasticity and Aerodynamics of Cable-Supported Bridges
### Flutter-Aeroelasticity of the Deck
#### 3.1.2 Wind Tunnel Studies of Flutter  
The free vibration method was first proposed by [PERSON] and [PERSON] [50] to identify eight flutter derivatives of a 2-DOF bridge deck system. In this method, a sectional model is spring mounted in a wind tunnel where modal tests under various wind conditions are performed. Flutter derivatives can be identified from the recorded motions and corresponding wind conditions. Detailed mathematical derivation can be seen in the work of [PERSON] [4]. Given that flutter can occur in heave, pitch and sway directions of the bridge deck, [PERSON] and [PERSON] [53] extended [PERSON]'s theory to present a framework for the 3-DOF free vibration method. The free vibration method requires only a simple apparatus, and therefore is a low-cost option (given there is no need to record the aerodynamic forces acting on the testing model). There are, however, challenges associated with free vibration tests in wind tunnels reported in the literature, particularly in the estimation of flutter derivatives at high wind velocities [54]. As the wind velocity increases, the aerodynamic damping effect in the vertical mode becomes so high that vibrations of the model are too small to be accurately recorded. Although they proposed using models with larger mass values to solve this, the increased mass value is strictly limited by the capacity of the suspension system used in the test. [PERSON] et al. [55] aimed to identify flutter derivatives from complex modal parameters; however, they only showed that this method could analyse cases of high velocity on idealised thin-plate sections. Despite recent improvements in sensor technology, this problem still exists in state-of-the-art free vibration tests [56]. [PERSON] [57] showed that flutter derivatives can be affected by the turbulence intensity and since the turbulence condition also depends on the wind velocity, most free vibration tests are performed under smooth air. Compared to the free vibration method, the forced vibration method requires less mathematical effort but more experimental data. In the free vibration method, only the displacement of the testing model is recorded, while during the forced vibration method, both the displacement and forces acting on the model are recorded simultaneously, and ultimately the flutter derivatives can be directly identified. The main advantages of using the forced vibration method are its simplicity in extracting flutter derivatives, its adherence to the theoretical framework and its greater control of the oscillation amplitude. Therefore,the forced vibration method has become a popular option in the industry. For instance, during the design of the Musi III cable-stayed bridge, a series of wind tunnel vibration tests were performed to determine the flutter derivatives and critical flutter velocities of the bridge [58]. However, the wind tunnel forced vibration test has some significant limitations. Firstly, it is essential to simultaneously record the unsteady signals of dynamic forces and structural motions during the test. To achieve this, a complex apparatus is required, such as high-frequency balance, electronic scanning valve and sensors to record acceleration and displacement. This can potentially increase the instrumental error. Secondly, the accurate extraction of aeroelastic forces from recorded dynamic forces is challenging. The total forces recorded in the experiment can include not only inertia forces and mechanical interference forces, but also buffeting forces caused by turbulence. [PERSON], [PERSON] and [PERSON] [59] conducted and experiment in smooth air conditions to neglect the buffeting forces. [PERSON] et al. [60] limits the turbulence intensity to 0.01 in their forced vibration test. However, such a solution will limit the test to a relatively low wind velocity condition where turbulence effects can be neglected. This also leads to the third limitation of the forced vibration method.