## 1 Introduction  
The exploitation and utilization of marine resources, such as oil and gas, lead to the development of offshore structures. Risers which act as a transport component between the production platforms and sub-sea wellheads are an indispensable part for the offshore exploitation and transportation system. Currently, risers are normally made from high grade steel. Their extreme weight results in the significant increase of the requirement in top tension forces, thereby leading to the limitation of the numbers of risers that can be attached to current platforms or larger platforms to carry the same number of risers with the increase of depths. It is well acknowledged that fiber reinforced polymer (FRP) composites have great mechanical properties and lower density; therefore, using FRP composites instead of steel can indeed reduce the weight of individual riser, thereby the requirement of top tension forces, which results in lower operational costs [1]. Meanwhile, FRP composites also have better performance in fatigue, corrosion and thermal insulation compared with steel, leading to lower maintenance costs [2]. It should be noted that the design results of a composite riser can be quite different, even for the same operational situation. The design variables of the geometries of a composite riser basically include liner and composite materials, stacking sequences of laminate, fiber orientations, lamina thicknesses, etc. Therefore, more challenges and complexities of design and analysis are produced for the use of composites in risers. During the past 40 years, several design studies and projects have been conducted to confirm the feasibility of composite risers. The initial attempt to fabricate and test composite risers was accomplished by Institut Francais du Petrole (IFP) and Aerospatiale of France [3] in the 1980s. In the 1990s, tests of mechanical capacities of the composite riser tube were performed by National Institute of Standards and Technology (NIST) and Advanced Technology Programs (ATPs) [4]. Then, more tests, including field tests and optimized designs of composite risers, were conducted by different research institutes and global enterprises [5; 6; 7; 8; 9; 10; 11; 12; 13]. These prototypes prove that FRP composite risers have significant benefits in weight saving compared to steel risers. In addition, using optimization methodologies in the designs would lead to more benefits for the composite risers with the same load-carrying capacity. Vortex-induced vibrations (VIV) are motions induced on bodies interacting with an external fluid flow, produced by--or the motion producing--periodical irregularities on this flow. VIV would cause the fatigue damage of risers, leading to the construction and environmental disaster. Therefore, many studies of VIV have been conducted in the past decades. The study of VIV started with experiment in 1960s using wind tunnel [14]; then, many tests were conducted for the VIV of risers [15; 16; 17; 18]. Besides tests and experiments, researchers proposed different empirical models to solve the VIV problem of risers. Initially, [PERSON] and [PERSON] built the lift-oscillator model [19], and then this model was developed and applied in the VIV study of flexible slender cylinders [20]. More recently, the wake oscillator models were modified and developed by different researchers according to different parameters and situations [21; 22; 23; 24; 25; 26]. Nowadays, computational fluid dynamics (CFD) has been employed in the VIV simulation and different models and methodologies have been set up. 2D simulation of risers was done by [PERSON] and [PERSON] [27]. [PERSON] and [PERSON] et al. simulated the VIV response of in-line two risers [28; 29]; and a top tension riser was used as an example to examine fatigue safety factor of the riser and the effects of the random coefficient [30]. From the previous studies including tests, theoretical analyses and CFD simulations, the VIV of conventional steel riser were understood.