Prediction of vortex-induced vibration (VIV) in fluid dynamics has been challenging due to its strong nonlinearity. Nonlinear resonance and non-linear dissipation occur during VIV, which makes the response data collected highly nonlinear. The response of VIV is influenced by the flow velocity, model geometry, and system stiffness. Here we employ Physics-informed Neural Network (PINN) that embeds the physical equation to learn the VIV response under different stiffness. Several sets of VIV response data by adjusting the structural stiffness were used to train the model, and the learned errors of response and system stiffness are within 9%. The trained model can predict the VIV response and deduce the system stiffness, which provides strong support for further simplifying the hydrodynamic analysis.
Vortex-induced vibration refers to a physical phenomenon in a bluff body periodically de-vortex in the medium fluid at a certain velocity to form a Karmen vortex street, which provides a periodic lift to the bluff body to generate vibration (Wang et al., 2020). As one of the important fluid-structure interaction problems in fluid mechanics, VIV has been widely found and studied in many fields, such as civil engineering, aerospace engineering, and ocean engineering, in the past few decades (Ma et al., 2022). Many engineering examples show that the vibration frequency of VIV is approximate to the structure's natural frequency in some specific cases. Such vibration will cause the resonance of the structure and have disastrous consequences. Therefore, the study of VIV is of great significance to the design of buildings and marine devices.
Scholars have made considerable achievements in the study of VIV. Since Bearman (1984) published his outlook on the research direction of VIV in the Annual Review of Fluid Mechanics, many scholars have conducted impressive research on VIV at low Reynolds numbers. Shiels et al. (2001) simulated the VIV at the Reynolds number of 100 (Re = 100) and found that the essence of VIV is a Karmen vortex street generated by a blunt body without mass, spring, and damping. At the same time, experimental fluid mechanics scientists are also greatly interested in this phenomenon. Govardhan and Williamson (2000) deduced the vortex force from the direct experimental measurement of the total flow force through the VIV experiment. The vortex force (FVORTEX) and the total fluid force (FTOTAL) in the VIV problem are divided, which provides more support for the lift oscillator model. In this paper, the problem of VIV is studied by collecting the total force of fluid (FTOTAL) (Fan et al., 2019). The formula of the lift oscillator model introduced in the next chapter is written in the form of Eq. 1.
