Two-degrees of freedom flow-induced vibration of circular cylinder with nonlinear stiffness

Nonlinear stiffness is widespread in engineering field, which normally caused by deformation of anisotropic structures or support gaps between structures. In this work, two-degrees of freedom flow-induced vibration (FIV) of a circular cylinder with nonlinear stiffness supporting is numerically investigated in a wide reduced velocity range (3=U*=20). The amplitude and frequency responses, force acting on the cylinder, and the near-wake structures are analyzed to understand the influence of nonlinear stiffness on the FIV behavior. Results show that the FIV responses of cylinder can be divided into two parts according nonlinear strength: low nonlinear strength range (0=? = 4) range and high nonlinear strength range (4 < ? = 10). Low value of ? can amplify the amplitudes in two vibration directions when compared with that of ? = 0. The maximum amplitudes of 0.34D (? = 4, U* = 14) and 1.12D (? = 0.25, U* = 7) are obtained in flow and cross flow directions, respectively. Typical trajectories of "8" shape are observed for all cases, which means that the vibrate frequency in flow direction is double to that of cross flow direction for a given reduced velocity and nonlinear strength. In addition, bending trajectory can be captured with the rise of ?. The vortex shedding patterns of 2 S, P + S, and 2 P are obtained under low nonlinear strength (0=? = 4) and only the 2 S pattern can be observed under high nonlinear strength (4 < ? = 10).