Fluid-structure-acoustic responses of a nonlinearly supported rigid circular cylinder in viscous flow

This paper investigates the synchronization mode modulation and fluid-structure-acoustic responses of a rigid circular cylinder supported by a nonlinear spring subjected to viscous flow. A strongly coupled fluid–structure interaction (FSI) model of the cylinder based on the arbitrary Lagrangian–Eulerian (ALE) framework is developed. Direct numerical simulation is employed to model the compressible viscous flow. Four distinct branches of the sound waves generated by the vibrational cylinder are identified, i.e., the initial branch, upper branch, lower branch, and desynchronized branch. Nonlinear vibration of the cylinder governs the synchronized sound waves, directing their propagation toward the fore-field via balanced lift and drag dipole sound mode interactions. In contrast, desynchronized sound waves, dominated by the transversal lift dipole sound mode at high flow velocities, propagate exclusively toward the backfield. The nonlinear stiffness of the spring is shown to modulate frequency and phase relationships of the fluid-structure-acoustic interaction system, regulating the lock-in range and facilitating transitions between synchronization and desynchronization states of the cylinder. It also influences higher-order harmonic contributions, altering the phase relationship between the response and flow excitation of the cylinder and enabling transitions between the in-phase and the out-phase modes of the cylinder.