Computational study of vortex-induced vibration of a sprung rigid circular cylinder with a strongly nonlinear internal attachment

Capture into slow-invariant-manifold in the fluid–structure dynamics of a sprung cylinder with a nonlinear rotator

“…The coupled system of equations (11,12) and the discretized equations governing the motion of the fluid flow, used to evaluate the lift coefficient, are solved in a staggered fashion; i.e., we have assumed that, in the solution of the fluid-structure interaction problem, there is no need for equilibrating iterations in each time step, since the structure considered here is rigid, and provided that the time-step size is chosen small enough. This assumption was shown to be satisfactory by Tumkur [33], who performed computations in which the fluid and structural responses at each time step were computed iteratively, with insignificant effects on the response of the system (compared to the solution obtained without equilibrating iterations).…”

“…A prototypical VIV model consists of the flow past a circular cylinder mounted on a grounded linear spring, and constrained to move in the cross-flow direction. Recent studies have investigated the dynamics of a system in which the dimensionality of the standard VIV configuration is augmented by coupling the cylinder with an essentially nonlinear dissipative attachment (or nonlinear energy sink, NES), which is free to translate and/or rotate inside the cylinder (with no gravitational effects) [33][34][35]. The NES, because it features a dissipative element and strong inertial nonlinearity, has the capacity to absorb vibrational energy from the primary structure to which it is attached, over broad frequency and energy ranges and for various types of narrowband or broadband excitations.…”

“…The addition of a rotational NES to the transverse VIV model has been shown to result in drastic passive suppression of vibrations of the cylinder at intermediate Reynolds number (60 ≤ Re ≤ 120) [33]. Although there is no direct interaction between the NES and the infinite-dimensional flow, the rotational attachment has an indirect effect on the flow, i.e., through the dynamics of the cylinder to which it is inertially coupled [36].…”

“…One notable VIV suppression mechanism of particular interest that has been identified consists of repetitive cycles of slowly decaying oscillations of the cylinder followed by intermediate chaotic bursts [36]. This interesting nonlinear dynamical phenomenon has been attributed to the presence of the rotating internal NES, since no similar results have been found for the case of the translational NES [33,34]. Moreover, during the slowly decaying part of the cycle, the rotational NES performs phase-locked steady rotations, and this is accompanied by a noticeable reduction of the lift and drag coefficients of the cylinder, as well as profound effects on the wake; in particular, vortex street elongation occurs, resulting in partial stabilization of the wake behind the cylinder.…”

Suppression of limit cycle oscillations using the nonlinear tuned vibration absorber

“…In [17], a nonlinear damping element was added in parallel with the LTVA to decrease the maximum LCO amplitude. Other nonlinear vibration absorbers, including the autoparametric vibration absorber [18,19], the nonlinear energy sink (NES) [20][21][22][23][24][25][26][27][28] and the hysteretic tuned vibration absorber [29], have also been considered to increase the effectiveness of vibration attenuation. In particular, the NES exhibited three different mechanisms to suppress LCOs, namely complete, partial and intermittent suppression.…”