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Title:Modal interactions and targeted energy transfers in laminar vortex-induced vibrations of a rigid cylinder with strongly nonlinear internal attachments
Author(s):Tumkur Revannasiddaiah, Ravi Kumar
Director of Research:Bergman, Lawrence A.; Vakakis, Alexander F.
Doctoral Committee Chair(s):Bergman, Lawrence A.; Vakakis, Alexander F.
Doctoral Committee Member(s):Masud, Arif; Pearlstein, Arne J.
Department / Program:Aerospace Engineering
Discipline:Aerospace Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):vortex-induced vibration (VIV)
nonlinear energy sink
targeted energy transfer
passive VIV suppression
passive wake modification
bifurcations in laminar VIV
sub-critical Re VIV
Abstract:We study the effect of coupling an essentially nonlinear element to a sprung rigid circular cylinder undergoing ``vortex-induced vibration'' (VIV) in an incompressible flow. The essentially nonlinear device is termed a ``nonlinear energy sink'' (NES); in this work we use two configurations of NES: translational NES and rotational NES. For the translational NES, consisting of a mass, a linear damper, and an essentially nonlinear spring, the NES mass is constrained to move perpendicular to the mean flow. For the rotational case, the NES mass is constrained to rotate at a fixed radius about the oscillating center of the cylinder. Using a variational multiscale residual-based stabilized finite-element method, we consider the intermediate Reynolds number (Re) regime 20 ≤ Re≤ 120, with the cylinder motion constrained to be perpendicular to the mean flow. The nonlinear interaction of the NES and flow via the rigid body motion of the cylinder leads to several new response regimes of the coupled system of flow-cylinder-NES. The translational NES promotes nearly one-way transfer of energy to itself from the primary structure (the cylinder) and the flow, resulting in reduction of the amplitude of the limit-cycle oscillation (LCO) by as much as 75%, depending on the parameters characterizing the NES. Various mechanisms of VIV suppression by the NES are discussed. A reduced-order model (ROM) based on a single-degree-of-freedom (DOF) self-excited oscillator is developed to approximate the limit-cycle oscillation of the cylinder undergoing VIV. This self-excited oscillator models the interaction of the flow and the cylinder and, in principle, is similar to other phenomenological ROMs considered in the literature. Then, a coupled two-DOF reduced-order model for the system with the internal NES is constructed by coupling the single-DOF NES to the single-DOF self-excited oscillator. Hence, the infinite-dimensional system of flow-cylinder-NES is reduced to a two-DOF model. We examine carefully the range of system parameters where the coupled ROM is valid. The two targeted energy transfer mechanisms responsible for passive VIV suppression that are observed in the finite-element computations are fully reproduced using the two-DOF reduced-order model within the range of validity of the ROM. This reduction of the dynamics to a tractable low-dimensional reduced-order model facilitates the approximate analysis of the underlying dynamics and provides the basis for predictive design of the NES for VIV suppression. Two other approaches of model reduction to obtain a more advanced ROM that can be predictive were also considered, the first based on ``proper orthogonal decomposition'' (POD), and the second based on dynamics of the pressure around the cylinder. We show that, besides passive VIV suppression, the rotational NES can also lead to a flow state that is qualitatively different from the usual K´arm´an vortex street, with the length and width of the attached vortices significantly altered, and the amplitude and frequency of the lift force and cylinder displacement significantly modified. In fact, our finding is that the nonlinear action of the rotational NES can drastically alter the wake structure downstream, which indicates that the internal NES can affect the external flow, even though no direct contact between the NES and the flow exists. We also explore the dependence of the critical $Re$ for the Hopf bifurcation (from steady, symmetric flow past a motionless cylinder to oscillatory, asymmetric flow past a moving cylinder) on the stiffness of the sprung cylinder, and discuss the effect of a rotational NES on the bifurcation diagram. In addition, we demonstrate the existence of multiple long-time solutions of the Navier-Stokes equation in the presence of a rotational NES. Finally, we discuss an approximate analytical approach to explain some of the numerical findings, which provides good agreement with our computational results. This work provides a first study of flow-structure interaction of a bluff body possessing a strongly nonlinear internal attachment, and examines the interesting nonlinear dynamic phenomena that exist in such a system. The underlying nonlinear dynamics that govern these phenomena is passive targeted energy transfer from the flow and the bluff body to the NES, which introduces new interesting dynamics with no counterparts in analogous linear settings. As such, this work can be regarded as a contribution in the new field of constructive use of intentional strong nonlinearity in mechanics and design.
Issue Date:2014-01-16
Rights Information:Copyright 2013 Ravi Kumar Tumkur Revannasiddaiah
Date Available in IDEALS:2014-01-16
Date Deposited:2013-12

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