Turbulence, Coherent Structures, Dynamical Systems and SymmetryP. Holmes, J. L. Lumley, G. Berkooz, and C. W. Rowley, 2nd ed., Cambridge University Press, Cambridge, England, U.K., 2012, 386 pp., $90

Nonlinear dissipative devices in structural vibration control: A review

Nonlinear energy sink (NES) is an appropriately designed nonlinear oscillator without positive linear stiffness. NES can suppress vibrations over a wide frequency range due to its targeted energy transfer characteristics. Thus, investigations on NES have attracted a lot of attention since a NES was proposed. Designs, analysis, and applications of NESs are still active since different configurations are needed in various practical circumstances. The present work provides a comprehensive review of state-of-the-art researches on NESs. The work begins with a survey of the generation of a NES and its important vibration control characteristics. The work highlights possible complex dynamics resulting in a NES coupled to a structure. The work also summarizes some significant design on the implements of optimal damping effects and the offsets of NES shortcomings. Then, the work details the applications of NESs in all engineering fields. The concluding remarks suggest further promising directions, such as NESs for multidirectional vibration reduction, NESs with nonlinearities beyond the cubic, potential deterioration caused by a NES, low-cost NESs, NESs for extremely low frequency range, and NESs integrated into active vibration controls. There are 383 references in the review, including some publications of the authors.

Designs, analysis, and applications of nonlinear energy sinks

Elementary Finite Elements.- Nonconforming Finite Elements.- Mixed Finite Elements.- Discontinuous Finite Elements.- Characteristic Finite Elements.- Adaptive Finite Elements.- Solid Mechanics.- Fluid Mechanics.- Fluid Flow in Porous Media.- Semiconductor Modeling.

Finite element methods and their applications

Force and particle image velocimetry measurements were conducted on a NACA 0012 airfoil undergoing small-amplitude sinusoidal plunge oscillations at a poststall angle of attack and Reynolds number of 10,000. With increasing frequency of oscillation, lift increases and drag decreases due to the leading-edge vortices shed and convected over the suction surface of the airfoil. Within this regime, the lift coefficient increases approximately linearly with the normalized plunge velocity. Local maxima occur in the lift coefficient due to the resonance with the most unstable wake frequency, its subharmonic and first harmonic, producing the most efficient conditions for high-lift generation. At higher frequencies, a second mode of flowfield occurs. The leading-edge vortex remains nearer the leading edge of the airfoil and loses its coherency through impingement with the upward-moving airfoil. To capture this impingement process, high-fidelity computational simulations were performed that showed the highly transitional nature of the flow and a strong interaction between the upper and lower-surface vortices. A sudden loss of lift may also occur at high frequencies for larger amplitudes in this mode.

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Lift enhancement by means of small-amplitude airfoil oscillations at low Reynolds numbers

Numerical bifurcation analysis of static stall of airfoil and dynamic stall under unsteady perturbation

Effects of local oscillation of airfoil surface on lift enhancement at low Reynolds number

Dynamic responses of a two-dimensional (2D) perimeter-reinforced (PR) membrane wing in laminar viscous flows are investigated numerically. The 2D Navier–Stokes equations and a one-dimensional nonlinear equation for membrane vibration are coupled to describe the flow-induced vibrations of the membrane wing in laminar flows. The modified characteristic-based split scheme, Galerkin finite element method, spring analogy technique and loosely coupled partitioned approach are employed, respectively, for the flow simulation, computation of the membrane response, mesh movement of the flow domain and fluid–structure interaction. The accuracy and stability of the proposed numerical method and corresponding codes are validated using a benchmark model of fluid–membrane interaction. Finally, the bifurcation characteristics of the membrane dynamic response and vortex structure near the membrane wing with respect to the angle of attack, Reynolds number, rigidity and pre-strain are analysed in detail. This paper could give people more information about the dynamic behaviours of the PR membrane wing in the laminar flow regime.

Nonlinear dynamic responses of a perimeter-reinforced membrane wing in laminar flows

Lagrangian analysis of mass transport and its influence on the lift enhancement in a flow over the airfoil with a synthetic jet

The flow-induced vibration of two-dimensional wing coupled with two nonlinear energy sinks (NESs) under freestream is studied by numerical methods, and the relationship between the vibration suppression and targeted energy transfer (TET) of the system is analyzed in detail. First, the model of the coupling system, which includes heave and pitch modes, is presented, and the NESs are located at the leading edge and trailing edge (NES1 and NES2) separately. Then, the vibrations suppressed by NESs are also investigated from the viewpoint of energy transfer, and the resonance captures (RCs) in the nonlinear coupling system are studied by using spectrum analysis. Furthermore, the ensuing TET through the modes of wing (heave and pitch) and the NESs is discussed in detail. The results show that the NESs can absorb the energy from every single mode of the wing, and the TET and RCs between modes can be more significant in the coupling system. Therefore, the TET is more efficient between the wing and NESs. It leads to the increase of the critical velocity of freestream under which the nonlinear vibration of wing can be suppressed by NESs effectively.

Jiazhong Zhang

Papers

Numerical bifurcation analysis of static stall of airfoil and dynamic stall under unsteady perturbation

Effects of local oscillation of airfoil surface on lift enhancement at low Reynolds number

Nonlinear dynamic responses of a perimeter-reinforced membrane wing in laminar flows

Lagrangian analysis of mass transport and its influence on the lift enhancement in a flow over the airfoil with a synthetic jet

Targeted energy transfer between 2-D wing and nonlinear energy sinks and their dynamic behaviors