Linear Tuned Vibration Absorber Research Articles

Analysis of a piecewise linear aeroelastic system with and without tuned vibration absorber

The dynamics of a two-degrees-of-freedom (pitch–plunge) aeroelastic system is investigated. The aerodynamic force is modeled as a piecewise linear function of the effective angle of attack. Conditions for admissible (existing) and virtual equilibria are determined. The stability and bifurcations of equilibria are analyzed. We find saddle-node, border collision and rapid bifurcations. The analysis shows that the pitch–plunge model with a simple piecewise linear approximation of the aerodynamic force can reproduce the transition from divergence to the complex aeroelastic phenomenon of stall flutter. A linear tuned vibration absorber is applied to increase stall flutter wind speed and eliminate limit cycle oscillations. The effect of the absorber parameters on the stability of equilibria is investigated using the Liénard–Chipart criterion. We find that with the vibration absorber the onset of the rapid bifurcation can be shifted to higher wind speed or the oscillations can be eliminated altogether.

Effects of modal energy scattering and friction on the resonance mitigation with an impact absorber

A linear vibration absorber can be tuned to effectively suppress the resonance of a particular vibration mode. It relies on the targeted energy transfer into the absorber within a narrow and fixed frequency band. Nonlinear energy sinks (NES) have a similar working principle. They are effective in a much wider frequency band but generally only in a limited range of excitation levels. To design NES, their working principle must be thoroughly understood. We consider a particular type of NES, a small mass undergoing impacts and dry friction within a cavity of a base structure (vibro-impact NES or impact absorber). The nonlinear dynamic regimes under near-resonant forcing and resulting operating ranges are first revisited. We then investigate how off-resonant vibration modes and dissipation via impacts and dry friction contribute to the vibration suppression. Moreover, we assess the effectiveness of the impact absorber for suppressing multiple resonances in comparison to a linear tuned vibration absorber (LTVA) and a pure friction damper with the same mass.

Experimental Passive Flutter Suppression Using a Linear Tuned Vibration Absorber

The current drive for increased efficiency in aeronautic structures such as aircraft, wind-turbine blades, and helicopter blades often leads to weight reduction. A consequence of this tendency can be increased flexibility, which in turn can lead to unfavorable aeroelastic phenomena involving large-amplitude oscillations and nonlinear effects such as geometric hardening and stall flutter. Vibration mitigation is one of the approaches currently under study for avoiding these phenomena. In the present work, passive vibration mitigation is applied to a nonlinear experimental aeroelastic system by means of a linear tuned vibration absorber. The aeroelastic apparatus is a pitch and flap wing that features a continuously hardening restoring torque in pitch and a linear restoring torque in flap. Extensive analysis of the system with and without absorber at precritical and postcritical airspeeds showed an improvement in flutter speed of around 36%, a suppression of a jump due to stall flutter, and a reduction in limit-cycle oscillation amplitude. Mathematical modeling of the experimental system is used to demonstrate that optimal flutter delay is achieved when two of the system modes flutter at the same flight condition. Nevertheless, even this optimal absorber quickly loses effectiveness as it is detuned. The wind-tunnel measurements showed that the tested absorbers were much slower to lose effectiveness than those of the mathematical predictions.

Absorption of Resonant Vibrations in Tuned Nonlinear Jointed Structures

A novel concept for the passive mitigation of forced, resonant vibrations is presented. The key to this concept is an absorption phenomenon which relies on the energy conversion from low to high frequencies by means of nonlinearity. The vibration energy of a resonantly driven substructure is transferred to an internally resonant substructure within the system. Compared with the well-known linear tuned vibration absorber (LTVA), the main advantage of the proposed concept is that no separate absorber is required, but instead the existing modal structure is properly tuned and inherent nonlinearities are utilized. Just like the former concept, however, the proposed concept is limited to a narrow frequency bandwidth, which represents its main drawback of the approach. The concept is exemplified for a system of two beams connected via a nonlinear joint with a soft, unilateral-elastic characteristic. It is demonstrated that when the system is appropriately tuned, its vibration level is reduced by 60–80%, i.e., by a factor of 2.5–5. Moreover, it is shown how the efficacy and robustness of the concept can be optimized.

Nonlinear generalization of Den Hartog׳s equal-peak method

This study addresses the mitigation of a nonlinear resonance of a mechanical system. In view of the narrow bandwidth of the classical linear tuned vibration absorber, a nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA), is introduced in this paper. An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is tailored according to the nonlinear restoring force of the primary system. The NLTVA parameters are then determined using a nonlinear generalization of Den Hartog׳s equal-peak method. The mitigation of the resonant vibrations of a Duffing oscillator is considered to illustrate the proposed developments.

Generalization of Den Hartog’s Equal-Peak Method for nonlinear primary systems

This study addresses the mitigation of one problem nonlinear resonance of a mechanical system. In view of the narrow bandwidth of the classical linear tuned vibration absorber, a new nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA), is introduced in this paper. One unconventional aspect of the NLTVA is that the mathematical form of its restoring force is tailored according to the nonlinear restoring force of the primary system. The NLTVA parameters are then determined using a nonlinear generalization of Den Hartog’s equal-peak method. The mitigation of the resonant vibrations of a Duffing oscillator is considered to illustrate the proposed developments.

The Nonlinear Tuned Vibration Absorber

The objective of this paper is to introduce a new nonlinear dynamical absorber, the nonlinear tuned vibration absorber, through a rigorous nonlinear extension of the tuning rule for the linear tuned vibration absorber. This nonlinear tuning methodology combined with the increased suppression bandwidth brought by the intentional use of nonlinearity leads to the development of an absorber that is effective in wide ranges of frequencies and motion amplitudes. The results are illustrated using a one-degree-of-freedom primary system.