A Review on Invariant Manifolds and Targeted Energy Transfer

We present a review on one of the latest developments in the field of dynamical systems, The nonlinear Targeted Energy Transfer (TET). The great significance of the phenomenon lies in the fact that the systems in which Nonlinear TET occurs present a form of self-tuning and can transfer energy over a wide variety of frequencies (resonances). This makes nonlinear TET particularly suitable in practical applications where it is necessary to extract energy from multiple ways of oscillation. Dynamical systems where nonlinear TET occurs are systems with different time scales and are singular. This property allows us to study such systems with the use of singular perturbation theory. It has been shown that Nonlinear TET is related to the bifurcation of the Slow Invariant Manifold of such systems and their slow flow.

Dynamics of a Linear Oscillator Coupled to a Bistable Light Attachment: Numerical Study

The conservative and dissipative dynamics of a 2DOF, system composed of a grounded linear oscillator coupled to a lightweight mass by means of both strongly nonlinear and linear negative stiffnesses is investigated. Numerical studies are presented aiming to assess the influence of this combined coupling on the transient dynamics. In particular, these studies are focused on passive nonlinear targeted energy transfer from the impulsively excited linear oscillator to the nonlinear bistable lightweight attachment. It is shown that the main feature of the proposed configuration is the ability of assuring broadband efficient energy transfer over a broad range of input energy. Due to the bistability of the attachment, such favorable behavior is triggered by different nonlinear dynamic mechanisms depending on the energy level. For high energy levels, strongly modulated oscillations occur, and the dynamics is governed by fundamental (1:1) and superharmonic (1:3) resonances; for low energy levels, chaotic cross-well oscillations of the nonlinear attachment as well as subharmonic resonances lead to strong energy exchanges between the two oscillators. The results reported in this work indicate that properly designed attachments of this type can be efficient absorbers and dissipators of impulsively induced vibration energy.

Vibration Reduction Using an Attached Local Nonlinear Passive Absorber Based on a Clamped-Clamped Thin Blade

The concept of nonlinear targeted energy transfer also named energy pumping can be used to passively reduce the vibrations of a primary system by attaching to it an essentially nonlinear damped oscillator also named Nonlinear Energy Sink (NES). In this paper, a thin blade clamped beam is considered as a NES device and studied experimentally. This NES configuration is an alternative way to design an essential stiffness nonlinearity. The behavior of the thin blade structure is first analyzed experimentally and numerically using a 1 DOF nonlinear oscillator. Next, experimental results are presented to demonstrate that the thin blade NES can efficiently reduce the vibrations of a flexible structure. The test set-up is composed of a primary system and the NES. The primary system is a steel beam clamped at one of its end and the NES is attached at the primary structure by its rigid base. Experimental results are discussed and also compared to simulated results obtained from a model.

Numerical Investigation of Rotating Nonlinear Energy Sink for Shock Mitigation

Passive nonlinear targeted energy transfer (TET) is addressed here by investigating a lightweight rotating nonlinear energy sink (NES). The rotating sink mass has an essentially nonlinear inertial coupling with the two degree-of-freedom linear system (the primary test structure). The proposed rotating NES is numerically investigated where it is found to passively absorb and rapidly dissipate a considerable portion of the initial energy induced by impulse to the linear structure. The parameters of the rotating NES are optimized for the best performance in the vicinity of intermediate and high loads. The fundamental mechanism for significant energy transfer to the NES is its rotational mode; the oscillatory mode of the NES dissipates far less energy. The frequency-energy dependences are investigated through the frequency-energy plot (FEP). Early and strong resonance capture at the lowest modal frequency is observed between the rotator and the structure, at which a significant portion of the induced energy is transferred and dissipated by the rotator. The performance of this device is found to be comparable to existing, stiffness-based NES designs. However, this device is less complicated and more compact.

Vibration Suppression of an Axially Moving String with Transverse Wind Loadings by a Nonlinear Energy Sink

Nonlinear targeted energy transfer (TET) is applied to suppress the excessive vibration of an axially moving string with transverse wind loads. The coupling dynamic equations used are modeled by a nonlinear energy sink (NES) attached to the string to absorb vibrational energy. By a two-term Galerkin procedure, the equations are discretized, and the effects of vibration suppression by numerical methods are demonstrated. Results show that the NES can effectively suppress the vibration of the axially moving string with transverse wind loadings, thereby protecting the string from excessive movement.