Alireza Ture Savadkoohi

Efficient Targeted Energy Transfer With Parallel Nonlinear Energy Sinks: Theory and Experiments

In this paper the targeted energy transfer (TET) phenomenon between a linear multi- DOF master structure and several slave parallel nonlinear energy sink (NES) devices during a 1:1 resonance capture is investigated. An analytical method is proposed for tuning optimal NES parameters, which leads to efficient TETs. Then, the procedure is intentionally narrowed for a 4DOF master structure with two parallel NESs at the last DOF in order to grasp optimum NES parameters of a prototype structure that is built and tested at the Civil Engineering and Building Department Laboratory of the ENTPE. The aim is to control the first mode of the compound nonlinear prototype system by demonstrating the efficiency of designed parallel NESs by the suggested method.

Multi-resonance capturing in a two-degree-of-freedom system under two different harmonic excitations:

In this paper we consider two coupled oscillators which exhibit energy transfer from master ‘linear’ degrees of freedom submitted to resonant external excitation with two different harmonics to a slave ‘nonlinear’ energy sink (NES). By endowing the idea of the relative mode, splitting harmonics and iterative techniques, we prove that control of the two one-to-one resonances of the system is possible simultaneously; moreover, the iterative technique gives us a better outlook over effects of the NES parameters on the overall behavior of the system. Then, analytical procedure for multi-resonance capture are explained and commented on. Finally, the obtained analytical results are compared with numerical evidence.

Vibratory Energy Localization by Non-smooth Energy Sink with Time-Varying Mass

We study nonlinear interactions of two coupled oscillators at different time scales. The main oscillator which is linear is coupled to a nonlinear energy sink with non-smooth (piecewise linear) potential and time-dependent mass. The overall time is embedded to fast and slow time scales and the behavior of the system at each one of them is revealed.The invariant of the system at fast time scale is detected. Then we try to have further information about the overall system behavior at the first slow time scale. Finally, analytical developments are compared with numerical results and the possibility of the passive control of the main system by means of the time-dependent NES is commented upon.

Multiple resonance capture of a compound system under harmonic excitation

Vibration exchange between a master linear oscillator and a slave Nonlinear Energy Sink (NES) under harmonics excitation by means of several resonance capture is investigated and commented upon. The importance of higher frequencies by introducing the concept of the relative mode is pinpointed. A fast and special iterative technique and then the more general form of it is introduced in order to evaluate the system unknowns. Finally, the effect of the correct resonance paring on detecting the actual system behavior is illustrated by an example.

Targeted Energy Transfer With Several NES in Parallel: Theory and Experiments

The crucial point in the field of seismic engineering is to diminish the induced vibration energy as much as possible in a fast and almost irreversible manner. Recently the concept of Nonlinear Energy Sink (NES) has been developed such that the imposed energy to a linear single Degree of Freedom (DoF) substructure is transferred to one or series of strongly nonlinear light attachments; the mechanism is based on a 1:1 resonance capture. Nonlinear attachments can be designed to passively vibrate with any frequency; hence the system is efficient for both of transient and periodic excitations. Some drawbacks of these systems are as follows: they cannot kill the first peak of oscillation in the free time response that is linked to the energy activation of NES; moreover, the transformation of energy vanishes in time due to decrease of the strength of energy pumping. Using NES in series even cannot accelerate the phenomenon of energy pumping and some strange behavior due to the delay in the cooperation of NES in series is noticed. In this study, the transient dynamic behavior of multiple DoF systems with trees of parallel NES at each DoF is investigated, then experimental and numerical results of a four DoF structure with two parallel NES at the top floor are demonstrated and commented upon.© 2009 ASME

Passive Control of Differential Algebraic Inclusions - General Method and a Simple Example

In this chapter, we consider a master system consisting of a nonlinear differential inclusion and an algebraic equation of constraint (resulting in a Differential Algebraic Inclusion (DAI) system). This system is coupled to a nonlinear energy sink (NES) corresponding to a one degree-of-freedom essentially nonlinear differential equation. We examine how a resonance capture can lead to a reduced order dynamical system. To obtain this reduced order model, we describe a multiple time scale analysis governed by the introduction of multi-timescales via a small parameter \(\varepsilon \) that is finite and strictly positive. The mass of the NES is small versus the mass of the master system, and it governs a mass ratio defining the small parameter \(\varepsilon \). The first timescale is the fast scale. Introducing the Manevitch complexification leads to the definition of slow time envelope coordinates. These envelope coordinates either do not directly depend on the fast time scale or do not depend on this fast time scale via introduction of the so-called Slow Invariant Manifold (SIM). The slow time dynamics of the master system components is analyzed through introduction of equilibrium points, corresponding to periodic solutions, or singular points (governing bifurcations around the SIM), corresponding to quasi-periodic behaviors. We present a simple example of semi-implicit Differential Algebraic Equation (DAE), including a friction term coupled to a cubic NES. Analytical developments of a 1:1:1 resonance case permit us to predict passive control of a DAI by a NES.

LOCALIZATION OF VIBRATORY ENERGY OF A LINEAR SYSTEM IN A CHAIN OF FOUR NONLINEAR OSCILLATORS

Abstract. In this paper, dynamics of a five degree-of-freedom system formed by a main linear oscillator coupled to four light nonlinear systems in series is studied. The aim is to control and/or to harvest the energy of the main structure under harmonic excitations around its resonance. A multiple scales method is used to derive the behavior of the system at different time scales. At fast time scale, detected slow invariant manifold gives an overall comprehension of the possible behaviors that the system can undergo. At slow time scale, the modulated behavior of the system around its invariant is described by traced equilibrium and singular points. The former predict periodic regimes, while the latter hint at strongly modulated responses characterized by persisting bifurcations of the system around its unstable zones. All analytical results are validated by numerical simulations.