Targeted energy transfer with parallel nonlinear energy sinks. Part I: Design theory and numerical results

Abstract

In this paper, we study a Targeted Energy Transfer (TET) problem between a p degreesof-freedom (dof) linear master structure and several coupled parallel slave Nonlinear Energy Sink (NES) systems. In detail, each lth dof l = 1, 2, . . . , p contains n l parallel NES; so the linear structure has (n 1 + n 2 + · · · + n l + · · · + n p ) NES. We are interested to study analytically the TET phenomenon during the first mode of the compound system. To this end, complexification, averaging, and multiple scales methods are used.The system is studied under 1:1 resonance for the transient regime and under harmonic excitation. The influence of the system parameters is observed through dimensionless variables. An analytical criterion is defined to tune NES parameters which lead to an efficient TET for the transient and the forced regimes. It will be demonstrated that analytical results are in good agreement with numerical ones. This paper will be followed by a companion paper which mainly deals with the governing equations for compound nonlinear systems with trees of NES devices at each dof; then experimental results of a four storey structure with two parallel NES at the top floor which are tuned by the mentioned technique in the current paper will be demonstrated and commented upon.

Performance Comparison Between a Nonlinear Energy Sink and a Linear Tuned Vibration Absorber for Broadband Control

“…Since in our case, the forcing amplitude is considered fixed, the tuning procedure consists in finding appropriate value of (λ, K) for the NES. Critical forcing amplitude can be converted into critical nonlinear stiffness by using the forcing-nonlinearity equivalence principle [18] which states that if the ratio G 2 /K = cst, the behavior of the system, compared to the supplied energy, remains unchanged. By doing so, the sizing chart depicted in Fig.…”

Vibration mitigation of a bridge cable using a nonlinear energy sink: design and experiment

“…These kinds of equations have been studied in [2,5] investigating the behaviour of regular nonlinearities.…”

“…Then multiple scales are introduced in derivatives with fast time ߬ 0 = ߬ and ߬ ݆ = ߝ ݆ ߬ for j=1, 2,.. slow time scales. As exposed in [2,5,6,7] there is a nonlinear relation between ܰ 1 and ܰ 2 if we consider ߬ 0 → ∞, i.e. to analyse fixed points of the system.…”

“…This study aims at performing vibration mitigation of the first horizontal linear mode of a bridge cable using an essentially cubic NES prototype. The first part focuses on the experimental modal analysis of the cable, then a theoretical design analysis [2] using complexification of variables and time-multiple scales analysis is performed on a simplified 2-dof model of the first mode of the cable-NES system. The design is numerically tested for a step release excitation and then the prototype system is built and experimentally tested on a cable mounted in a tensioning bench.…”

Dynamics of a forced 2 dof piece-wise linear system by consideration of the weight

“…It has been proved that a system can be passively controlled by endowing nonlinear innate of coupled cubic systems, namely nonlinear energy sink (NES) to the main one [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. There has been some attempts to consider the nonsmooth NES systems instead of cubic ones.…”