caa a22 4500 445361727 CHVBK 20180317142917.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s11071-011-9949-x doi (NATIONALLICENCE)springer-10.1007/s11071-011-9949-x Targeted energy transfer with parallel nonlinear energy sinks. Part I: Design theory and numerical results [Elektronische Daten] [Bastien Vaurigaud, Alireza Ture Savadkoohi, Claude-Henri Lamarque] In this paper, we study a Targeted Energy Transfer (TET) problem between a p degrees-of-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. Springer Science+Business Media B.V., 2011 Transient regime nationallicence Stationary regime nationallicence Complexification nationallicence Multiple scales nationallicence Bifurcations nationallicence Tuning nationallicence NES in parallel nationallicence c n , j : damping of NES j attached to the dof n nationallicence k n , j : stiffness of NES j attached to the dof n nationallicence q 1 : first mode generalized displacement of the linear system nationallicence x n , j : displacement of NES j attached to the dof n nationallicence $C_{1}^{*}$ : first mode modal damping of the linear system nationallicence F n ( t ) : external forcing on dof n nationallicence $K_{1}^{*}$ : first mode modal stiffness of the linear system nationallicence $M_{1}^{*}$ : first mode modal mass of the linear system nationallicence φ n ,1 : first mode modal shape of the linear system at dof n nationallicence Vaurigaud Bastien Université de Lyon, ENTPE/DGCB/FRE CNRS 3237, 3 rue Maurice Audin, 69518, Vaulx-en-Velin Cedex, France aut Ture Savadkoohi Alireza Université de Lyon, ENTPE/DGCB/FRE CNRS 3237, 3 rue Maurice Audin, 69518, Vaulx-en-Velin Cedex, France aut Lamarque Claude-Henri Université de Lyon, ENTPE/DGCB/FRE CNRS 3237, 3 rue Maurice Audin, 69518, Vaulx-en-Velin Cedex, France aut Nonlinear Dynamics Springer Netherlands 66/4(2011-12-01), 763-780 0924-090X 66:4<763 2011 66 11071 https://doi.org/10.1007/s11071-011-9949-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-011-9949-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Vaurigaud Bastien Université de Lyon, ENTPE/DGCB/FRE CNRS 3237, 3 rue Maurice Audin, 69518, Vaulx-en-Velin Cedex, France aut NATIONALLICENCE 700 1- Ture Savadkoohi Alireza Université de Lyon, ENTPE/DGCB/FRE CNRS 3237, 3 rue Maurice Audin, 69518, Vaulx-en-Velin Cedex, France aut NATIONALLICENCE 700 1- Lamarque Claude-Henri Université de Lyon, ENTPE/DGCB/FRE CNRS 3237, 3 rue Maurice Audin, 69518, Vaulx-en-Velin Cedex, France aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 66/4(2011-12-01), 763-780 0924-090X 66:4<763 2011 66 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer