ENOC-2008, Saint Petersburg, Russia, June, 30–July, 4 2008 TARGETED ENERGY TRANSFER IN A SYSTEM WITH SOFT NONLINEARITY Oleg V. Gendelman Faculty of Mechanical Engineering Technion – Israel Institute of Technology Technion City, Haifa, 32000, Israel E-mail: ovgend@tx.technion.ac.il Abstract Targeted energy transfer (TET) in a 2DOF system consisting of primary linear oscillator and nonlinear energy sink (NES) with non – polynomial potential is investigated. Use of non – polynomial and even non – analytic potential functions is motivated by needs of practical design. It is demonstrated that the "complexification – averaging" technique of analysis developed before can be successfully extended for these cases with proper modifications. Key words: Targeted energy transfer, nonlinear energy sink, soft nonlinearity 1 Description of the model and numeric demonstration Targeted energy transfer, i.e. almost irreversible passive transfer of mechanical energy from linear substructure to essentially nonlinear attachment (nonlinear energy sink, NES) has attracted a lot of attention of researches in few last years [Gendelman, 2001, Gendelman, 2004, Lee et al, 2006, Panagopulos et al, 2007, Gourdon and Lamarque, 2006]. In majority of these models, stiff nonlinear attachments (commonly, purely cubic spring) were used. In many applications – especially those where geometric nonlinearity is involved – the nonlinear springs are soft. Demonstration and investigation of the effect of the targeted energy transfer in a system with soft essentially nonlinear attachment is the goal of this work. For the sake of modelling, the potential of the attachment is chosen in the form 2 () ln(1 ) Vz k z ε = + , providing linear limit with stiffness coefficient 2εk for small deformations z and softening while z grows. Primary system is chosen to consist of linear oscillator with unit frequency and mass, without damping. The nonlinear attachment is adopted to have small mass ε<<1 and linear damping with coefficient ελ. Equations describing the system dynamics are 1 2 1 1 1 2 2 1 2 2 1 2 2 1 2 1 2 2 ( ) ( ) 0 1 ( ) 2 ( ) ( ) 0 1 ( ) ky y y y y y y y ky y y y y y y ε ελ ε ε ελ − + + − + = + − − + − + = + −       (1) where y 1 and y 2 are the displacements of the primary oscillator and the attachment respectively. The phenomenon of the targeted energy transfer may be demonstrated numerically if System (1) is modelled with initial conditions: 1 1 2 2 (0) 0, (0) , (0) 0, (0) 0 y y Ay y = = = =   In order to demonstrate the targeted transfer, we plot the relative instantaneous energy /( ) att primary att R E E E = + stored in