APPLYING L. MANEVITCH’S COMPLEXIFICATION – AVERAGING METHOD TO ANALYZE CONDITIONS FOR OPTIMAL TARGETED ENERGY TRANSFER IN COUPLED OSCILLATORS WITH ESSENTIAL STIFFNESS NONLINEARITY

摘要

We study targeted energy transfer (TET) [1] from a linear damped oscillator (LO) to a light attachment with essential stiffness nonlinearity, caused by 1:1 transient resonance capture (TRC). First, we study the underlying Hamiltonian dynamics and show that for sufficiently weak damping, the nonlinear damped transitions of the system are strongly influenced by the underlying topological structure of periodic and quasiperiodic orbits of the hamiltonian system. Then, we formulate conditions that lead to effective or even optimal TET from the linear system to the nonlinear attachment. Direct analytical treatment of the governing strongly nonlinear damped equations of motion is performed by applying L. Manevitch’s complexification – averaging (CX-A) method [2] to perform slow-fast partition of the transient responses, and analytically model the dynamics in the region of optimal TET. This analysis determines the characteristic time scales of the dynamics that influence the capacity of the nonlinear attachment to passively absorb and locally dissipate broadband energy from the linear oscillator in an optimal fashion.