Abstract
We study complex damped and undamped dynamics and targeted energy transfers (TETs) in systems of coupled oscillators, consisting of single-degree-of-freedom primary linear oscillators (LOs) with vibro-impact attachments, acting, in essence, as vibro-impact nonlinear energy sinks (VI NESs). First, the complicated dynamics of such VI systems is demonstrated by computing the VI periodic orbits of underlying Hamiltonian systems and depicting them in appropriate frequency–energy plots (FEPs). Then, VI damped transitions and distinct ways of passive TETs from the linear oscillators to the VI attachments for various parameter ranges and initial conditions are investigated. As in the case of smooth stiffness nonlinearity [Y. Lee, G. Kerschen, A. Vakakis, P. Panagopoulos, L. Bergman, D.M. McFarland, Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment, Physica D 204 (1–2) (2005) 41–69], both fundamental and subharmonic TET can be realized in the VI systems under consideration. It is found that the most efficient mechanism for VI TET is through the excitation of highly energetic VI impulsive orbits (IOs), i.e., of periodic or quasiperiodic orbits corresponding to zero initial conditions except for the initial velocities of the linear oscillators. In contrast to NESs with smooth essential nonlinearities considered in previous works, VI NESs are capable of passively absorbing and locally dissipating significant portions of the energies of the primary systems to which they are attached, at fast time scale. This renders such devices suitable for applications, like seismic mitigation, where dissipation of vibration energy in the early, highly energetic regime of the motion is a critical requirement.
Highlights
To study the underlying dynamical mechanisms and associated transient resonance captures (TRCs) that govern passive targeted energy transfers (TETs) in systems with vibro-impact nonlinear energy sinks (VI nonlinear energy sinks (NESs)), and to demonstrate the complexity that a single VI NES can induce in the dynamics, we consider the simplest primary system — VI NES configuration, namely a single-degree-of-freedom (SDOF) linear oscillators (LOs) coupled to a VI NES (Fig. 3)
We aim to study the efficiency of VI TET in the system of Fig. 3 by introducing certain definitions related to the capacity of the VI NES to passively absorb and dissipate vibration energy from the LO, as well as the time required for this VI dissipation to occur
We showed that an SDOF primary linear oscillator (LO) with an attached vibro-impact nonlinear energy sink (VI NES) possesses very complicated dynamics
Summary
Broadband targeted energy transfer (TET) refers to the one-way directed transfer of energy from a primary subsystem to a nonlinear attachment; this phenomenon is realized in damped, coupled, essentially nonlinear oscillators through resonance captures and escapes along intrinsic periodic or quasiperiodic orbits of the underlying Hamiltonian systems [1,2]. An NES generally requires two elements: an essentially nonlinear (i.e., nonlinearizable) stiffness and a (usually, linear viscous) damper The former, which is smooth in many cases, enables the NES to resonate with any of the linearized modes of the primary system to which it is attached, whereas the latter acts as dissipator of the vibrational energy transferred through resonant modal interactions (see [3,4] for an overview of the dynamics governing TET and its various applications). Better vibro-impact shock absorption is anticipated for weak coupling stiffness between the primary systems and the attached NESs, and relatively large values of NES masses compared to the masses of the corresponding primary systems These results are in agreement with findings of Georgiades et al [8]
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