Dynamics of a system containing a linear oscillator, linearly coupled to an essentially nonlinear attachment, is considered. A damping is taken into account. It is assumed that some initial excitation implies vibrations of the linear oscillator. Envelops of the subsystem's kinetic energies are selected to use the numerical investigation of transient in the system. The parametrical optimization approach is used to obtain regions of effective energy transfer in the system parameter space. It is demonstrated that this efficient energy transfer may be obtained for a rather small value of the attachment mass.
Energy pumping in a two-degrees-of-freedom system with linear and essentially nonlinear oscillators is studied. The kinetic energy envelopes of the linear and nonlinear subsystems are chosen to be the main characteristics of the process under consideration. A criterion that the energy of the linear oscillator excited at time zero is completely pumped over into the nonlinear oscillator is established together with an additional condition whereby the energy does not return to the linear subsystem. Optimal energy pumping mode is established using global optimization. The effect of the parameters of the system on the main characteristics is assessed Keywords: linear and nonlinear oscillators, energy pumping, energy localization, global optimization Introduction. Vibration damping problems are of critical importance for modern engineering. The vibrations of the main system are frequently suppressed with an attached passive damper, which redistributes the vibrational energy from the main system to the damper. In many cases, it could be effective to use linear dampers of large mass; however, using them in real systems is more often than not impossible. Therefore, it would be of interest to study nonlinear passive dampers and, in particular, the process of energy transfer to a small nonlinear structure added to the system.The classical damper, as we know it today, was first proposed by Frahm [18]. He supplemented the main vibrating system with an auxiliary system with a mass, a spring, and a damper to neutralize the external disturbance. Den Hartog [15] and many other authors studied linear passive dampers in detail. Arnold [13] and Roberson [32] analyzed nonlinear vibration absorbers without friction connected to the vibrating system via a cubic spring. The analyses have revealed that a nonlinear spring improves the absorber by extending its frequency range. Later, many types of nonlinear absorber, which could be much more efficient than linear ones, were analyzed. A general nonlinear theory of vibration damping is outlined in [3]. A vibration absorber in the form of a beam attached to a mass-string system was examined in [23]. Forced resonances of a system with a nonlinear vibration absorber were studied in [33]. A general theory of linear and nonlinear vibration dampers was outlined in [1]. The possibility of using pendulums to reduce torsional vibrations was theoretically and experimentally examined in [22,26]. The use of impact vibration absorbers was analyzed in [12, etc.]. Methods of the theory of nonlinear normal vibrations are used in [29] to analyze stationary modes in the vibration damping problem with an essentially nonlinear oscillator as a damper. The possibility of using a Mises truss for efficient damping of elastic vibrations is demonstrated in [14]. The optimal strategy to control the passive viscous damping of structures is presented in [10].The problem of vibration damping and energy localization in a vibration absorber is closely related to the general energy-transfer problem. Vitt and Gorelik [2] we...
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