Stability of steady-state vibrations of a nonlinear,imperfectly elastic two-mass system subjected to harmonic excitation

A study is made of the stability of steady-state vibrations of harmonically excited two-mass systems with allowance for the imperfect elasticity of the materials and cubic nonlinearities. It is shown that, in the general case, when imperfect elasticity is accounted for by the model constructed by G. S. Pisarenko, an increase in the inflection of the skeleton curves with an increase in the amplitude of the vibrations may lead to the appearance of regions of instability and amplitude jumps. The averaging method is used to determine the conditions under which the amplitudes will be stable. Resonance curves of amplitude are constructed for a two-mass system modeling an imperfectly elastic dynamic vibration damper. The range of stable amplitudes is also determined for this system. It is shown that a cubic nonlinearity can either reinforce or offset the inflections caused by inelasticity.Translated from Problemy Prochnosti, No. 8, pp. 69–76, August, 1994.