Modeling a vibrating mechanical system with an acceleration-feedback controlled frictional electromagnetic damper

Abstract

The efficiency of an acceleration-feedback controlled frictional electromagnetic damper is proved. An oscillator with a controlled damper is modeled by three ordinary differential equations of the first order with discontinuous right-hand side. An oscillator with acceleration-dependent energy dissipation is described by a simpler model: one equation of the second order with discontinuous coefficients. The exact solution of this equation is found. An approximate law of damping is established. It is shown that the damping parameter is in the base of the exponential function. Double nonstationaryphase–frequency resonance is examined