Passive and active vibration absorption in Duffing mechanical systems excited by multi-frequency harmonic forces

This paper deals with the multi-frequency harmonic vibration suppression problem in forced Duffing mechanical systems using passive and active linear mass-spring-damper dynamic vibration absorbers. A passive/active vibration absorption scheme is proposed to extend the vibrating energy dissipation capability of a passive dynamic vibration absorber for multiple excitation frequencies and, simultaneously, to perform desired position reference trajectory tracking tasks. Parameter variations, exogenous multiple time-varying frequency perturbation forces and possibly input unmodeled dynamics are lumped into an unknown time-varying perturbation input signal affecting the differentially flat nonlinear vibrating mechanical system dynamics. The lumped perturbation signal is modeled locally by a family of Taylor polynomials and estimated by using a differential flatness-based high-gain dynamic observer. Some numerical simulation results are provided to show the effective, robust and efficient performance of the proposed active vibration absorption scheme as well as the closed-loop system global stability when the primary mechanical system is subjected to resonant frequency harmonic excitations.