Improving performance of a nonlinear absorber applied to a variable length pendulum using surrogate optimization

The paper investigates a nonlinear vibration mitigation strategy of a variable length pendulum subjected to a harmonic external excitation. A nonlinear absorber in a form of a tri-pendulum system is used to reduce the response of the primary pendulum. Thus, the paper investigates a non-stationary problem of nonlinear vibration mitigation of the primary pendulum using another nonlinear passive pendulum absorber. Due to genuine interest in capturing the nonlinear dynamic interaction, the paper numerically studies the performance of the primary mass and absorber, first, by constructing 2D maps in the unrestrained parametric space, which demonstrate the qualitative behavior of the system. Then, the surrogate optimization technique is used to tune the absorber's parameters within a given bounded set of parameters' values. The optimization is conducted based on a priori known reeling speed or acceleration/deceleration of the primary pendulum, thereby completely removing the need for acquiring a current system states essential for active feedback control. The obtained numerical results validate the proposed strategy and demonstrate high performance of the nonlinear passive absorber when it is properly tuned.