Vibration Suppression of a Cantilever Beam by Open-Loop Control of an Attached Stiffness Element
In this numerical study new findings on parametric resonances of beam structures are presented. A uniform cantilever beam attached to a stiffness element with a non-linear time-periodic parameter value is investigated. The beam structure is discretized by a Finite Element approach. The linearized equations of motion describing the planar vibrations of the beam structure lead to a system with time-periodic stiffness coefficients. The stability of the system is investigated by a numerical method based on Floquet's theorem. Numerical simulation is employed to calculate time series of the transient beam deflections. It is demonstrated, that suppression of free vibrations can be more effective, if the structure is excited by a non-resonant parametric combination resonance frequency. Numerical studies show how the location of the attached time-periodic stiffness element affects the performance of the proposed method. Morevoer, the influence of a typical cubic nonlinearity is investigated.