Numerical and Experimental Stability Investigation of a Parametrically Excited Cantilever Beam at Combination Parametric Resonance

Abstract

BackgroundThe presence of parametric excitation in dynamic structures, caused by friction, crack, varying compliance, electromagnetic field, etc. may generate unbounded responses. In the literature there exist several numerical analyses of systems affected by parametric excitation, while experimental studies are less frequent.ObjectiveThe goal of the paper is to create a demonstrator of a parametrically excited system, whose stability can be modified through a controlled physical parameter. This work also investigates the applicability of the recently developed stability analysis method named Jacobian Based Approach (JBA).MethodsThis paper studies a simple experimental set-up comprising of a cantilever beam mounted on a spring with time – varying stiffness, achieved through the use of an electromagnet. The test rig allows measuring directly the magnetic force without any preknowledge of the values of electrical parameters. Results obtained from the test rig are compared with numerical results obtained from the Finite Element model. In this study, Hill’s method and JBA are employed to obtain the stability plot highlighting the regions of parametric instabilities.ResultsGood agreement is found between experimental and numerical data and the presence of unstable behavior is verified through the use of the well – known Hill’s method and the JBA. Furthermore, this study demonstrates that the stability plot, highlighting the unstable regions, computed by JBA is in complete agreement with the one obtained by Hill’s method.ConclusionsIt is shown how the parametric instability can be triggered through the regulation of a simple physical parameter, i.e. the gap between the electromagnet and the beam. The numerical model analyzed by the ad – hoc technique proposed by the authors i.e. JBA has been proven to have predictive capabilities in studying a system under parametric excitation and could be a potential substitution for state-of-the-art stability analysis techniques such Hill’s method.