Experimental analysis of the influence of damping on the resonance behavior of a spherical pendulum

This study describes the experimental and numerical dynamic analysis of a kinematically excited spherical pendulum. The stability of the response in the vertical plane was analyzed in the theoretically predicted auto-parametric resonance domain. Three different types of the resonance domain were investigated the properties of which depended significantly on the dynamic parameters of the pendulum and the excitation amplitude. A mathematical model was used to represent the nonlinear characteristics of the pendulum, which includes the asymmetrical damping. A special frame was developed to carry out the experiments, which contained the pendulum supported by the Cardan joint and two magnetic units attached to the supporting axes of rotation, and this was able to reproduce linear viscous damping for both of the principal response components. The stability analysis of the system was compared with the numerical solution of the governing equations and experimental observation. The most significant practical outcomes for designers are also summarized.