A time-varying inertia pendulum: Analytical modelling and experimental identification

• Experimental study of a time-varying inertia pendulum subject to large amplitudes.
• Theoretical models for both the flexural and the nonlinear swinging motion, which are uncoupled.
• Fixed mass case: estimation of the nonlinear effect in the swinging motion.
• Moving mass case: good agreement between predicted and identified swinging frequencies.

In this paper two of the main sources of non-stationary dynamics, namely the time-variability and the presence of nonlinearity, are analysed through the analytical and experimental study of a time-varying inertia pendulum. The pendulum undergoes large swinging amplitudes, so that its equation of motion is definitely nonlinear, and hence becomes a nonlinear time-varying system. The analysis is carried out through two subspace-based techniques for the identification of both the linear time-varying system and the nonlinear system.The flexural and the nonlinear swinging motions of the pendulum are uncoupled and are considered separately: for each of them an analytical model is built for comparisons and the identification procedures are developed. The results demonstrate that a good agreement between the predicted and the identified frequencies can be achieved, for both the considered motions. In particular, the estimates of the swinging frequency are very accurate for the entire domain of possible configurations, in terms of swinging amplitude and mass position.