Experimental evaluation of damping models for a nonlinear pendulum system

Abstract

Popular damping models for a single pendulum system were experimentally evaluated in this study. The comparison between the numerical and experimental responses showed that neither linear viscous damping model nor squared velocity proportional viscous damping model was able to well capture the free vibration amplitudes of the pendulum in both large and small amplitude ranges. Specifically, the amplitudes of the numerical model with linear viscous damping decreased slower at the large amplitude vibration but faster at the small amplitude vibration than the experimental amplitudes did. The trend was reverse in the numerical model with the squared velocity proportional viscous damping model. Based on the experimental data and a numerical method combined with a fitting approach, a complete quadratic viscous damping model for the pendulum was derived. The model was able to confidently predict the free vibration amplitudes of the pendulum in both large and small amplitude ranges. This study provides analysts with the sense of the accuracy of some popular damping models for a nonlinear pendulum system. It also demonstrates the use of a fitting approach to retrieve physical properties of a system from experimental data. The contents of this paper are suitable for gifted high school students and undergraduate students.