Non-linear model-based estimation of quadratic and cubic damping mechanisms governing the dynamics of a chaotic spherical pendulum

Abstract

We investigate the non-linear damping mechanisms that govern the dynamics of a chaotic spherical pendulum. We reproduce the conditions of the celebrated chaotic experiment of Tritton (1986) , and identify the bifurcation regions that correspond to periodic, quasi-periodic and chaotic-like response. Construction of the pendulum frequency and damping backbone curves from free vibration decay data reveal the existence of non-negligible non-linear damping. A non-linear model-based estimation procedure enables extraction of both quadratic and cubic damping coefficients which are deduced from a non-linear Rayleigh-type gradient dissipation function. Comparison of experimental results with solutions obtained via numerical analysis of the strongly non-linear pendulum model, augmented by the estimated damping mechanisms, sheds light on the possible cause of documented discrepancies in similar whirling systems between measurements and theoretical predictions obtained from models with only linear damping.

A Numerical Method to Model Non-linear Damping Behaviour of Martensitic Shape Memory Alloys

“…Few researchers have focused on the use of phenomenological nonlinear damping models. Gottlieb and Habib [33] used a phenomenological nonlinear damping model to understand the large amplitude vibrations of a spherical pendulum. Eichler et al [27] used a damping model containing a nonlinear term proportional to the square of the vibration amplitude multiplied by the velocity.…”

Time resolved measurements of vortex-induced vibrations of a positively buoyant tethered sphere in uniform water flow

“…The maximum normalized amplitude (not shown), A 2 =D À Á max , reaches 0.8 in agreement with the magnitude of the estimated mass-damping parameter, (m n þC A ) z E 0.018 (see Govardhan and Williamson, 2005). Here, the damping factor, z E 2 Â 10 À 2 , was estimated from a free decay experiment in air using a backbone curve analysis (Gottlieb and Habib, 2011). The streamwise amplitude response shown in Fig.…”

Experimental and Numerical Characterization of High Damping Martensitic CuAlMn Sheets

“…Few researchers have focused on the use of phenomenological nonlinear damping models. Gottlieb and Habib [19] used a phenomenological nonlinear damping model to understand the large amplitude vibrations of a spherical pendulum.…”