Modeling and Dynamic Analysis for a Motion of Mounted-Based Axisymmetric Rigid Body under Self-Excited Vibrations in an Attractive Newtonian Field

In this article, the mathematical modeling and dynamic analysis for a motion of a rigid body mounted on a vibrating base affected by a strongly nonlinear damping and an attractive Newtonian field are investigated. The governing equations are derived, and specific conditions for asymptotic stability of the motion are stated. Results of analytical analysis are used to identify some distinct types of motion, including the cases that are apparently regular or chaotic. A reduction technique via averaging is used to obtain the amplitude equation and the response diagrams to identify regions where the jump phenomenon may occur. Moreover, a simple analytical relationship between the parameters of the system, describing whether the jump phenomenon will be possible, is obtained. Homoclinic bifurcation diagrams are used to argue apparently that the chaotic behavior is slowly approaching a strange attractor at specific values of system parameters. Results of numerical solutions using the fourth-order Runge-Kutta method are closely coincided with the analytical ones to verify all types of motion.