Nonlinear dynamics characteristics of a tumbler on an arc

A tumbler oscillates around its geometric axis with a period under external disturbances. Due to the oscillation mechanism differs from traditional mass-spring-dampers, the dynamic response of tumblers is still a challenge. This work considers the dynamics behaviors of a tumbler on an arc surface. A tumbler prototype is designed and the corresponding equation of motion is derived according to the Lagrange's equation. Both the simulation and experimental efforts are performed to study the dynamics characteristics of the tumbler on an arc. The results demonstrate that the natural frequency of the tumbler can be 2.7 Hz, which is considerable to design low-frequency vibration devices in a new tunable perspective, such as vibration isolators or energy harvesters. The motion of the tumbler is periodic or quasi-periodic under a smaller excitation amplitude, and will be chaotic under a small damping. This work opens a window for the design and application of tumbler-inspired structures.

Automated summary

This study investigates the dynamics behavior of a tumbler on an arc surface. The results demonstrate the potential for designing low-frequency vibration devices and open up new possibilities for tumbler-inspired structures.