Periodic and Chaotic Response of a Macro-Scale Tuning Fork Gyroscope

Abstract

In this paper, the dynamic behaviour of a macro-scale tuning fork gyroscope is presented. The gyroscope consists of two inverted pendulums on a suspension mass. The suspension mass is subjected to force excitation generated by an electromagnetic shaker. The dynamics of the shaker are included in the analysis. It is shown that the system is a parametrically excited system. Parametric excitation can lead to vibration in the horizontal motion of the suspension mass, when the two pendulums are in phase. The problem is particularly interesting for energy harvesting. Due to the interaction between the system’s degrees of freedom, the energy is transferred from vertical (base excitation) to horizontal direction. Initial parametric studies are carried out to analyse the dynamic behaviour of the system by varying the initial conditions, base excitation frequency and amplitude. It is demonstrated that under certain parameters the system can exhibit complex dynamic behaviour such as chaotic motion.