Nonlinear dynamics of new magneto-mechanical oscillator

Abstract

This study presents modelling and analysis of a new magneto-mechanical (MM) oscillator (Wiercigroch et al., 2020), which pays a special attention to mechanical and magnetic nonlinearities for large amplitude responses. The oscillator is comprised of a box structure made of two parallel leaf springs with one end fixed and the other clamped with a proof mass, and an electromagnetic actuator. A solenoid and a permanent magnet are the main parts of the actuator, which acts directly on the proof mass providing an accurate and versatile excitation by varying intensity and frequency of the input current. The new model for a beam of large deflection is based up the constitutive relation of nonlinear beam theory. A new design of the electromagnetic actuator with a pair of identical solenoids and a new concept of quasi-constant force (QCF) are proposed, which aims to generate a nearly constant amplitude force for a constant input current. The mathematical model of the MM oscillator is systematically developed and discussed for different types of excitations depending on designs and parameters of the electromagnetic actuator. The undertaken nonlinear dynamics analysis demonstrates versatility of the electromagnetic actuator to generate a wide spectrum of excitations. The prediction from the modelling were validated by the previous work (Costa et al., 2020). The study exemplify that the electromagnetic actuator provides a wide range of excitation patterns and can be used to study experimentally subtle nonlinear phenomena.