Study of Gravitational Force Effects, Magnetic Restoring Forces, and Coefficients of the Magnetic Spring-Based Nonlinear Oscillator System

The aim of this article is to analyze the design of a magnetic spring-based nonlinear oscillator system and investigate its magnetic properties, the effect of gravitational force, the accuracy of the modeled magnetic restoring force, the coefficient of the magnetic restoring force, and the nonlinear response of the proposed system. The proposed magnetic spring-based nonlinear oscillator system consists of a nonmagnetic shaft, floating magnet, and two fixed magnets where all magnets are placed in such a way that each magnet can repel the other. The magnetic properties of the proposed system are studied numerically and analytically to provide insight into its role in the nonlinear oscillatory behavior of the system. The effect of the gravitational force, which changes the equilibrium position and the nonlinear behavior of the magnetic spring, is studied. The numerical analysis of the magnetic flux density and magnetic restoring force is validated using an analytical and experimental analysis. Different orders of polynomial curve fittings, such as cubic and quintic, are used to model the magnetic restoring force between the moving magnet and the two fixed end magnets. Finally, the linear and nonlinear coefficients of the magnetic spring-based system for different positions of the floating magnet are investigated.