A theoretical platform is developed to study design guidelines and strategies for implementation of nonlinear magnetic springs that are traditionally encountered in variety of vibration systems. The adopted magnetic spring consists of two fixed top and bottom ring magnets and a third solid magnet that is levitated between the two fixed magnets. Approximate analytical forms for the equivalent linear and nonlinear stiffness coefficients of the magnetic spring are derived and used to investigate the effect of different design parameters on behavior of the magnetic spring. Magnetic damping force model is presented. Experimental work is also carried out to validate model simulations. Results show excellent agreement between model and measured data. Findings from this work suggest that linear and nonlinear stiffness coefficients are often coupled. Outer diameter of the fixed ring magnets can be used to control the nonlinearity of a given magnetic springbased vibration system in order to achieve hardening nonlinear, softening nonlinear, or linear dynamic behavior. The work presented here serves as a roadmap for design and analysis of variety of magnetic spring-based vibration systems including vibration energy harvesting systems and vibration attenuation systems.
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