This article presents a tunable multi-stable piezoelectric energy harvester. The apparatus consists of a stationary magnet and a cantilever beam whose free end is attached by an assembly of two cylindrical magnets that can be moved along the beam and a small cylindrical magnet that is fixed at the beam tip. By varying two parameters, the system can assume three stability states: tri-stable, bi-stable, and mono-stable, respectively. The developed apparatus is used to validate two models for the magnetic restoring force: the equivalent magnetic point dipole approach and the equivalent magnetic 2-point dipole approach. The study focuses on comparing the accuracy of the two models for a wide range of the tuning parameters. The restoring forces of the apparatus are determined dynamically and compared with their analytical counterparts based on each of the models. To improve the model accuracy, a model optimization is carried out by using the multi-population genetic algorithm. With the optimum models, the parametric sensitivity of each of the models is investigated. The stability state region is generated by using the optimum second model.
This paper presents an optimal design of a large-capacity Magnetorheological (MR) damper suitable for off-road vehicle applications. The damper includes an MR fluid bypass valve with both annular and radial gaps to generate a large damping force and dynamic range. An analytical model of the proposed damper is formulated based on the Bingham plastic model of MR fluids. To establish a relationship between the applied current and magnetic flux density in the MR fluid active regions, an analytical magnetic circuit is formulated and further compared with a magnetic finite element model. The MR valve geometrical parameters are subsequently optimized to maximize the damper dynamic range under specific volume and magnetic field constraints. The optimized MR valve can theoretically generate off-state and on-state damping forces of 1.1 and 7.41 kN, respectively at 12.5 mm/s damper piston velocity. The proposed damper has been also designed to allow a large piston stroke of 180 mm. The proof-of-concept of the optimally designed MR damper was subsequently fabricated and experimentally characterized to investigate its performance and validate the models. The results show that the proposed MR damper is able to provide large damping forces with a high dynamic range under different excitation conditions.

