Analysis and Numerical Evaluation of H_∞ and H₂ Optimal Design Schemes for an Electromagnetic Shunt Damper

The electromagnetic coupling effect can generate electromagnetic damping to suppress disturbance, which can be utilized for vibration serviceability control in civil engineering structures. An electrodynamic actuator is used as a passive electromagnetic damper (EMD). Ideally, the EMD is assumed to be attached between the ground and the structure. The kinetic energy of the vibrating structure can be converted to electrical energy to activate the electromagnetic damping. To induce appropriate damping, the two terminals of the damper need to be closed and cascaded with a resonant shunt circuit as an electromagnetic shunt damper (EMSD). In this study, an resistance–inductance–capacitance (RLC) oscillating circuit is chosen. For determination of optimal circuit components and comparing against the tuned mass damper (TMD), existing H_∞ design formulae are applied. This work extends this with a detailed development of an H₂ robust optimization technique. The dynamic properties of a footbridge structure are then selected and used to verify the EMSD optimal design numerically. The vibration suppression performance is analytically equivalent to the dynamic characteristic of the TMD and has feasible installation and better damping enhancement. To further evaluate the potential application of the EMSD, multi-vibration mode manipulation via connecting multiple RLC resonant shunt circuits is adopted. The multiple RLC shunt circuit connecting to EMD is an alternative to the single mode control of a traditional TMD. Therefore, the EMSD can, in principle, effectively achieve suppression of single and multiple vibration modes.