A novel multimode negative inductance negative resistance shunted electromagnetic damping and its application on a cantilever plate

Based on the characteristic of the electromagnetic damping, a novel multimode vibration control treatment, negative inductance negative resistance electromagnetic shunt damping (NINR-EMSD), is proposed and employed to control multimode vibration of a cantilever plate. The negative inductance of the shunt impedance can cancel the inherent inductance of the electromagnet, and the impedance of circuit consisted of the coils and shunt will be a pure resistance and the shunt current will be frequency independent when the inductance of the shunt and the electromagnet are equal with each other. The negative resistance cancels the resistance of electromagnet, and as a result the resistance and the current of the closed circuit will change, which make it feasible to control the multimode vibration of the system. Electromechanical coupling coefficient is obtained based on the equivalent current method. The governing equation of the plate with the electromagnetic shunt damping (EMSD) is established according to Hamilton's principle. Multimode vibration control of the system is simulated and experiments are carried out to verify the performance of the NINR-EMSD. The numerical predictions and experimental results agree well with each other and show that: the negative inductance negative resistance (NINR) of the shunt impedance can increase the damping of the structure notably; the decrease of the resistance of shunt impedance have a significant contribution to the improvement of vibration control performance; the first four modes vibration of the plate can be suppressed simultaneously with the NINR-EMSD.