Hysteresis Modeling of Smart Structure MR Devices Using Describing Functions

Magnetorheological (MR) devices have been quite promising for semiactive control, thanks to their capability of adjusting structural parameters, under a low-power control signal, to effectively withstand severe dynamic loadings including seismic events. MR devices, using visco-elastic and ferromagnetic materials, are subject to hysteresis, which may degrade the performance of smart structures. Therefore, this multivalued nonlinearity needs to be properly modeled and characterized for control and health monitoring. As engineering structures operate as low-pass filter in normal conditions, it is suitable to use the classical describing function (DF) method for modeling and analysis of the hysteretic behaviors in MR device-based smart structures. Data obtained from characterizing tests are recorded in look-up tables to obtain the DFs for these devices, using a curve-fitting technique. The proposed DFs are then useful in structural frequency analysis. Experimental results are reported for a steel beam with MR pin joints subject to quake-induced vibrations provided by a shake table.