Building structures, subject to dynamic loadings or external disturbances, may undergo destructive vibrations and encounter different degrees of deformation. Modeling and control techniques can be applied to effectively damp out these vibrations and maintain structural health with a low energy cost. Smart structures embedded with semi-active control devices, offer a promising solution to the problem. The smart damping concept has been proven to be an effective approach for input energy shaping and suppressing unwanted vibrations in structural control for buildings embedded with magnetorheological fluid dampers (MRDs). In this paper, the dissipation energy in MRD is studied by using results from induced hysteretic effect of structural vibrations while the fluid is placed under a controlled magnetic field. Then, a frequency-shaped second-order sliding mode controller (FS2SMC) is designed along with a low …