A shape memory alloy-tuned mass damper inerter system for passive control of linked-SDOF structural systems under seismic excitation

•A new SMA-TMDI system for vibration control of linked-SDOF structures is proposed.•Displacement mean square expressions under white noise excitation are developed.•Parametric analysis is carried out under white noise excitation.•Performances under stationary and non-stationary excitation are investigated.•RMS control forces transferred to the host structures are investigated. This work introduces a passive control device, shape memory alloy tuned mass damper inerter (SMA-TMDI), for the control of linked-single degree of freedom (SDOF) systems subjected to base excitation. The adjacent SDOF systems are connected through a device called inerter with force proportional to the relative acceleration of the individual SDOF oscillators of the linked-SDOF systems. The SMA element of SMA-TMDI dissipates the energy of primary oscillator through the hysteretic phase transformation, while, the mass-amplification effect of the inerter is utilized to reduce displacement of the secondary oscillator of the linked-SDOF systems. The mean square displacement responses of both the oscillators of the linked-SDOF systems subjected to white noise base excitation are derived based on stochastic equivalent linear parameters of the SMA spring through an iterative process. Parametric studies under white noise excitation are conducted and based on the results obtained, a multi-objective optimization is performed considering displacement variances of both the SDOF oscillators as the objective function. Under white noise excitation, the optimal performances of SMA-TMDI and TMDI systems are analyzed in terms of displacement mean square responses and the root mean square control forces transferred to the linked-SDOF systems are also examined. Further, the performance comparison of the SMA-TMDI and TMDI passive control devices are carried out under non-stationary Kanai-Tajimi excitation based on an Ito-Taylor formulation of the mean square stochastic differential equations. Based on the results obtained for both white noise and ground motion base excitation cases, it can be observed that the SMA-TMDI system performs better in comparison to the TMDI system with significantly lesser requirement on total damper mass and inertance.