To improve structure control efficiency, both inerter and negative stiffness elements can be employed. In this study, an innovative combination of negative stiffness and an inerter control mechanism is used to protect a structure under severe seismic loadings. To this end, the numerical analysis determines the tuning frequency ratio and optimum damping of white noise stationary and earthquake excitation filtered white noise acting on a base-isolated structure with a tuned inerter negative stiffness damper. The criteria for the optimum parameter are to maximize the energy dissipation index, the relative displacement of the mean square minimization, and the absolute acceleration of the isolated structure. Dynamic system applications are utilized to derive the tuning frequency and TINSD damping for white noise excitation via explicit curve fitting equations. For the proposed empirical expressions, the base-isolated structure with supplementary TINSD device design is determined to have less inaccuracy. Next, a comparison is made between non-stationary seismic excitations acting on the bare and TINSD base-isolated structures. Accordingly, base-isolated structure response reduction in displacement and acceleration with TINSD by optimum parameter is observed with a rise in greater mass ratio. This study proves that under broadband earthquake excitations, the initial optimal design is found to be effective for bearing displacement of a base-isolated structure with TINSD.
