A variant design of tuned mass damper with negative stiffness for vibration control of a damped primary system

In this paper, the optimal design of a non‐traditional tuned mass damper (NTTMD) with negative stiffness for a damped primary system is studied in detail. The dynamical differential equation is established and the analytical solution of the system is obtained. Closed‐form expression for the optimum tuning parameter is analytically derived using the fixed‐points approach based on the assumption that the damped primary structure is lightly or moderately damped. Then, the optimum damping ratio and the optimum negative stiffness ratio of NTTMD are found numerically by solving a set of nonlinear equations established by Chebyshev's equioscillation theorem. Extended numerical simulations are carried out to examine the efficiency of the optimally designed NTTMD as well as the sensitivity of the optimal parameters. Finally, the utmost control performance of the proposed NTTMD is compared with those of two existing typical TMDs, which were presented by Pennestri and Liu, respectively. The comparison results show that the proposed non‐traditional TMD with negative stiffness can significantly improve the vibration control performance in terms of mitigating the normalized frequency responses of damped primary structures and confining the stroke length of NTTMDs.