Optimal design of TVMD with linear and nonlinear viscous damping subjected to white-noise excitation

This paper investigates the optimal design of the tuned viscous mass damper (TVMD) with linear and nonlinear viscous damping subjected to white-noise excitation. The TVMD consists of a parallel-connected inerter and dashpot, and a spring attached to the main structure. To examine the vibration control performance of the TVMD, both theoretical analysis and numerical optimization are conducted to obtain the optimal parameters. In this paper, a closed-form solution of optimal design for the linear TVMD is proposed. Compared with the traditional TMD, the optimized linear TVMD has comparable and even better control performance, but less damping and real physical mass are required. For the nonlinear TVMD, the influences of the damping exponent on the optimal parameters and control performance are analyzed. The results show that the optimal damping coefficient is significantly affected by the damping exponent and associated with the inherent structure damping ratio and the given mass ratio. However, the damping exponent has few effects on the optimal frequency ratio and the control performance. To well understand the control principle of the nonlinear TVMD, a numerical example under harmonic excitations is considered, and the results show that the damping exponent is related to negative stiffness, which dominates the control performance of TVMD. Under several natural ground motions selected, the analytical results show that the nonlinear TVMD does not always improve the control performance compared with the linear TVMD, particularly for a stronger earthquake than the designed for. Nevertheless, in such case, larger values of damping exponent, 2.0 for instance, can significantly suppress the internal force transferred to the main structure with a smaller sacrifice of control effectiveness. The main structure and the TVMD device can then be simultaneously protected to some degree.