Optimal design of TVMD with linear and nonlinear viscous damping for SDOF systems subjected to harmonic excitation

Abstract

Summary This paper investigates the optimal design of the tuned viscous mass damper (TVMD) with linear and nonlinear viscous damping properties for a single degree‐of‐freedom structure subjected to harmonic excitation. The TVMD consists of a parallel‐connected inerter and viscous damper, and a spring that mounts them to the structure. To examine the vibration control performance of the TVMD, both theoretical analysis and numerical optimization are conducted to obtain the optimal parameters of the TVMD with either linear or nonlinear viscous damping. The influence of the damping exponent of the nonlinear viscous damper on the optimal parameters and performance of the TVMD is analyzed. The results show that much better control effectiveness and robustness can be achieved by the TVMD when compared with tuned mass damper (TMD). Furthermore, it is also of great practical importance to show that the static deformation of the supporting spring due to the self‐weight of the inerter is only a small fraction of the traditional TMD in case of vertical vibration control. Compared with the linear TVMD, the nonlinear TVMD can achieve comparable or even slightly better control performance. The optimal damping coefficient depends largely on the damping exponent, and the loading intensity fluctuation also has an influence on the performance of the nonlinear TVMD. Moreover, it is shown that that the nonlinear TVMD with damping exponent ν = 2 has the best control performance on the peak displacement response of the main structure, and the TVMD with linear viscous damping optimized for the harmonic excitation can also effectively suppress the wind‐induced vibration.

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

“…The TVMD‐structure system then degenerates to a linear one. Considering this system subjected to harmonic excitations, Ikagao et al 22 and Huang et al 52 had provided closed‐form solutions of optimal design parameters of TVMD. However, under white‐noise excitations, a closed‐form solution of optimal control design has not been well addressed.…”

“…The results showed that less damping coefficient is required in the system for the same control effectiveness compared with the linear case of viscous damping. Huang et al 52 investigated the optimal design of the TVMD with nonlinear viscous damping and showed that the nonlinear TVMD with damping exponent two achieves the best control performance. It should be noted that the previous studies on TVMD mostly concentrated on the harmonic excitation.…”

Parametric optimization of electromagnetic tuned inerter damper for structural vibration suppression

“…Then, Ikago et al 8 proposed the tuned viscous mass damper (TVMD), composed of a viscous mass damper combined with an additional tuning spring that can add another tuning frequency for the damper to improve the effectiveness. The TVMD has been well investigated for both single‐degree‐of‐freedom (SDOF) structures and multiple‐degree‐of‐freedom (MDOF) structures 8–12 . To further improve the performance of the TVMD, the rotational inertia double‐TMD was introduced in Garrido et al, 13 by replacing the viscous damping element of the TMD with a TVMD.…”

Optimal design and performance evaluation of a novel hysteretic friction tuned inerter damper for vibration control systems

“…When only single number of the inertial element, the damping element or the spring element is involved, the combination of these elements can form following types: parallel type, series type, and mixed I and mixed II 13 so far in the literature. Among them, the mixed II is also called tuned viscous mass damper (TVMD) 24 in civil engineering, which is a vibration absorber composed of an inertial and a damping element in parallel and then in series with a spring element. The TVMD was found good in controlling the structural response of the structure under earthquake.…”