Impulsive resistant optimization design of tuned viscous mass damper (TVMD) based on stability maximization

Abstract

Recently, inerter based dynamic vibration absorbers (IDVAs) have been extensively investigated to control the harmonic and stochastic vibrations. Numerous studies on the theoretical H∞ and H2 optimizations and numerical analysis have been presented for various structures under different excitations. The variance of the stochastic vibration responses can be largely reduced by using these approaches. However, for excitations with non-stationary impulsive characteristics, such as near-fault earthquake and transient gusty wind, the control of peak responses is also concerned. But there are few related investigations on this topic. In order to address this problem, this paper investigates the vibration control performance of tuned viscous mass damper (TVMD) for impulsive stochastic excitations. Firstly, the transfer function (TF) and impulsive response function (IRF) of the vibrating system are analytically derived. Subsequently, the stability maximization (SM) result is obtained by optimizing poles of TF. The control performances of TVMD and TID based on H∞ and SM solutions subjected to impulsive excitations are compared, and the effectiveness of the SM-based TVMD is demonstrated. Considering the practical requirement of TVMD, an integrated optimization procedure that considers the balance of damping force and control performance is proposed. The corresponding empirical formulas for the optimal TVMD design are established. Through a numerical example, the effectiveness of the proposed method and empirical formulas are validated. In addition, the resulting optimal TVMD design outperforms the design based on H∞ optimization. Statistically, the resulting peak responses induced by the impulsive earthquake and wind can be reduced up to 41.0% and 22.1%, respectively.