Explicit Formulas for Optimum Parameters of Viscoelastic-type Tuned Mass Dampers

Abstract

Tuned mass dampers (TMDs) are passive vibration control devices that are attached to a primary system to reduce the dynamic vibrations under exciting motion. The Voigt-type TMD, which is the most widely used one, is known as a standard model of dynamic vibration absorber (DVA). The purpose of this study is to improve the vibration control performance of passive control devices by using viscoelastic-type tuned mass dampers (V-TMDs). The study adopts the Zener model to represent the viscoelastic behavior of V-TMD. In this study, the fixed-point method is used to determine the optimum parameters of a V-TMD. The displacement amplification factor (DAF) of the coupled system is obtained in the frequency domain. The optimal parameters of the V-TMD system attached to an undamped single degree-of-freedom (sdof) main system are obtained by minimizing the DAF (symbolized with 𝛽) under the effect of base excitation. The optimum parameters, such as damping ratio (ξ) and stiffness ratio (𝜅) of the coupled system are derived, and explicit expressions corresponding to the optimum parameters are presented for engineering designs. Moreover, the change in DAF values for different mass ratios (µ) is also discussed. It is proven that V-TMD is very effective in reducing the amplitudes of vibration. The study also provides valuable insights for engineering practitioners who want to design and implement V-TMDs for vibration control applications because accurate expressions, which are simple and easy to use, are derived in order to obtain optimum parameters, and step-by-step procedures are explained.