H-infinity optimization of a variant design of the dynamic vibration absorber—Revisited and new results

Abstract

The H ∞ optimum parameters of a dynamic vibration absorber (DVA) with ground-support are derived to minimize the resonant vibration amplitude of a single degree-of-freedom (SDOF) system under harmonic force excitation. The optimum parameters which are derived based on the classical fixed-points theory and reported in literature for this non-traditional DVA are shown to be not leading to the minimum resonant vibration amplitude of the controlled mass. A new procedure is proposed for the H ∞ optimization of such a dynamic vibration absorber. A new set of optimum tuning frequency and damping of the absorber is derived, thereby resulting in lower maximum amplitude responses than those reported in the literature. The proposed optimized variant DVA is also compared to a ground-hooked damper of the same damping capacity of the damper in the DVA. It is proved that the proposed optimized DVA has better suppression of the resonant vibration amplitude of the controlled system than both the traditional DVA and also the ground-hooked damper if the proposed design procedure of the variant DVA is followed.

Optimal design of a novel tuned mass-damper–inerter (TMDI) passive vibration control configuration for stochastically support-excited structural systems

“…[7,8] and references therein), the above discussed "classical" TMD configuration (mass attached via a spring and a dashpot in parallel) is the most widely studied in the literature and the most commonly used one for passive vibration control of various mechanical and civil engineering structures and structural components. In particular, motivated mostly by earthquake engineering applications, substantial research work has been devoted to investigate the potential of using the classical TMD to mitigate the motion of stochastically support-excited primary structures.…”

A simple method for choosing the parameters of a two degree-of-freedom tuned vibration absorber

“…Finally, substituting all the parameters into Eq. (11) and searching numerically for the damping coefficient which gives the minimum area of the transmissibility yields z¼0.1510. The obtained parameters of the 2dof TVA are listed in Table 1.…”

“…For example, Snowdon [9] considered a three-element TVA in which the damper is connected in series with a spring and showed that such a device can be more effective than a conventional TVA of the same mass. More recently Cheung and Wong [10][11][12] studied a TVA where the damper is connected to the ground instead of the mass of the host structure. Other researchers have tried also to introduce nonlinearities in the TVA to improve the performance, for example [13,14].…”

Floor acceleration control of super‐tall buildings with vibration reduction substructures

“…Therefore, how to optimize the parameters of TMDs (e.g., the natural frequency, the mass, and the damping ratio) to achieve a best vibration effect subjected to constrained budget is a key challenge. Single degree‐of‐freedom (SDOF) systems have been used by many researchers (e.g., Sadek et al, Krenk and Høgsberg, Cheung and Wong, Xiang and Nishitani) to study the parameter optimization of TMDs. However, single degree‐of‐freedom systems are clearly unsuitable for super‐tall buildings.…”