具短衝程阻尼器之調諧質量阻尼器研究

Abstract

現有調諧質量阻尼器之模型，阻尼器與質量塊之衝程相同，因此須選用較長衝程之阻尼器，在工程設計上必須預留相當阻尼器長度之空間及預期衝程距離，且長衝程阻尼器之高精度需求，於施工上也需要較佳的技術，使其造價較高且維護不易。根據此特性，本研究針對降低被動式TMD之阻尼器衝程，提出「具短衝程阻尼器之調諧質量阻尼器(SSD-TMD)」，將TMD之勁度分成兩段，並將阻尼器與第一段勁度並聯，再與第二段勁度串聯，接在質量塊之上，使其產生之衝程不相同，期望能大幅降低阻尼器之衝程，減少種種設計與施工上的困難。首先提出SSD-TMD之模型，沿用傳統TMD最佳化設計參數提出SSD-TMD之設計參數，利用直接搜尋法求得SSD-TMD所需之最佳化設計參數－最佳化勁度因子與最佳化阻尼係數因子，並求出SSD-TMD與傳統TMD之減振效果比、阻尼器衝程比與質量塊衝程比，接著利用曲線擬合與迴歸法提出單自由度結構加裝SSD-TMD最佳化設計公式。最後提出台北101結構案例分析，利用特徵分析、頻率反應函數及風力歷時數值模擬，綜合比較單自由度結構、單自由度結構加裝傳統TMD及單自由度結構加裝不同勁度比之SSD-TMD的減振效果，並進行SSD-TMD之勁度因子與阻尼係數因子敏感度分析。分析結果顯示SSD-TMD能有效大幅降低阻尼器衝程，且在適當的設計下，減振效果及質量塊衝程都略優於傳統TMD，但阻尼器必須付出較傳統TMD大之阻尼力。

The damper stroke and the mass stroke are the same for currently used conventional TMD, therefore, a long-stroke damper is required for engineering applications. In addition, a considerable space for the damper stroke is reserved in the design. Due to the high-accuracy requirement for manufacture of long-stroke damper, higher technology is requested. Besides, higher budget and the difficulty for maintenance are issues for long-stroke damper as well. According to the above features, a “Short-Stroke Damper assembled in Tuned Mass Damper (SSD-TMD)” is proposed in order to reduce the damper stroke of conventional TMD. The stiffness of SSD-TMD is separated into two parts. The first part is connected in parallel with the damper. Furthermore, the paralleled system is connected in series with the second part of stiffness which is further attached to the mass block. The assemblage will produce a different stroke between the damper and mass in order to significantly mitigate the damper stroke and solve the difficulties for both engineering applications and design. In this article, the model of SSD-TMD is firstly proposed. The design parameters of SSD-TMD is proposed following the optimal design parameters for conventional TMD. By using the Direct Search Method, the optimal deign parameters of SSD-TMD, optimal stiffness factor and optimal damping coefficient factor, will be able to determine. After that, the vibration reduction ratio, damper stroke ratio and mass stroke ratio of SSD-TMD to conventional TMD are further determined. By using curve fitting and the regression method, the optimal design formulae for a single degree of freedom (SDOF) structure implemented with SSD-TMD are defined. Finally, by a case study of Taipei 101, three different kinds of system: SDOF structure, SDOF structure with conventional TMD, SDOF structure with SSD-TMD, are compared by characteristic analysis, frequency response function and time history simulation, respectively. In addition, the sensitivity analysis of stiffness factor and damping coefficient factor is carried out. The results show that SSD-TMD can significantly reduce the damper stroke. Besides, both effectiveness of vibration reduction and mass stroke for SSD-TMD with suitable design can be better than the conventional TMD. However, the damping force of SSD-TMD is greater than the conventional one.