2001-08-012024-05-14https://scholars.lib.ntu.edu.tw/handle/123456789/660275摘要：本計劃為兩年期計畫，旨在研究摩擦振動控制理論，包括摩擦定律、運動方程式的計算分析架構、半主動控制律三大問題。第一年計畫著重前二問題，第二年以第三個問題為主，前二問題為輔。本報告為第一年進度報告。 本計畫推廣庫倫摩擦定律，使滑動不限於一維，可發生於二維面，甚至n維空間，且滑動時的摩擦力可不限定定值，而是與其滑動歷程有關，此乾摩擦組成模式具有Poincare群雙曲線射影的內在對稱性。 在多自由度的工程結構裡，如果配備一個摩擦阻尼器，則整個工程結構的運動如何分析計算？本計劃以二層樓剪力屋架結構為例，在結構物的部分柱底加裝摩擦阻尼器，導入庫倫摩擦的滑動規則與互補三元，並分別建立黏&#30528;相與滑動相的動力平衡方程式，進而以振態疊加法求得解析解，並撰寫時間歷時計算處理程式。利用程式，求得側位移與加速度反應譜，並對三種最大消能減振效益指標做分析與討論。 如果不只配備一個摩擦阻尼器，如何有系統地分析計算？對此，本計畫釐清摩擦阻尼器可有轉動型及滑動型，分別相當於塑鉸及塑梢，因此分析方法即相當於塑性結構分析，其分析計算架構可以數學動態規劃法系統性地建構之。 進一步，摩擦阻尼器在半主動控制的<br> Abstract: The two-year project was proposed to study friction vibration control of engineering structures under external disturbances, including the problems of friction laws, analytic-dynamic framework, and semi-active control laws. The former two problems were studied in the first year whereas the third as well as some ensuing issues of the former two will be studied in the second year. The present report is the first year progress report. For friction laws, we generalized the Coulomb friction law in which the friction force remains constant during sliding and the friction sliding is allowed in only one dimension, to be non-constant and two-dimensional and even n-dimensional. The resulting two-dimensional dry friction law allows the sliding friction force to have a path effect with possible sliding on a two-dimensional plane, and features internal symmetry characterized by the hyperbolic sphere projection of the Poincare group SEo(2,1). When a friction damper is installed in an engineering structure, modal analysis procedures were developed for both the sticking and sliding phases to effectively analyze and compute dynamic responses. Parametric study revealed how friction affects structural behavior and three indices were defined to evaluate the effectiveness of the friction damper in depressing the vibration level of the structure. When several friction dampers are installed in an n-degrees-of-freedom structure, a systematic framework for analysis of the friction vibration problem can be established by recognizing the model similarity between plastic hinges and rotational friction dampers. Thus it is basically plastic analysis of structures with additional considerations of plastic sleeves for sliding friction dampers and of dynamics for inertia effect of the structural mass. In the next year, we will try to find out a better or an optimal control law for vibration abatement using semi-active control by the friction dampers, exploring the possibility of adapting the newly-established method of contractive symplective group.摩擦庫倫摩擦乾摩擦滑動黏&#30528摩擦阻尼器振動最佳消能減振效益半主動控制控制律frictionCoulomb frictiondry frictionslidingstickingfriction dampervibrationanti-vibration indexsemi-active controlcontrol law.