2002-08-012024-05-17https://scholars.lib.ntu.edu.tw/handle/123456789/691273摘要：本計劃為兩年期計畫,旨在研究摩擦振動控制理論,包括摩擦組成律、摩擦運動之分析動力學架構、半主動控制三大問題。第一年計畫著重前二問題,第二年以後二問題為主,第一個問題為輔。本報告為第二年結案報告。 本計畫推廣庫倫摩擦定律,使滑動不限於一維,可發生於平面,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,得到幾種均具有射影羅倫茲 (Lorentz) 群或射影龐卡萊 (Poincare) 群對稱性的摩擦組成律,它們有不同的定義域與群參數。 本計畫成功地建立結構摩擦運動的哈氏架構,結合運動律及組成律得出其哈氏量及哈氏正則方程式。顯然它們具有辛群對稱性。 在主動控制方面，本計畫將強健性納入縮辛群控制律中，得到強健主動縮辛群控制律。進一步將被動控制的摩擦阻尼器與主動控制律結合， 而得到具強健性的半主動縮辛群控制律。 <br> Abstract: The two-year project was proposed to study friction vibration control of engineering structures under external disturbances, including the topics of friction laws, analytic-dynamic framework, and semi-active control. The former two problems were studied in the first year whereas the last two as well as some ensuing issues of the first one were studied in the second year. The present report is the second year final report. For friction laws, we generalize 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 moreover n-dimensional. The resulting two or n-dimensional friction laws allow the sliding friction force to have a path effect with possible sliding on a plane or $n$-dimensional space, and all feature internal symmetry characterized by the projective Lorentz or Poincare groups with different domains of definition and group parameters. We succeed in establishing an analytic-dynamic framework for motion and constitutive laws and obtaining its Hamiltonians and canonical equations. Thus, we reveal their inherent symmetries characterized by symplectic groups. For active control of engineering structures, embracing robustness into our previously developed control law of contractive symplectic group (CSG), we obtain a robust active CSG control law. Furthermore, we combine the active control with the passive control by friction damper, resulting in a robust semi-active CSG control law for vibration abatement.摩擦摩擦阻尼器振動半主動控制強健控制哈氏量辛群羅倫茲群。frictionfriction dampervibrationsemi-active controlrobust controlHamiltoniansymplectic groupLorentz group.