洪宏基2006-07-252018-07-092006-07-252018-07-092003http://ntur.lib.ntu.edu.tw//handle/246246/2811The 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 Poincar´e 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.application/pdf810517 bytesapplication/pdfzh-TW國立臺灣大學土木工程學系暨研究所frictionfriction dampervibrationsemi-active controlrobust controlHamiltoniansymplectic groupLorentz groupreporthttp://ntur.lib.ntu.edu.tw/bitstream/246246/2811/1/912211E002071.pdf