| Summary: | 碩士 === 國立臺灣大學 === 土木工程學研究所 === 100 === In order to improve the dynamic characteristics, the stiffness and the damping of civil engineering structures to achieve a certain energy dissipation effect, and the active structural control is exerted additional force by the control elements to the traditional structural system. The active structural control system consists of three core components: the sensor, the control law and actuator. Sensors are used to measure the dynamic response which layout in structures and controllers of the civil engineering. According to the response of the structure and controllers, decide the timing, size and the direction of control being imposed on the structure. The actuator is developed the institutions by the control force and which is applied to structures of civil engineering through a series of dynamical systems. In the study of optimal control theory for nonlinear structures, one often encounters two-point boundary-value problems (TPBVPs). In this study, the numerical solution for two-point boundary value problem is the Lie group shooting method (LGSM), and then with the fourth-order Runge-Kutta method (RK4). The LGSM is a powerful technique to search the unknown initial conditions. These methods are gradually derived based on the closure property of the group, the Lie group property and the length preserving property in GPS, some simple mathematical derivation, the mid-point rule. And it will be used to this numerical solution of the linear optimal control, the single degree nonlinear Duffing osillator, as well as two degrees nonlinear Duffing osillator. In this thesis, we use programming language FORTRAN for the numerical analysis and plot the numerical results by the GRAPHER. Finally, we want to apply this method on the development of the civil engineering in the future.
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