Abstract
Modern tall buildings use lighter construction materials that have high strength and less stiffness and are more flexible. Although this results in the improvement of structural safety, excessive wind-induced excitations could lead to occupant discomfort. The optimal control law of a linear quadratic Gaussian (LQG) controller with an active tuned mass damper (ATMD) is used for reducing the along-wind response of a tall building. ATMD consists of a second mass with optimum parameters for tuning frequency and damping ratio of the tuned mass damper (TMD), under the stationary random load, was used. A fluctuating along-wind load, acting on a tall building, was treated as a stationary Gaussian white noise and was simulated numerically, in the time domain, using the along-wind load spectra proposed by G. Solari in 1993. Using this simulated wind load, it was possible to calculate the along-wind responses of a tall building (with and without the ATMD), using an LQG controller. Comparing the RMS (root mean square) response revealed that the numerically simulated along-wind responses, without ATMD, are a good approximation to the closed form response, and that the reduced responses with ATMD and LQG controller were estimated by varying the values of control design parameters.
Highlights
The majority of today’s tall buildings are made from lighter construction materials that are both stronger and more flexible
The simulation procedure used in this study was taken from Schueller and Shinozuka [26] and Deodatis [25]. Using this simulated fluctuating along-wind load, the estimated along-wind responses of a tall building were undertaken with and without an active tuned mass damper (ATMD), while the linear quadratic Gaussian (LQG) controller revealed the effectiveness of the ATMD and the LQG controller in reducing the along-wind response of a tall building
The building is modeled as an equivalent single degree of freedom system with a generalized mass m1, damping c1, and stiffness k1, which corresponds to the first mode modal mass, damping, and stiffness of the building. md, cd, and kd are the corresponding quantities of mass, damping, and stiffness constant of tuned mass damper (TMD), while f(t) represents the along-wind force. u(t) is the active control force of the LQG controller
Summary
The majority of today’s tall buildings are made from lighter construction materials that are both stronger and more flexible. The across-wind response is mainly due to the vortex-shedding reattachment and wake flow which occur on the side face of leeward side and cannot be formulated theoretically [6] Studies on mitigating such an excessive wind-induced vibration have been conducted over several decades [2,3,4]. The simulation procedure used in this study was taken from Schueller and Shinozuka [26] and Deodatis [25] Using this simulated fluctuating along-wind load, the estimated along-wind responses of a tall building were undertaken with and without an ATMD, while the LQG controller revealed the effectiveness of the ATMD and the LQG controller in reducing the along-wind response of a tall building
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