ABSTRACT
While Den Hartog considered harmonic loading only Warburton and Ayroinde derived optimum parameters of TMD for a undamped main system under harmonic and white noise random excitations (Ayoringde 1980). If the mass ratio is small and the main system’s damping ratio is small relative to that of TMD, Krenk derived the optimum parameters for tuning frequency and applied damping ratio of TMD for damped main system (Krenk 2008). A number of TMDs have been installed in tall buildings to suppress wind-induced vibrations of a tall building (Housner et al. 1997)
At that time, it was accepted as a fact that the performance of TMD could be enhanced by incorporating a feedback controller through the use of an actuator as an active control force in the design of TMD, which was called Active Tuned Mass Damper (ATMD) (Chang 1980, 1995). ATMD design for suppressing wind-induced vibration of a tall building using assumed deterministic harmonic wind load was presented by Chang and Soong (1980). That is a first active control study for mitigating wind-induced vibration of a tall building installed in ATMD using Linear Quadratic Regulator (LQR) controller. Then many advanced studies including Linear Quadratic Gaussian (LQG), H2 and H∞ control theories for reducing dynamic responses of a tall building under earthquakes and wind loads have been developed and a number of
1 INTRODUCTION
Suppressing the seismic-excited responses of a tall building has been much attention to structural engineers. In last three decades, many control devices, passive, active and hybrid, have been developed to control structural vibration due to dynamic loads such as earthquakes and wind loads (Chang 1995). Tuned Mass Damper (TMD) is a classical vibration control device consisting of a mass, a spring and a damper supported by the main vibrating system (Lee et al. 2006). The concept of TMD is that if the natural frequency of TMD is tuned to the natural frequency of the vibrating main system, then the vibration energy is dissipated through the damping in the TMD, so reducing the main system’s vibration (Ayoringde 1980). The original idea of TMD is from Frahm in 1909, who invented vibration control device called a vibration absorber using a spring supported mass without damper (Frahm 1909). That was only effective when absorber’s natural frequency was tuned to a frequency close to the excitation frequency. This shortcoming was improved by introducing damper in the spring supported mass by Ormondroyd and Den Hartog (Ormondroyd 1928). Later Den Hartog derived optimal frequency tuning and damping ratio for the undamped main system under harmonic load (Den Hartog 1956).
