TAILIEUCHUNG - On the optimal control force applied to tuned mass dampers for multi-degree-of-freedom systems

The design of active TMD for multi-degree-of-freedom systems subjected to second order coloured noise excitation is considered using the linear quadratic optimal theory. A detailed numerical study is carried out for a 2-DOF system. It is shown that the effectiveness of active TMD is better than the one of passive TMD. | · Vietnam Journal of Mechanics, VAST, Vol. 26 , 2004, No. 1 (1 - 10) ON THE OPTIMAL CONTROL FORCE APPLIED TO TUNED MASS DAMPERS FOR MULTI-DEGREE-OF-FREEDOM SYSTEMS NGUYEN DONG ANH 1 AND NGUYEN CHI 8ANG 2 1 2 Institute of Mechanics Hanoi Research Institute of Mechanical Engineering ABSTRACT. The design of active TMD for multi-degree-of-freedom systems subjected to second order coloured noise excitation is considered using the linear quadratic optimal theory. A detailed numerical study is carried out for a 2-DOF system. It is shown that the effectiveness of active TMD is better than the one of passive TMD. 1 Introduction Under environmental loading structures and machines may produce large undesired vibrations, which can reflect into their quality and durability. The use of tuned mass dampers (TMDs) helps to reduce the undesired vibrations in the primary systems. The passive TMDs [1-6] can only store or dissipate vibration energy, hence their application to the reduction of undesired vibrations is limited. This disadvantage of passive TMDs can be improved by applying to the passive TMDs an actuator force. In this case passive TMD becomes active TMD [7-11], which can change the system energy. In the paper [6] the design of optimal passive TMD for MDOF systems subjected to the second order coloured noise excitation has been investigated in order to minimize the sum of response mean square components of the primary system with a given ranking priority. In this paper an active TMD is considered based on the designed passive TMD. The main problem is to determine the optimal control force applied to the passive TMD. 2 Second order coloured noise excitation The second order coloured noise process p(t) is considered as a stationary response of the following filter of white '. noise v(t) + 2hp(t) + n 2v(t) = O"~(t), (2 .1) where h, fl,(]" are positive constants, ~(t) is the stationary Gaussian white noise process with unit intensity. The spectral density .

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• On the optimal control force applied
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