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Tham khảo tài liệu 'vibration control part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Semi-active Vibration Control Based on Switched Piezoelectric Transducers 239 For the same reason as for the short circuit case the resonance angular frequency and the amplitude of the displacement are given by. oc 0 a --_ C0. u. -fm_ M Um . 13 Obviously the stiffness of the piezoelectric transducer in the open circuit condition is a2 Koc Ksc a . 14 The piezoelectric transducer exhibits higher stiffness in the open circuit condition and the resonance frequency of the system in open circuit condition is higher than that in the short circuit condition. The voltage on the piezoelectric transducer and the displacement and velocity of the mass are illustrated in Fig.2. In this state the net converted energy from mechanical to electrical in a cycle of vibration is zero that is the last term in Eq. 6 is zero. K y z .- Fig. 2. Voltage displacement and velocity in the open circuit condition Obviously the difference between the resonance frequency in the short circuit condition and that in the open circuit condition is due to the electro-mechanical coupling of the piezoelectric transducer in the structure. To quantitatively characterize its electromechanical property the following parameter kstruct is defined as the electro-mechanical coupling factor of the structure k. a 2- a 2 struct a 15 The resonance frequencies aO and a0c of the structure with the piezoelectric transducer under open and short circuit conditions respectively can easily be measured experimentally. Hence the electro-mechanical coupling factor of the structure can easily be estimated from experimentally results. After kstruct is obtained the force factor a can easily be calculated from the following equation a k .ás C . struct 0 0 16 3 Resistive shunt condition When the piezoelectric transducer is shunted by a resistor R that is ZSU R Equations 8 and 9 can be expressed as 240 Vibration Control V jpg m . 02 u ip o n 1 C0 u 1 F Ke - Mm2 jCm ipa fOn Íp ữl 0n 1 17 in the frequency domain where mn is an .
