tailieunhanh - Vibration Analysis and Control New Trends and Developments Part 2

Tham khảo tài liệu 'vibration analysis and control new trends and developments part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Adaptive Tuned Vibration Absorbers Design Principles Concepts and Physical Implementation 15 High accuracy is guaranteed here by solving the frequencies ã a ã m for K 39 which means that 20 symmetric free-free plain beam flexural modes were considered. Now for the equivalent two-degree-of-freedom system in Fig. lb one can write the attachment point receptance as Kidner Brennan 1997 2 2 rAA 2_DOF 2 a red a red 15 where ma eff Rma m red ự-R ma m 16a-c The non-zero resonance of the function in eq. 15 is given by 12-DOF eff ữ reíl 17 For equivalence ffi m 2DOF om in eq. 17 . Hence by substituting this condition and eqs. 16a b into eq. 17 an expression can be obtained for the proportion R of the total absorber mass m that is effective in vibration attenuation R x a l- ãll ãm 2 18 .where ã a ãm are the roots of eqs. 12 13 . Also from eq. 15 and eqs. 16 the non-dimensional attachment point receptance of the equivalent system can be written as -2 -2 Í 2 ũ Ũ rAA G x a I __ mựởi rAA ứ I __ ------ r. 19 AA I2-DOF Ơ 1 AA I2-DOF 1 v 1 7j ffi j 1 -R a - ffir The equivalent two-degree-of-freedom model is verified in Fig. 17 against the exact theory governing the actual continuous ATVA structures of Fig. 16 for 7 5 and two given settings x . For each setting of X the corresponding values of ã a and R were calculated using eqs. 12 13 18 and used to plot the function rAA x cr DOF in eq. 19 . Comparison with the exact receptance fAA ũ x ơ f computed from eqs. 9 and 11 shows that the equivalent two-degree-of-freedom system is a satisfactory representation of the actual systems in Fig. 16 over a frequency range which contains the operational frequency of the ATVA a a n . Next using eqs. 12 13 18 the variations of 0 a and R with ATVA setting X for various fixed values of 7 are investigated for both types of ATVA in Fig. 16. The resulting characteristics are depicted in Fig. 18. With reference to Fig. 18a it is evident that as 7 is increased the tuning frequency characteristics .