tailieunhanh - Encyclopedia of Smart Materials (Vols 1 and 2) - M. Schwartz (2002) Episode 7

Tham khảo tài liệu 'encyclopedia of smart materials (vols 1 and 2) - m. schwartz (2002) episode 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Frequency Hz 4 Frequency Hz 9 Ư 2_J - Di il Si 0 -1 -2 -3 4 10-1 100 101 Frequency Hz 102 10-1 Frequency Hz Frequency Hz Figure 16. DTF and RTF response of free-free beam structure a V0 F3 b V1 F3 c V2 F3 d V3 F3 e V4 F3 f V5 F3. consider me nxeu-iree beam shown in Fig. 17. me leit end of the beam is fixed and the right end is free. Energy is input into this beam by F3 0. The conventional reverberated transfer function matrix of this five-element beam can be obtained experimentally. The inverse of the RTF is the dynamic stiffness matrix of the beam. EI1pA1 EI2pA2 EI3PA3 EI4pA4 0123 F3 Figure 17. Fixed free beam that has five e Kị K2 K22 0 - K32 K2 K3 K23 RTF-1 K33 K43 K K24 0 K34 KK K K K35 K45 40 dereverberated responses depends on the w ary conditions are treated. A controller is n free-free beam to extend the free end to infi for the fixed-free beam element 1 is ignored needs to be extended to the left to infinity. T K is the affecting part from element 1 ar element 2. As previously shown for the free-free beam the vertical displacement and angular displacement of each node are fed back into local controllers to generate control forces that can eliminate wave reflection at each node. Controllers can be attached at all nodes except for the node at the fixed end of the fixed-free beam. The DTF responses with respect to input F3 can be obtained from the following expression DAMAGE DETECTION APPROACH BASED ON DTF RESPONSE Detecting the Presence and Location of Damaị In the previous section collocated noncaus were developed to obtain the DTF response - V1 - F3 0 0 01 F3 V2 F3 02 F3 V3 F3 03 F3 V4 F3 04 F3 V5 F3 05 -F3 -K G21 Gal Ữ2l 0 RTF-1 02x2 0 G4r G5r Gbr _ 7 0 1 0 0 DTF 0 0 0 0 where K41 can be obtained because the physical properties of the first element are known. The RTF and DTF responses are shown in Fig. 18 Comparing the expressions in Eqs. 39 and 41 the difference between the free-free beam and the fixed-free beam spring-mass structural