TAILIEUCHUNG - Advances in Vibration Analysis Research Part 14

Tham khảo tài liệu 'advances in vibration analysis research part 14', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Vibration Analysis of a Moving Probe with Long Cable for Defect Detection of Helical Tubes 379 i Node 0 Node j-li Node j a - j-th beam element Node 0 Node j-l Node 0 b 1 d. . I. fj ti j-th beam element c Node -1 Node ý 1 - j-th beam element Fig. 10. Concept of the TICM a connections of jth beam element and node j. b After the connection of jth beam element and c after the following connection of node j. This is the concept of the TICM. A structure after the connection of jth beam element and following connection of node j are illustrated in Fig. 10 b and c respectively. In the formulation of the TICM for a step-by-step time integration a relationship between the displacement vector dj ti and the force vector fj ti illustrated in Fig. 10 b before the connection of node j is defined as follows d j ti Tj ti fj ti Sj ti 19 We call the 3X3 square matrix Tj ti and three-dimensional vector Sj ti a dynamic influence coefficient matrix and an additional vector of the left-hand side of node j respectively. The additional vector Sj ti represents an influence of external forces which act on the preceding nodes 0 to j-1 to displacement vector at node j. Similarly a relationship between dj ti and fj ti illustrated in Fig. 10 c after the connection of node j is defined as d j ti Tj ti fj ti Sj ti 20 where the matrix Tj ti and the vector sj ti are called a dynamic influence coefficient matrix and an additional vector of the right-hand side of node j respectively. The additional vector Sj ti represents an influence of external forces which act on the preceding nodes 0 to j-1 and newly connected node j. In the algorithm of the TICM the matrices Tj ti Tj ti and vectors Sj ti Sj ti are successively computed from node 0 root of the probe to node n top of the probe at first. Subsequently the displacement vectors are computed in the reverse order from node n to node 0. Substituting Eq. 20 with subscript j-1 and Eq. 6 into Eq. 18 yields dj ti lT Tj 1 ti Lj fj ti - - Fj 1 fj ti L 1 OBv -I

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