TY - JOUR
T1 - Free Vibration Analysis of a Tree Structure by the Transfer influence Coefficient Method (1st Report, Formulation for a Two-Dimensional Tree Structure)
AU - Kondou, Takahiro
AU - Sueoka, Atsuo
AU - Yasuda, Yuji
AU - Moon, Deok Hong
PY - 1991
Y1 - 1991
N2 - The authors apply the transfer influence coefficient method to a two-dimensional tree structure, and formulate a general algorithm to analyse in-plane longitudinal and flexural coupled free vibration. The tree structure, which is mainly found in the Γ-shaped structure of machine tools, pipeline systems and so on, has some crooked parts and subsystems but has no closed loop in the system. It is modeled as a distributed mass system in the present algorithm. It is theoretically confirmed that some merits of the transfer influence coefficient method are kept also for the two- dimensional tree structure; that is, boundary conditions are easily controlled by the spring constants, and false roots in the use of the bisection method as a solution to the frequency equation can readily be eliminated by using the values obtained in the computational process. The occurrence mechanism of false roots is discussed in detail.
AB - The authors apply the transfer influence coefficient method to a two-dimensional tree structure, and formulate a general algorithm to analyse in-plane longitudinal and flexural coupled free vibration. The tree structure, which is mainly found in the Γ-shaped structure of machine tools, pipeline systems and so on, has some crooked parts and subsystems but has no closed loop in the system. It is modeled as a distributed mass system in the present algorithm. It is theoretically confirmed that some merits of the transfer influence coefficient method are kept also for the two- dimensional tree structure; that is, boundary conditions are easily controlled by the spring constants, and false roots in the use of the bisection method as a solution to the frequency equation can readily be eliminated by using the values obtained in the computational process. The occurrence mechanism of false roots is discussed in detail.
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U2 - 10.1299/kikaic.57.1091
DO - 10.1299/kikaic.57.1091
M3 - Article
AN - SCOPUS:84998237454
VL - 57
SP - 1091
EP - 1098
JO - Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C
JF - Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C
SN - 0387-5024
IS - 536
ER -