Free Vibration Analysis of a Tree Structure by the Transfer influence Coefficient Method (1st Report, Formulation for a Two-Dimensional Tree Structure)

Takahiro Kondou, Atsuo Sueoka, Yuji Yasuda, Deok Hong Moon

Research output: Contribution to journalArticle


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.

Original languageEnglish
Pages (from-to)1091-1098
Number of pages8
JournalTransactions of the Japan Society of Mechanical Engineers Series C
Issue number536
Publication statusPublished - Jan 1 1991
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering

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