Free Vibration Analysis of a Tree Structure by the Transfer Influence Coefficient Method : 2nd Report, Treatment of a Three-Dimensional Tree Structure and Numerical Computational Results

An algorithm for a two-dimensional tree structure formulated in the previous report by applying the transfer influence coefficient method is extended in order to analyse the longitudinal, flexural and torsional coupled free vibration of a three-dimensional tree structure. Moreover, adequate selection of a nonzero state variable as an initial standard value in the computation of characteristic modes and the problem of false roots which occur in the analysis for a structure with subsystems by applying the transfer matrix method are also discussed. The superiority of the present method over the transfer matrix method in the computational accuracy and the computation speed is confirmed by the numerical computation for typical models of both two-and three-dimensional tree structures.