Linear Forced Vibration Analysis of Two- and Three-dimensional Tree Structures by the Transfer Influence Coefficient Method

An algorithm for free vibration analysis of a tree structure formulated in the previous reports by applying the transfer influence coefficient method is extended in order to analyze forced vibration of a tree structure which is mainly found in pipeline systems. The tree structure has some crooked parts and subsystems but has no closed loop in the systems. It is modeled as a distributed mass system with consideration of structural damping, and the present algorithm is formulated for both two- and three-dimensional tree structures. It is theoretically confirmed that some merits of the transfer influence coefficient method for free vibration analysis, for example, excellence in both computation accuracy and speed are also realized for the forced vibration analysis. Moreover, the present algorithm enables us to easily analyze a vibrating system excited by forced displacement by changing the corresponding spring constants conveniently.