Free Vibration Analysis of Systems with Variable Parameters by the Modified Transfer Influence Coefficient Method (Formulation for a Beam with Variable Cross-Sectional Area)

The concept of the transfer influence coefficient method is extended and modified so that it is applied to the free vibration analysis of systems with variable parameters. In the present modified transfer influence coefficient method, four dynamic coefficient matrices are introduced to analyse the free vibration of a beam with a variable cross-sectional area. Since the solution of every differential equation for the dynamic coefficient matrices has poles in the domain of integration, the numerical integration of the field transfer rule is executed by selecting an adequate differential equation from among them, whose solution is not a pole at every integration point. The results of the simple computational examples on a personal computer demonstrate the validity of the present algorithm; that is, the high numerical accuracy and the high speed of the present method, as compared with the transfer matrix method.