A revised version of the transfer matrix method to analyze one-dimensional structures

Abstract

A new and general method to analyze both free and forced vibration characteristics of one-dimensional structures is discussed in this paper. This scheme links for the first time the classical transfer matrix method with the recently developed integrating matrix technique to integrate systems of differential equations. Two alternative approaches to the problem are presented. The first is based upon the lumped parameter model to account for the inertia properties of the structure. The second releases that constraint allowing a more precise description of the physical system. The free vibration of a straight uniform beam under different support conditions is analyzed to test the accuracy of the two models. Finally some results for the free vibration of a 12th order system representing a curved, rotating beam prove that the present method is conveniently extended to more complicated structural dynamics problems.