Application of Differential Transform Method to Free Vibration of Gabled Frames with Rotational Springs

Abstract

This paper is concerned with the free vibration of a gabled frame with rotational springs at intersecting joints. Each member of the frame may have different mechanical or geometrical properties. The problem at hand is to solve the gabled frame vibration problem for the natural frequencies by applying the differential transform method (DTM). Special attention is directed towards the derivation of the governing differential equations along with boundary and compatibility conditions of the problem. Some plots of mode shapes are also presented. The problem was also solved by using the finite element method to provide an independent check on the solutions.