Transverse vibration of double cracked beam using assumed mode method

Abstract

This paper presents transverse vibration of double cracked beam using assumed mode method. First we described the assumed mode method for transverse vibration of continuous systems. Assumed mode method has been used for continuous models, Also Assumed mode method may be used to derive the equations of motion of other linearly elastic systems. For the Bernoulli-Euler beam the strain energy and kinetic energy have been derived. General coordinates of model are assumed as function of time and coordinate. The admissible function that considered must be satisfied the boundary conditions. Then the mass and stiffness matrix have been obtained from strain and kinetic energy. Only steps those are actually required in using the Assumed-Modes Method to arrive at the equations of motion of an N-DOF model of a continuous system.