Vibration analysis of cracked microbeams by using finite element method

Abstract

A finite element method procedure applicable for calculating the free vibration of cracked microbeams is presented in this study. The basic mathematical theory and the background of the cracked microbeam is shown, which included the kinematic energy and the total potential energy of the cracked microbeam. Euler- Lagrange equation and the kinematic boundary conditions are obtained with the help of first variation of cracked microbeam. The accuracy, efficiency, and generality of the proposed approach are fully verified and demonstrated through numerical examples involving different values of the crack location.