Study of crack’s effect on the natural frequencies of bi-directional functionally graded beam

Abstract

In this article, we analyze the effect of transverse cracks on the natural frequencies of Euler–Bernoulli functionally graded beam, the studied beam was Discretized into finite elements and the global matrices of the governing equation of motion are determined applying the Lagrange's equation on the kinetic and strain energies of the beam. The material properties are considered vary in the both; thickness and width; directions of the beam, the gradation is described by the power–law distribution, the stiffness of the cracked element is determined based on the reduction of the cross section of the beam. The numerical results obtained are compared with those available in previous study. Finally, case studies were conducted to analyze the influence of power law index, depth, and crack location on the natural frequencies of the beam for different boundary conditions; these studies demonstrate the advantage of the bidirectional FG beam over to the pure metallic and unidirectional FG beams.

Keywords:

• FG beam
• natural frequency
• finite element method
• crack

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.