Natural Frequencies of Exponential Functionally Graded Beams based on Classical Beam Theory

Abstract

 In this paper, the natural frequencies of exponential functionally graded beams are determined from two separate formulations, one based on an analytical approach and the other based on a numerical approach. The classical beam theory is carried out with various boundary conditions. The results obtained in this paper are presented and compared with other results in the references to verify the correctness in implementing the formula and writing the Matlab code. This paper can help researchers have an overview of the vibration characteristics of the exponential functionally graded beams. Furthermore, they can enhance their research by modifying more advanced materials such as beams reinforced by graphene platelets, beams' shape, etc. Last but not least, with the strong application of the functionally graded material in real life, it would be good if there were more data related to this issue.