Free vibration of axially or transversely graded beams using finite-element and artificial intelligence

Abstract

The effect of grading direction on the natural frequencies of heterogeneous isotropic beams is investigated and the artificial neural network approach is conducted to estimate the free vibration characteristics. The two-dimensional beam is graded in axial or transverse direction according to the power-law form. An artificial neural network model has been developed to estimate relationship between material properties and model, grading direction, slenderness ratio as an input layer and natural frequencies obtained by Finite-Element method as an output layer. The Levenberg–Marquardt back-propagation method is used as a training algorithm. The novelty of this study is that it deals with the estimation of free vibration characteristics of beams made of functionally-graded material using aforementioned input layer for the first time. The proposed artificial neural network model can predict the natural frequencies without the need for a solution of any differential equation or time-consuming experimental processes. The results show that artificial intelligence techniques can be efficiently adopted to free vibration problems of functionally graded beams. The influence of grading direction on the natural frequency is also demonstrated.

Keywords

• Free vibration
• Functionally-graded materials
• Beams
• Artificial neural network
• Finite-element method