Free vibration analysis of open-cell FG porous beams: analytical, numerical and ANN approaches

Abstract

This paper constitutes an attempt to explore the influence of porosity on free vibration analysis of functionally graded (FG) beams with different boundary conditions using different efficient analytical and numerical approaches. The material properties of open-cell FG porous beams are estimated using a modified power-law with two different types of porosity distributions through the thickness direction of the FG beam namely even and non-even distributions. Hamilton's principle is used to derive the equations of motion of the FG porous beam with high-order shear deformation theory. The state-space approach is utilized to solve the problem in the analytical solution section. In addition to the theoretical solution, a simulation based on a displacement type of finite element method (FEM) was utilized to verify the analytical solution. For this purpose, three-dimensional shell beams were modeled using ABAQUS for the solution of the vibration problem of the FG porous beam. Furthermore, the Artificial Neural Networks (ANNs) technique is used to predict the effects of porosity distributions, porosity coefficient, slenderness ratio and boundary conditions on natural frequency variations of porous FG beam. The ANNs technique allows for an investigation of the effects of various parameters, including beam characteristics, material properties, geometric details and porosity distributions.