Title : Frequency analysis of functionally graded material circular beams
Abstract:
Functionally graded materials (FGMs) are widely used in many engineering structures due to their attractive elastic properties. FGMs are a combination of two materials in which their properties are continuously graded either through the thickness and/or along the length using different gradation rules such as the power-law or sigmoid law or exponential law or Mori Tanaka’s law. An elasticity solution for the free vibration analysis of composite beams involves complex mathematics which is sometimes very difficult to solve. Therefore researchers have developed approximate theories for the analysis of circular beams made up of composite materials. The study of fundamental frequencies of the curved beam is an important aspect when it is made up of advanced composite materials. This article is focused on the frequency analysis of functionally graded material sandwich circular beams considering the influence of transverse normal strain. A fifth-order circular beam theory considering the effects of transverse shear and normal strains is developed in this study. The theory assumes fifth-order variation of axial displacement and fourth-order variations of transverse displacements. Hamilton’s principle is employed to derive equations of motion. Analytical solution of the circular beam is obtained using the Navier technique. Symmetric and anti-symmetric functionally graded circular beams are considered for numerical studies. The material properties of face sheets are graded in the thickness direction according to the power law. The fundamental frequencies are obtained for different values of radius of curvature, the power-law index, and lamination schemes. The numerical values of frequencies obtained using the present theory are compared with the past literature and found in good agreement with those. Based on the comparison of the numerical results and discussion it is concluded that the present theory is in good agreement with other theories while predicting the fundamental frequencies of circular beams. It is also concluded that for the same length and thickness, the value of non-dimensional fundamental frequency increases as the radius of curvature is decreased.
What will audience learn from your presentation
- All those who are doing research in the area of shear deformable beams, plates, and shells made up of advanced composite materials such as functionally graded materials.
- This presentation will help young researchers to expand their research in the area of mechanics of laminated composite beams, plates, and shells.
- Laminated composite beams, plates, and shells are widely used in mechanical, civil, aerospace, offshore, and marine industries. This presentation will help researchers to solve real-life problems and to provide accurate design solutions to composite structures.
