Free Vibration Analysis of Anti-Symmetric FGM Sandwich Circular Beams Using a Fifth-Order Circular Beam Theory
Main Article Content
This paper focused on the fundamental frequency analysis of anti-symmetric FGM sandwich circular beams. A fifth-order circular beam theory considering the influence of transverse shear and normal strains is developed in this study. The theory assumes fifth-order variation of thickness coordinate in axial (tangential) displacement and fourth-order variations of thickness coordinate in transverse (radial) displacements. Hamilton’s principle is applied to derive equations of motion. An exact solution for the frequency analysis of a simply-supported circular beam is obtained using the Navier technique. Anti-symmetric FGM sandwich circular beams are considered for numerical studies. The material properties of face sheets are graded in the thickness direction of the beam according to the power-law whereas the core of the beam is made up of isotropic material. The fundamental frequencies are obtained for different values of radius of curvature (R), the power-law index (p), and lamination schemes of FGM sandwich circular beams. For the validation purpose, fundamental frequencies for straight beams obtained using the present theory are compared with the previously published papers and found in good agreement with those. This study also presents benchmark results of the FGM sandwich circular beams. Based on the comparison of the numerical results and discussion it is concluded that for the same length and thickness, the value of non-dimensional fundamental frequency increases as the radius of curvature is decreased. Also, the non-dimensional frequency decreases as the power-law index increases.
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