AI Summary & Key Takeaways
AI InsightThe effects of shear deformation, thickness stretching, material distribution, aspectratios and boundary conditions on the free vibration frequencies and critical buckling loads of the 2D-FGBs are investigated.
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Abstract
This study presents the free vibration and buckling behavior of two directional (2D) functionally graded beams (FGBs) underarbitrary boundary conditions (BCs) for the first time. A four-known shear and normal deformation (Quasi-3D) theory where theaxial and transverse displacements are assumed to be cubic and parabolic variation through the beam depth is employed based onthe framework of the Ritz formulation. The equations of motion are derived from Lagrange’s equations. The developedformulation is validated by solving a homogeneous beam problem and considering different aspect ratios and boundaryconditions. The obtained numerical results in terms of dimensionless fundamental frequencies and dimensionless first criticalbuckling loads are compared with the results from previous studies for convergence studies. The material properties of thestudied problems are assumed to vary along both longitudinal and thickness directions according to the power-law distribution.The axial, bending, shear and normal displacements are expressed in polynomial forms with the auxiliary functions which arenecessary to satisfy the boundary conditions. The effects of shear deformation, thickness stretching, material distribution, aspectratios and boundary conditions on the free vibration frequencies and critical buckling loads of the 2D-FGBs are investigated.