Abstract
Box beams have been used widely in engineering fields. This paper proposes a higher-order shear deformation beam theory to investigate the transverse vibration and stability of box beams in pure bending, especially free vibration and buckling of functionally graded box beams. A warping shape function is constructed for the first time to take shear deformation and rotary inertia of the hollow-core rectangular cross section into account simultaneously during bending. The governing equation and boundary conditions are derived. The frequency equations for typical end supports are given. The characteristic equations for buckling and critical loads are determined. Numerical results are evaluated. Besides its simplicity and easy-to-implement, the proposed theory has sufficient accuracy on the mechanical behavior of the box beams. By comparing the obtained results with the simulation results based on three-dimensional finite element method, the accuracy of the numerical results obtained is verified. The effects of parameters such as aspect ratio, gradient index, and wall thickness on the natural frequencies and critical loads are explored in detail. When box beams become rectangular beams, our model reduces to the well-known Levinson beam model.
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