Abstract
A refined beam theory that takes the thickness-stretching into account is presented in this study for the bending vibratory behavior analysis of thick functionally graded (FG) beams. In this theory, the number of unknowns is reduced to four instead of five in the other approaches. Transverse displacement is expressed through a hyperbolic function and subdivided into bending, shear, and thickness-stretching components. The number of unknowns is reduced, which involves a decrease in the number of the governing equation. The boundary conditions at the top and bottom FG beam faces are satisfied without any shear correction factor. According to a distribution law, effective characteristics of FG beam material change continuously in the thickness direction depending on the constituent’s volume proportion. Equations of motion are obtained from Hamilton’s principle and are solved by assuming the Navier’s solution type, for the case of a supported FG beam that is transversely loaded. The numerical results obtained are exposed and analyzed in detail to verify the validity of the current theory and prove the influence of the material composition, geometry, and shear deformation on the vibratory responses of FG beams, showing the impact of normal deformation on these responses which is neglected in most of the beam theories. The obtained results are compared with those predicted by other beam theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of FG beams.
Highlights
Graded materials (FGMs) are new types of composites obtained by mixing ceramic and metallic constituents [1,2,3,4]
The higher-order SDT aims to eliminate the failure of CBT and the first-order SDT by assuming a higher-order variation through functionally graded (FG) beam thickness for transverse displacement without providing any shear correction
It is obvious from these figures that the shear effect is more important on the two displacements, and it is greatest than the effect of thickness stretching for the transverse displacement
Summary
Graded materials (FGMs) are new types of composites obtained by mixing ceramic and metallic constituents [1,2,3,4]. Meradjah et al [35] integrated the thickness-stretching effects in a new shear strain theory to analyze the bending vibration of FG beams. A refined theory is presented to analyze the bending vibration of the thick FG beam, with supported ends and under transverse loading. This theory provides a constant transverse displacement and higher-order variation of axial displacement through the depth of the beam so that there is no need for any shear correction factors. The proposed higher-order normal deformation and shear theory is accurate, and provides an elegant and easy-to-implement approach to simulating the bending and vibration behaviors of thick FG beams
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