Abstract
For a thickness-wise functionally graded (FG) beam, the midplane does not coincide with its physical neutral plane. This paper presents a consistent shear beam theory that guarantees the warping of the cross-section with vanishing shear stress on the surfaces and maximal shear strain/stress at the physical neutral plane. The governing equation of the free vibration of FG beams is derived. For typical end conditions, the characteristic equations are obtained exactly. The numerical natural frequencies are calculated and verified for special cases by comparing the existing solutions. Effects of the exponential gradient of material properties on the natural frequencies are elucidated.
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