Accurate formula for determination of natural frequencies of FGM plates basing on frequencies of isotropic plates

The functionally graded materials (FGM) have many advantages especially in thermal environments, and in the recent years they have been used in many engineering applications. A FGM plate is an inhomogeneous composite made of two constituents (usually ceramic and metal), with both the composition and the material properties varying smoothly through the thickness of the plate. The FGM plate vibrations have a strong bending-stretching coupling effect. Large computational efforts are required for calculating by numerical methods the natural frequencies of such plates with different volume fractions of containing materials. Basing on the investigation of tendencies in frequency variation due to different volume fraction, the present study derives an empiric accurate formula that gives a correlation between the frequencies of FGM plate and isotropic ones made of containing materials, even with different Poisson ratio. The formula gives immediately accurate results for different vibrational modes and for various volume fractions of containing materials without expending much computational effort. Numerical example is presented in order to demonstrate the accuracy, applicability and convenience of using the suggested formula. The natural frequencies calculated with the presented formula are compared with those obtained through other numerical method for thick FGM annular plates.