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In this study, vibration frequency analysis of three layered functionally graded material (FGM) cylinder-shaped shell is studied with FGM central layer whereas the internal and external layers are of the same isotropic materials. Sander’s shell theory is applied for strain and curvature-displacement relationships. The Rayleigh Ritz method is employed to attain the shell frequency equation. Influence on natural frequencies (NFs) is observed for various volume fraction laws. The characteristic beam functions are used to estimate the dependence of axial modal functions. Results are obtained for thickness to radius ratios and length to radius ratios for different edge conditions. The validity of this method is checked for numerous results found in the open literature.

Madiha Ghamkhar, M. Nawaz Naeem, Muhammad Imran. (2020) Vibration frequency analysis of three-layered cylinder shaped shell with FGM middle layer under effect of various volume fraction laws, Punjab University Journal of Mathematics, Volume 52 , Issue-12.
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