Free vibration analysis of FGM cylindrical shells under non-uniform internal pressure

In this paper,free vibration of fgm thin cylindrical shells under non uniform linear and nonlinear internal pressure is investigated and the impact of non-uniform internal pressure on free vibrations and natural frequencies have been analyzed. the boundary conditions used in this study were two simple supported and in order to derive the equations,the theory of sanders thin shells and rayleigh-ritz method is used. the effect of various parameters on natural frequencies and free vibrations of shells under internal pressure,such as linear and nonlinear pressure profile,material,thickness to radius and the ratio of length to diameter have been investigated. additionally,the effect of internal pressure on the natural frequencies profile,in different longitudinal modes and environment has been derived. the results of this study validated by data in the literature and abaqus software that reflects the accuracy and can be used as a reference for future designers and researchers.