Simply supported boundary condition for bifurcation analysis of functionally graded material: Thickness control by exponential fraction law

In this study, the bifurcation analysis of functionally graded material is done using exponential volume fraction law. Shell theory of Love is used for vibration of shell. The Galerkin Galerkin’s method is applied for the formation of three equations in eigen value form. This eigen form gives the frequencies using the computer software MATLAB. The variations of natural frequencies (Hz) for Type Type-I and Type Type-II functionally grade d cylindrical shells are plotted for exponential volume fraction law. The behavior of exponent of volume fraction law is seen for three different values. Moreover, the frequency variations of Type Type-I and -II clamped simply supported FG cylindrical shell wit h different positions of ring supports against the circumferential wave number are investigated. The procedure adopted here enables to study vibration for any boundary condition but for brevity, numerical results for a cylindrical shell with clamped simply supported edge condition are obtained and their analysis with regard various physical parameters is done.