Vibration of functionally graded cylindrical shells based on higher order shear deformation plate theory with ring support

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Vibration characteristics of FGM circular cylindrical shells using wave propagation approach (2009, background): “Najafizadeh and Isvandzibaei [ 9 ] studied the vibration of a thin cylindrical shell with ring supports made of functionally graded material composed of stainless steel and nickel.”
Vibrations of functionally graded cylindrical shells based on elastic foundations (2010, background): “Najafizadeh and Isvandzibaei [6] made a study on the vibration of thin cylindrical shells with ring support.”
Free vibration analysis of functionally graded panels and shells of revolution (2009, background): “Matsunaga [10], Najafizadeh and Isvandzibaei [ 11 ], Nguyen and Bonnet [12], Patel et al. [13], Pelletier and Vel [14], Roque et al. [15], Singh et al. [16, 17], Sofiyev [18], Sofiyev et al. [19], Yang and Shen [20], Vena [21], Wu and Tsai [22], Zenkour [23], Zhou and Wang [24]).”
A unified formulation for vibration analysis of functionally graded shells of revolution with arbitrary boundary conditions (2013, methodology): “A number of analytical and numerical methods have been developed and proposed to deal with the free vibration problems of such shells, such as the closed-form wave solution [21,22], Rayleigh–Ritz method [23–29], differential quadrature method [30,31], Galerkin method [32], and finite element method ”