Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh–Ritz method

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Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory (2014, background): “Based on the different shear deformation theories, though many works on these problems for FG beams are available ([1]-[13]), research on vibration and buckling of FG sandwich beams is a few in number.”
Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory (2013, background): “works on static ([3]-[11]) and free vibration ([12]-[18]) as well as buckling analysis ([19],[20]) of FG”
Free vibration of functionally graded beams and frameworks using the dynamic stiffness method (2018, methodology): “amongst these are the applications of direct analytical procedure using the governing differential equations of motion [5e19], finite element [20e22], Rayleigh-Ritz [23], finite volume [24e26], differential quadrature [27], differential transformation [27,28] and transfer function [29,30] methods.”
Fundamental frequency analysis of functionally graded sandwich beams based on the state space approach (2016, methodology): “Pradhan and Chakraverty [11, 12] employed Rayleigh-Ritz method using the CBT, FOBT and HOBT to”