An analytical method for free vibration analysis of functionally graded beams

An analytical method for the vibration and buckling of functionally graded beams under mechanical and thermal loads

“…In addition, another analytical solution based on the state space approach, which can deal with different boundary conditions, was proposed by Khdeir and Reddy [21][22][23] to study the behaviour of cross-ply laminated beams. This approach was also applied for the vibration analysis of FG and FG sandwich beams [24,25]. Regarding the thermal environment, FG beams can be designed in a smart way to adapt the environment changes, which results in a good attention in studying such behaviours.…”

Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories

“…The first-order shear deformation beam theory (FBT) known as Timoshenko beam theory has been proposed to overcome the limitations of the CBT by accounting for the transverse shear deformation effect. Since the FBT violates the zero shear stress conditions on the top and bottom surfaces of the beam, a shear correction factor is required to account for the discrepancy between the actual stress state and the assumed constant stress state [4][5][6][7]. To avoid the use of a shear correction factor and have a better prediction of response of FG beams, higher-order shear deformation theories have been proposed, notable among them are the third-order theory of Reddy [8][9][10][11][12], the sinusoidal theory of Touratier [13], the hyperbolic theory of Soldatos [14], the exponential theory of Karama et al [15], and the unified formulation of Carrera [16][17].…”

Free Vibration of Functionally Graded Rayleigh Beam

“…Due to the advantages and increasing use of FGMs and importance of the beam structures in the engineering field, many studies have been performed on the vibration problems of FG beams [14][15][16][17][18][19][20][21][22].…”