Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure

Shape Effect on Free Vibration of Functionally Graded Plates

“…Yang et al [1] investigated the dynamic response of initially stressed functionally graded rectangular thin plates subjected to partially distributed impulsive lateral loads. Hosseini et al [2,3] obtained closed form solution of moderately thick and thick rectangular FGM plates for free vibration. Sheikholeslami et al [4] investigated free vibration of functionally graded thick rectangular plates with an analytical approach.…”

A Unified Accurate Solution for Three-dimensional Vibration Analysis of Functionally Graded Plates and Cylindrical Shells with General Boundary Conditions

“…Consequently, two auxiliary functions in every direction are supplemented, as shown in Eqs. (17)(18)(19). The auxiliary functions are given as follows:…”

“…The development of plate and shell theories has been subjected to significant research interest for many years, and many plate and shell theories have been proposed and developed. The main plate and shell theories can be classified into two categories: two-dimensional (2-D) plate and shell theories, including classic plate and shell theory (CPT) [1][2][3][4], the first-order shear deformation theory (FSDT) [5][6][7][8][9][10][11][12][13][14][15][16], and the higher order shear deformation theory (HSDT) [17][18][19][20][21][22][23][24][25][26], and three-dimensional (3-D) theory of elasticity [27][28][29][30][31][32][33][34][35]. However, all 2-D theories are approximate because they were developed based on certain kinematic assumptions that result in relatively simple expression and derivation of solutions.…”

A quasi-3D hyperbolic shear deformation theory for functionally graded plates

“…The FSDT [1][2][3][4][5][6][7][8][9] gives acceptable prediction, but requires a shear correction factor which is hard to find out consistently because of dependent on many parameters including geometry, boundary conditions, and loading conditions. The HSDTs [10][11][12][13][14][15][16][17] do not require a shear correction factor, but their equations of motion are more complicated than those of the FSDT. It should be noted that the thickness stretching effect (i.e., 0 z e = ) is ignored in both the FSDT and HSDTs by assuming a constant transverse displacement through the thickness of the plate.…”