Semianalytical Solution for Three-Dimensional Vibration Analysis of Thick Multidirectional Functionally Graded Annular Sector Plates under Various Boundary Conditions

Three-dimensional transient analysis of functionally graded material annular sector plate under various boundary conditions

“…It is noted that the present method and Tahouneh and Yas[31]'s method are the same when calculating fundamental frequencies. The results obtained by these methods are given in It is shown that the results obtained by Zhou, et al[50]'s method, Tahouneh and Yas[31]'s method and the present method are in an excellent agreement with each other for different plate thicknesses. However, as the plate thickness increases, the difference between Mindlin solution and other solutions increases, especially for Clamped-Clamped plates.…”

“…Mcgee, et al[49] gave the fundamental frequency parameters for annular sector plates with two simply supported radial edges by classical plate theory (CPT) and Mindlin plate theory. Zhou, et al[50] and Tahouneh and Yas[31] provided the fundamental frequency parameters by employing Chebyshev-Ritz method and SSM-DQM, respectively. It is noted that the present method and Tahouneh and Yas[31]'s method are the same when calculating fundamental frequencies.…”

“…Zhou, et al[50] and Tahouneh and Yas[31] provided the fundamental frequency parameters by employing Chebyshev-Ritz method and SSM-DQM, respectively. It is noted that the present method and Tahouneh and Yas[31]'s method are the same when calculating fundamental frequencies. The results obtained by these methods are given in It is shown that the results obtained by Zhou, et al[50]'s method, Tahouneh and Yas[31]'s method and the present method are in an excellent agreement with each other for different plate thicknesses.…”

“…The mechanical properties of the materials are assumed to vary continuously along the thickness direction and have the same exponential distribution. Based on the SSM and DQM, Tahouneh and Yas [30,31] investigated the free vibration of thick FGM sector plates on Pasternak elastic foundation and two-dimensional (2D) FGM annular sector plates. Alibeigloo and Kani [32,33] carried out static and free vibration analysis for laminated and FGM cylindrical shells, by employing SSM and DQM.…”

A review of theories for the modeling and analysis of functionally graded plates and shells

“…The 3D elasticity theory and the DQM were used to obtain the natural frequency of FG annular plates with various boundary conditions. Tahouneh and Yas [374] also adopted the 3D elasticity theory and the DQM to study the 3D free vibration response of FG annular sector plates under various boundary conditions. Sburlati and Bardella [375] presented exact 3D solutions for the bending of FG circular plates subjected to axisymmetric transverse loadings using Plevako functions.…”