Vibrations and buckling of orthotropic small‐scale plates with complex shape based on modified couple stress theory

Abstract

Free vibrations of microplates with non‐classical shape are considered in the paper. Governing equations are based on the modified couple stress theory and Kirchhoff–Love plate theory. It is assumed that the plate is isotropic or orthotropic and satisfy various boundary conditions. An analysis is performed by the variational‐structural method which is based on R‐functions theory and Ritz method. The testing of the proposed method is carried out by comparison with known in literature results and analytical solutions. The developed method is applied to the study of the influence of the material length scale parameter, boundary conditions, shape parameters, material characteristics on vibration frequencies. Also, size‐dependent analysis for buckling of the isotropic and orthotropic microplate subjected to uniaxial load is performed by the proposed approach. Critical loads for a plate with complex shape, different types of boundary conditions and material are calculated in order to study their effect on buckling.

Free vibrations of small-scale plates with complex shape based on the nonlocal elasticity theory

“…Figure 6 shows the values of the frequency parameter for isotropic (27) and orthotropic (28) plates in the case of simply supported and clamped nanoplates. Geometrical parameters here are taken as c 1 /a = 0.5, c 2 /a = 0.5.…”

“…Isogeometric analysis was applied to the study of large amplitude free vibration of porous skew and elliptical nanoplates based on nonlocal elasticity by Tao and Dai [26] . The studies devoted to the micro/nanoplates of complex geometry also include works [27][28][29] (plates with a hole, and L-shaped plate, and skew plate, respectively), where the authors use the modified couple stress theory accounting for the small-scale effects.…”

Stability analysis of arbitrary restrained nanobeam embedded in an elastic medium via nonlocal strain gradient theory

“…Also, we can calculate the buckling loads of the embedded NSG beam under the influence of the nonlocal and SG parameters using the eigen-value problem presented in equation (34). The solution of the eigen-value problem can be used to examine different situations between the two boundary conditions of simply supported and free.…”

“…Ebrahimi and Barati 10 have presented the hygrothermal and NSG impacts on the buckling of graphene. In addition to the articles summarized briefly above and dealing with NSG theory, there are various studies based on the other higher-order theories like nonlocal elasticity, [11][12][13][14][15][16][17][18][19][20][21][22][23] nonlocal couple stress theory, [24][25][26] modified couple stress theory, [27][28][29][30][31][32][33][34][35][36][37][38] SG theory, 39,40 doublet mechanics theory [41][42][43][44][45] in the literature.…”

A Hermitian Cn finite cylindrical layer method for 3D size‐dependent buckling and free vibration analyses of simply supported FG piezoelectric cylindrical sandwich microshells subjected to axial compression and electric voltages

“…Based on the 3D equations of linear couple stress elasticity, Zozulya [32] developed a new higher-order couple stress theory of plates and shells, all equations of which were derived in Cartesian and polar coordinates. Mazur et al [33] incorporated the kinematic model of Kirchhoff-Love plate theory into the MCST to study the free vibration and static buckling behaviors of orthotropic small-scale plates with complex shapes. Incorporating the displacement model of the TSDT into the MCST, Rao et al [34] investigated the size-dependent free vibration characteristics of cylindrical microshells.…”