Buckling analysis of restrained nanobeams using strain gradient elasticity

Three Dimensional Vibration of an Isotropic Plate Enclosed in a Rigid Body

“…This can be seen from Eq. (24). It is interesting to note that third set frequency is 1.87 times of the first set frequency approximately.…”

“…This fact can be seen from Eq. (24). More general vibration case can be obtained by setting all of the wave number integers to a nonzero value.…”

“…An extended separation of variable method for the free vibration of orthotropic rectangular plates has been presented in that study. In addition to the studies mentioned above, there are some important papers related to mechanical analyses of one-dimensional, two-dimensional and three-dimensional structures [21][22][23][24][25].…”

Free Vibration Response of a Steel Liquid Storage Tank with Porous and Perforated Columns via an Exact Continuum Method

“…In recent articles, it is seen that various solution methods, as in the generalized technique of differentiable quadrature, the Navier solution, separation of variables, the Ritz method, Stokes' transform, Fourier series, and the finite element method, attract attention. Previous studies in the literature provided examples of these methods [22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Various studies on free vibration analysis, one of the main subjects of our research, are also regularly featured in the literature.…”

A Finite Element Solution for Bending Analysis of a Nanoframe using Modified Couple Stress Theory

“…Structures such as rods, beams, plates, and frames have recently been modeled at nano and micro scales and their various analyzes like static, vibration and buckling have been carried out based on the mentioned size dependent theories. Navier's method [5][6][7][8][9][10][11], Fourier sine solution [12][13][14][15][16][17], finite element method [18][19][20][21][22][23][24][25][26][27][28][29], separation of variable procedure [30,31], generalized differential quadrature method [32][33][34][35][36], Ritz method have been frequently used by scholars to present the mechanical responses of various small scale structures such as nanobeam, nanoframe, nanotruss, nanorod, nanoplate, cracked microbeam with functionally graded material, cracked nanobeam, functionally graded nanobeam, porous nanotube etc. The above-mentioned solution methods and others have been also utilized for macro-dimensional porous plate [37][38][39], porous beam [40,41], beam [42], reinforced plate [43,44], functionally graded and laminated beam [45]…”