Transverse shear and normal deformation effects on vibration behaviors of functionally graded micro-beams

Abstract

A quasi-three dimensional model is proposed for the vibration analysis of functionally graded (FG) micro-beams with general boundary conditions based on the modified strain gradient theory. To consider the effects of transverse shear and normal deformations, a general displacement field is achieved by relaxing the assumption of the constant transverse displacement through the thickness. The conventional beam theories including the classical beam theory, the first-order beam theory, and the higherorder beam theory are regarded as the special cases of this model. The material properties changing gradually along the thickness direction are calculated by the Mori-Tanaka scheme. The energy-based formulation is derived by a variational method integrated with the penalty function method, where the Chebyshev orthogonal polynomials are used as the basis function of the displacement variables. The formulation is validated by some comparative examples, and then the parametric studies are conducted to investigate the effects of transverse shear and normal deformations on vibration behaviors.

Size effect on transverse free vibrations of ultrafine nanothreads

“…The modified Fourier series method combined with the penalty function method is utilized to numerically calculate the natural frequencies and corresponding vibration modes. [49,50] 3. Results and discussion…”

Investigation of the Influence of an Intermediate Hinge Support in the Problem of Bending of an Elastically Restrained Orthotropic Beam

“…In the scientific literature, you can find many works devoted to the description and application of different methods for studying the bending of Thin-Waled elements with different boundary conditions, including under the condition of an elastically restrained support [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] Conclusion.…”