Abstract
This work uses the Quasi-3D (Q3D) shear and normal deformation beam concept in combination with the length scale capturing theory through the “Modified Couple Stress Theory” (MCST) and the novel computational approach namely, Differential Quadrature Finite Element Method (DQFEM) to investigate free vibratory conducts of an imperfect BD-FG microbeams with a crack. To obtain the relevant governing equations, the Lagrange's rule is utilized. “The differential quadrature” (DQ) and “Gauss-Lobatto quadrature” procedures for weighting coefficient matrices are used to easily construct the mass and stiffness matrices. The Gauss-Lobatto node scheme is used to determine the griding knots. In order to show the efficiency and exactness of the described numerical resolution method, the attained outcomes are authenticated with the similar results found in the literature. The effects of the crack position, crack depth, beam thickness by material length scale aspect, the volume fraction of material imperfection, edge supports state types, length through thickness factor, and the two-way material grading indexes on the nondimensional natural frequencies of 2D porous FG microbeams are inspected. This work will provide a numerical basis for the design of FG microstructures in the field of micromechanics. These findings can be used to construct porous FG microstructures in engineering.
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