Size-Dependent Free Vibration of Non-Rectangular Gradient Elastic Thick Microplates

The free vibration of isotropic gradient elastic thick non-rectangular microplates is analyzed in this paper. To capture the microstructure-dependent effects microplates, a negative second-order theory with symmetry utilized. related equations motion and boundary conditions are obtained using energy variational principle. A closed-form solution presented for simply supported free-vibrational rectangular four edges. C1-type differential quadrature finite element (DQFE) applied to solve microplates. DQ rule extended straight-sided quadrilateral domain through coordinate transformation between natural Cartesian systems. Gauss–Lobato jointly used discretize strain kinetic energies generic plate element. Selective numerical examples validated against those available literature. Finally, impact various parameters on characteristics annular sectorial triangular shown. It indicates that inertia can result distinct changes both frequencies mode shapes.