In this paper, a non-classical plate model capturing the size effect is developed to study the forced vibration of functionally graded (FG) microplates subjected to a harmonic excitation transverse force. To this, the modified couple stress theory (MCST) is incorporated into the first-order shear deformation plate theory (FSDPT) to account for the size effect through one length scale parameter, only. Strong form of nonlinear governing equations and associated boundary conditions are obtained using Hamilton's principle. The solution process is implemented on two domains. The generalized differential quadrature (GDQ) method is first employed to discretize the governing equations on the space domain. A Galerkin-based scheme is then applied to extract a reduced set of the nonlinear equations of Duffing-type. On the second domain, through a time differentiation matrix operator, the set of ordinary differential equations are transformed into the discrete form on time domain. Eventually, a system of the parameterized nonlinear equations is acquired and solved via the pseudo-arc length continuation method. The frequency response curve of the microplate is sketched and the effects of various material and geometrical parameters on it are evaluated.

We used the generalized differential quadrature (GDQ) method to compute the transient responses of thermal stresses and center deflection amplitude in the magnetostrictive functionally graded material (FGM) square plate under rapid heating acting at its lower surface. We obtained the GDQ solutions in the three-layer of magnetostrictive FGM plates subjected to four simply supported edges. We presented the transient responses of thermal stress and center deflection amplitude of magnetostrictive FGM plates with/without velocity feedback control, respectively, under the effects of the ratio of length to thickness, the power law index, the temperature of environment and the applied heat flux.