Nonlinear strain gradient forced vibration analysis of shear deformable microplates via hermitian finite elements

Based on the modified strain gradient model (MSGM) and Mindlin-Reissner (M-R) plate theory, the geometrically nonlinear forced vibration of rectangular microplates via finite element (FE) method is investigated in this research. The nonlinear mathematical model of the problem is provided under the von Karman nonlinear kinematic relations within the M-R plate theory along with the MSGM. By the use of Hamilton’s principle and fully confirming rectangular hermitian finite elements, the stiffness and mass matrices, as well as the force vector, are obtained. Various numerical examples are represented to verify the efficiency and validity of the proposed model. By reducing the constitutive relations, the results for the modified couple stress model (MCSM) are also presented. Various numerical examples are given to investigate the impacts of length-scale parameter and geometrical parameters on the nonlinear forced vibration responses. •The nonlinear size-dependent forced vibration of microplates is studied based on the modified strain gradient theory.•The kinematic relations are presented using the Mindlin-Reissner plate model and von Kármán nonlinearity.•The hermitian finite elements are employed to numerically model the problem.•The impacts of the length-scale parameter and geometrical parameters on the nonlinear vibration response are investigated.