Vibration analysis of size-dependent functionally graded micro-plates subjected to electrostatic and piezoelectric excitations

A size-dependent model based on the modified couple stress theory is developed to study free vibration, static deflection, and pull-in instability of a fully-clamped functionally graded (FG) micro-plate covered by piezoelectric layers subjected to both electrostatic and casimir forces. Considering the geometrically nonlinearities, the governing equations of motion and boundary conditions are derived by means of Hamilton's principle. The system of equations is solved numerically using finite element method. A Comprehensive Verification study is carried out to ensure the accuracy of the proposed model. Obtained results show that the volume fraction exponent, piezoelectric voltage, residual stresses, and MLSP considerably affect the natural frequency, maximum static deflection, and the electro-mechanical behavior of fully-clamped rectangular micro-plates. The results also reveal that the pull-in voltage could be maintained within a desirable range through proper utilizing of material properties, residual stresses, and piezoelectric voltages.