Thermal vibration and nonlinear buckling of micro-plates under partial excitation

Abstract

In this study, a finite element formulation is proposed to study bending, thermal vibration, and buckling behavior of a modified couple stress-based micro-plate under partial piezoelectric excitation. To this end, the micro-plate is modeled using the classical plate theory (CPT) in conjunction with von Kármán nonlinear strains. The modified couple stress theory is employed to take into account the size-dependent behavior of the system. The nonlinear equations of motion are derived using Hamilton's principle. In order to obtain numerical solutions to the problem, the displacement finite element model is developed. A parameter study is conducted to study the effects of different parameters, such as temperature rise, material length parameter scale (MLSP), boundary conditions, aspect ratio, and piezoelectric layers configurations on nonlinear behavior of micro-plates. The results are divided into three separate sections: static bending analysis, thermal vibration analysis, and thermal buckling analysis; in each section, the accuracy of the model is checked by comparing the results with the ones reported in the literature. Obtained results show that the bending behavior of the micro-plate is influenced by the size effects and piezoelectric configurations; furthermore, it is observed that applied voltage to the piezoelectric layers and temperature rise affect the fundamental frequency of the system. Finally, the effect of piezoelectric layers on the buckling behavior of the model is studied; the results show that the fully covered model is less prone to buckling under the thermal loading cases. The proposed model provides good control over the mechanical performance of plate-like components, which makes the model widely applicable in the design and optimization of Micro-Electro-Mechanical-Systems (MEMS).