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微观下材料内部结构将极大地影响材料的力学性能,对微纳米器件中典型的微平板结构尺度效应进行研究具有十分重要的意义.论文基于Cosserat理论推导出了微平板自由振动的微分方程,并根据四边简支边界条件假设振型函数,给出了固有频率的计算公式,对不同尺寸微平板固有频率的尺度效应进行了仿真分析.结果表明,考虑了尺度效应的微平板自由振动固有频率要高于经典理论中的固有频率.当特征长度与微平板厚度大小相当时,微平板固有频率表现出明显的尺度效应,并随着特征长度的增加而增大.同时,自由振动的尺度效应将随着微平板厚度的减小而逐渐增强,振动模态及长宽比不影响尺度效应.论文的研究将为微结构与系统的应用提供一定的理论基础.
The microstructure of the material will greatly affect the mechanical properties of the material, and it is very important to study the typical micro-plate structure scale effect in the micro-nano devices.According to the Cosserat theory, the differential equation of the free vibration of the micro-plate is derived According to the assumption of the mode shape function of simply supported boundary conditions on four sides, the calculation formula of natural frequency is given, and the scale effect of the micro-plate natural frequencies with different sizes is simulated and analyzed.The results show that the free-vibration natural frequency Which is higher than the natural frequency in the classical theory.When the feature length is equivalent to the thickness of the microplate, the natural frequency of the microplate exhibits a significant scale effect and increases with the increase of the feature length. Meanwhile, the scale effect of free vibration With the decrease of micro-plate thickness, the vibration mode and the aspect ratio do not affect the scale effect.The thesis will provide a theoretical basis for the application of microstructure and system.