基于Cosserat理论的微梁振动特性的尺度效应

SIZE EFFECT ON THE DYNAMIC CHARACTERISTIC OF A MICRO BEAM BASED ON COSSERAT THEORY

不少微观实验已经证实,微尺度领域材料的力学性能存在尺度效应。采用偶应力理论(又称Cosserat理论)研究微梁振动特性(主要是固有频率)的尺度效应。文中首先对偶应力理论进行简介,然后采用Hamilton变分原理推导基于Cosserat理论的微梁无阻尼自由振动的微分方程,分析微梁固有频率对微尺度的依赖性。结果表明,当微梁的厚度减小到可以和材料的本征长度相比时,微梁的固有频率将显著增大。

Many micro experiments have shown that the mechanical properties of materials at micro scale are size dependent. The vibration characteristic （ mainly the resonant frequency） of a micro beam has been analyzed theoretically using couple stress theory （ Cosserat theory）. Based on the couple stress elasticity theory the freely vibration equation of a micro beam in the absence of damping is derived using the Hamilton principle. The dependence of the resonant frequency of a micro beam on its size is analyzed, and the results show that the resonant frequency will increase markedly when the thickness of the beam decreases to a value which is comparable to the material length scale parameter.