Research On Coupled Electro-mechanical Theories And Numerical Methods For MEMS/NEMS

Micro-electro-mechanical system(MEMS) is a kind of micron scale electromechanical device highly integrated by "mechanical" and "circuit", which has small size, low power consumption, fast response and many other advantages. And it is widely used in many fields, such as aerospace, biomedical, automotive industry and daily necessities. In recent years, with the continuous and rapid development of micro/nano science and technology, nano-electro-mechanical systems(NEMS) with smaller characteristic scale has attracted the attention of many scholars at home and abroad. As the characteristic scale is smaller for NEMS, its sensitivity to tiny force and displacement is higher than MEMS.The mechanical properties of micro/nano structures are different from macro. They have been found from experiments that mechanical properties exhibit size effect for the specimens of different materials, such as metal materials, composite materials, polymer materials and semiconductor materials. As the structures size constantly decrease, and materials mechanics properties enhance unceasingly, the phenomenon of stiffness increases, that is size effect phenomenon. Compared to MEMS, size effect is more apparent in NEMS, so that NEMS has more high resonance frequency and can be applied to the production of more sophisticated sensitive electromechanical devices. However, the classical theory can’t explain the size effect phenomenon.Many theories have been developed and used to explain the phenomenon, such as surface effect theory, couple stress theory, nonlocal theory, gradient theory and strain gradient elasticity theory. But discussion results show that the strain gradient elasticity theory is one of the most suitable theories to explain and predict size effect in MEMS/NEMS. Among them, surface effect theory is widely used to study size effect in submicron. Thought, in the theory, the influence of surface effect is considered, and the internal characteristics of structure are ignored. Nonlocal theory is applicable to study the size effect showing structure soften. The couple stress theory, for example modified couple stress theory, considers the effect of rotation gradient tensors on the strain density, but ignores stretch gradient tensors. Although calculation is simplified by it, prediction accuracy is reduced. Gradient elasticity theory is obtained based on couple stress theory. It has the advantages of simple calculation, but prediction accuracy is also very low. By contrast, strain gradient elasticity theory combines the advantages and disadvantages of the former, based on couple stress theory, considering the contribution of both rotation gradient tensors and stretch gradient tensors on the strain density. Although its computation load is increased, the accuracy can be guaranteed.However, based on the strain gradient elasticity theory, the governing differential equation of NEMS contains six order differential item. And there is a saddle node bifurcation on solution branch. It is difficult to solve the kind of equation by local continuation methods. So, based on generalized differential quadrature method, the discrete and reduced-order governing equations was obtained, and combined with pesudo-arclength algorithm, iteration can smoothly pass inflection points and the complete solutions were calculated.In addition, the influence of micro force cannot be ignored for the study of NEMS, such as the Casimir force and Van der Waals force. Many scholars studied the influence of them in micro/nano structure, and gave a lot of opinions on the relationship between them. But so far there is still no accurate conclusion. In this paper, based on the strain gradient elasticity theory and Hamilton’s principle, the influence of them for the size effect and pull-in instability of electrostatically actuated NEMS is studied, respectively. The results show that Casimir force can reduce the external applied voltage. Moreover, there exists a minimum gap between two electrodes and a maximum beam length (detachment length) where pull-in instability occurs without voltage applied. In addition, comparisons are made between the results predicted from the present model with those of experimental data in literatures. Very good agreement is observed, which proves the new model is robust for describing the behavior of size-dependent pull-in instability for NEMS devices. Van der Waals force can also be reduced the external applied voltage, but compared with Casimir force, its effect is not obvious.