The Study And Application On Size Effect Of Micro-Structures

With the development of technology, MEMS (Micro-Electro-Mechanical-Systems: MEMS), with its small size, low power, conveniently controlling features, has been widely used in the field of aerospace, machinery, electronics, medical equipment and so no. According to the shape of the MEMS devices, it can be modeled as some simple structures, such as micro-beam or micro-plate, which is widely used typical structure in the MEMS field. Also, because the geometric dimensions are in micron or submicron, the mechanical or other properties are very different from those of the macroscopic devices.From the experiments in which the specimens are made of metallic materials, composite materials, polymer materials and silicone materials, it has been found that the mechanical properties exhibit size effect in micron and submicron. Such size effect, however, cannot be explained with the classical continuum theory. Therefore, it is essential to set up a new model that can perfectly explain and predict the size effect.Thought many theories have been developed to attempt to explain the size effect, the strain gradient elasticity theory is one of the best to explain such size effect. It contains three strain gradient tensors (the symmetric rotation gradient tensor, dilatation gradient tensor and the deviatoric stretch gradient tensor) on the strain density, and there are three material length scale parameters in the governing equation which enable the theory can predict the size effect. The governing equation and corresponding boundary conditions, which are more complicated than those in the classical model, can reduce to the corresponding ones if material length scale parameters are ignored. From this point of view, the strain gradient elasticity theory is an extended theory from the classical theory, that is a generalized continuum theory.In this paper, with electrostatically actuated MEMS as application background, based on the strain gradient elasticity theory and the Hamilton's principle, the micro scale models are developed for the micro-beam and micro-plate. The size-dependent mechanical properties are studied using the new models. Consequently, these new models are applied to the electrostatically actuated MEMS devices; the mechanical-electric coupled models are then developed. The size-dependent mechanical-electric coupled properties are studied based on the models, which provide a theoretical basis for the design of the MEMS devices. Based on strain gradient elasticity theory, a new size-dependent Timoshenko beam model is proposed. The model, containing three material length scale parameters, can predict the size effect for micro scale structures. The new boundary conditions are combined by the classical ones and the higher-order ones. This model can degenerate into the modified couple stress Timoshenko beam model or even the classical Timoshenko beam model if two or all material length scale parameters are taken to be zero respectively. The new model is applied to a simply supported Timoshenko beam: the size effect of the static deformation and rotation, natural frequency and Poisson's effect are studied respectively. The results are compared with those predicted by the modified couple stress model and by the classical model. The results show that there is much difference between three models when the characteristic size is comparable with material length scale parameters; however the difference decreases or even disappear with characteristic size increasing. The new model exhibits a "extreme point" phenomenon, which is different from what the classical model does.Based on strain gradient elasticity theory and the principle of minimum potential, the size-dependent Kirchhoff plate model is developed. The model can predict the size-dependent properties with three material length scale parameters included. As a validation, the boundary conditions of simply supported plate are derived, and then the static deformation, critical load and natural frequency are studied. The results of the simply supported plate are compared with those of modified couple stress model and classical model. It is shown that the normalized deformation, normalized critical load and normalized frequency are constants for the classical model, while those of the new model varies nonlinearly with different size devices.A size-dependent model of electrostatically actuated microbeam-based MEMS is developed based on strain gradient elasticity theory. The effect of material length scale parameters on the pull-in voltage is studied, and the results are compared with those of classical model. There is much difference between results of two models when the characteristic size (beam thickness) is comparable with material length scale parameters; however the difference decreases with characteristic size increasing. The model is applied to predict the reported experimental results, good agreement is achieved. The model can be used as a fundamental theory for the design and experimental testing of MEMS devices. Since some MEMS devices cannot be modeled as one dimensional beam, the size-dependent two dimensional plate (rectangular and circular plate) models are then developed based on strain gradient elasticity theory. The effect of material length scale parameters, Poisson's ratio, fringing field on the pull-in voltage are studied. The results of the model are compared with those of the classical plate model. The results show that the size effect can be ignored if the characteristic size (plate thickness) of the plate is more than 15 times the material length scale parameters; while the size effect is significant if characteristic size is comparable with material length scale parameters. The new model can be regarded as the extent of the classical model.