Static And Dynamic Behavior Analysis Of Microscale Structures

With the advancement of the micromachining technology, a new scientific and technological undertaking, micro-electro-mechanical systems (MEMS), has been developing and has a very broad application prospect in various fields, such as the information communication, aerospace, biomedical, and military. In various micro devices and micro machinery, the characteristic sizes of their structures are typically on the order of microns or even nanometers. In this scale, the size effect can not be ignored in the study on mechanical behavior of micro-structures. Therefore, the research on MEMS raises the demand of establishing theoretical models considering size effect to predict accurately the various mechanical behaviors of microscale structures.By using the modified couple stress theory or strain gradient theory, a set of theoretical models are established to analyze the static and dynamic behaviors (static deformation, vibration, buckling and so on) in this paper. In order to capture the size effect, the models based on the modified couple stress and strain gradient theories introduce one and three material length scale parameters dependent on the micro-structure respectively. By the analysis on the static and dynamic behavior of three microscale structures (microbeams, microplates and microscale pipes conveying fluid), this paper investigates the size effect on microscale structures and the parameters influencing the intensity of size effect. The main results are shown as follows:1. Based on the modified couple stress theory, the non-classical Bernoulli-Euler and Timoshenko beam models are established to analyze the dynamic characteristics and stability of microscale cantilevered pipes conveying fluid. The numerical examples show that the natural frequencies and damping properties are size-dependent. The results also show that the critical flow velocities predicted by the non-classical beam models are generally higher than those predicted by the classical beam models, indicating that the stability of microscale pipes is enhanced.2. By utilizing the strain gradient theory, another dynamic model of micropipes conveying fluid is presented to capture the size effect. From the comparison between results of the present model and the model based on the modified couple stress theory, it is found that micropipes conveying fluid take larger natural frequencies and higher critical flow velocities, and thus the size effect is stronger. This is because the former model has introduced the additional dilatation gradient tensor and the deviatoric stretch gradient tensor in addition to the rotation gradient tensor.3. On the bases of the modified couple stress theory, a theoretical model is developed for analyzing the vibration characteristic of microscale plates. Taking two different boundary value problems of rectangular micro-plates for example, the size effect on natural frequencies of microscale plates is investigated.4. A nonlinear model of microbeams is established using the modified couple stress theory and the static bending, postbuckling and free vibration of microbeams is analyzed. The results show that the static deflections of a bending beam subjected to transverse force, the critical buckling loads and buckled configurations of an axially loaded beam, and the nonlinear frequencies of a beam with initial lateral displacement are size-dependent.5. Applying the modified couple stress theory, a non-classical beam model accounting for the electromechanical coupling is further presented and the pull-in characteristic of electrostatically actuated microbeams is investigated. It is found that the size effect on electrostatically actuated microbeams exhibits smaller deflection and larger pull-in voltage. Furthermore, the intensity of size effect predicted by this model is independent on the length-width ratio.The all above researches explore that the characteristic size is an important parameter reflecting the intensity of size effect. The size effect becomes weaker with the increase of the characteristic size. When the characteristic size of a microscale structure (outside diameter of a pipe, plate thickness or beam thickness) becomes comparable to the material length scale parameter, the microstructure displays strong size effect. While the characteristic size is far greater than the material length scale parameter, the size effect is almost diminishing.The theoretical models established in this paper can be utilized to evaluate quantitatively the mechanical properties of MEMS structures, such as the strength, stiffness and stability. Moreover, the results can provide theoretical support for the design of MEMS devices.