| Summary: | 碩士 === 中華大學 === 機械工程學系 === 107 === Problem of nonlinear large-deflection of a simply supported and symmetrically layered circular piezoelectric plate with an elastic boss under pre-tension due to uniform lateral load is studied. Von-Karman plate theory for large deflection is employed and extended to a symmetrically layered plate including a piezoelectric layer with an elastic boss, to derive the nonlinear governing equation for large deflection. The small deflection condition is considered first to study a simplified linear problem. The associated analytical solution is developed following recurrence relations of special functions, and the limited cases of pure membrane and pure plate are studied. For the nonlinear problem, on the other hand, numerical solution is sought using a finite difference method incorporated with an iteration scheme, by taking the simplified linear solution as the initial guess. The developed approach is implemented with typical silicon-based semi-conducting materials. To verify the proposed method, however, a nearly monolithic plate with a shallow and wide boss under a very low applied voltage will be considered, first. The results are checked against those available in literature. In addition, the numerical examples also include the cases of different thickness ratios between center boss and annular plate, various radial sizes of the elastic boss, different applied voltages across the piezoelectric layer and a wide range of lateral loads and pre-tensions. The objective is to explore all kinds of geometric responses including the center deflection and curvature, lateral deflection, slope and the mechanical sensitivity (dimensionless maximum radial stress) and curvature as well as the transition behavior of the bossed piezoelectric plates. The influence of a variety of physical parameters such as the size of the elastic boss (including the thickness ratio and the radial size), the applied voltage, lateral loads and pre-tension will be intensively investigated for a thorough parametric study.
For a nearly monolithic plate with a shallow and wide boss under a low applied voltage, the results correlate well with those available for a single-layer plate with pure mechanical load in literature. Thus, the presented approach is checked. In addition, the numerical results show that piezoelectric effect may arise at a low mechanical loading condition and becomes more apparent when the center boss is widened and the applied voltage is increased. It will gradually diminish when the mechanical load is raised, however. Under a low initial tension condition, specifically, the influence of piezoelectric effect will be more apparent when a shallow but wide elastic boss is considered. Yet, thickening the center boss will moderate the influence of the piezoelectric effect but induces a more serious interface effect between the center boss and the annular plate.
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