篇名 | Analytical Solution for Large Deflection of Un-Symmetrically Layered Circular Plates Due to Lateral Load |
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卷期 | 39:4 |
作者 | Chen, Chun-fu |
頁次 | 239-249 |
關鍵字 | Large deflection 、 Un-symmetric layered plate 、 Von Karman plate theory 、 EI |
出刊日期 | 200712 |
An analytical solution for the linear problem of large deflection of a
clamped and un-symmetrically layered isotropic circular plate due to
uniform lateral pressure is presented. Governing equations based on Von
Karman plate theory for the case of an un-symmetrically layered isotropic
plate are developed first followed by neglecting the arising nonlinear terms.The coupled differential equations for the non-dimensional slope and radial force resultant of the plate are found to have polynomial-type close form solutions involving the coupling stiffness of the layered plate due to un-symmetry. For the special case of a slightly un-symmetric condition,the solution reduces to that for an isotropic single layered problem available in literature [2]. Two-layered un-symmetric isotropic plates made of typical silicon-based substrate and diaphragm materials are implemented with both regular and irregular layer thickness. The radial variations of geometrical responses and radial stresses on either sides of the plate representing the mechanical sensitivity of a sensing device are evaluated.The influence due to the deviation of layer moduli and layer thickness upon various structural responses is illustrated. For a regular two-layered plate,a deviation in Young’s moduli of the layers is found to have an apparent influence upon the geometrical responses, the out-of-plane stresses at the interface, and the mechanical sensitivity on the loading surface. For an irregular two layered plate, a significant influence due to the ratio between the layer thicknesses upon the out-of-plane shear stress is observed.