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NONLINEAR STUDY OF LARGE DEFLECTION OF SIMPLY SUPPORTED PIEZOELECTRIC LAYERED-PLATE UNDER INITIAL TENSION

机译:在初始张力下简单地支撑压电层板的大偏转的非线性研究

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The nonlinear problem of large deflection of a simply supported piezoelectric layered plate under initial tension is studied. The approach follows von Karman plate theory for large deflection for a symmetrically layered isotropic case including a piezoelectric layer. The thus derived nonlinear governing equations for the lateral slope and radial force resultant are solved using a numerical finite difference method with the aid of an iteration scheme, by taking the associated linear analytical solution as an initial guess. The case of a nearly monolithic plate under a very low applied voltage across the piezoelectric layer was implemented, first. The results for are found to correlate well with available solutions for a single-layered case under pure mechanical loading and thus the present approach is validated. For three layered symmetric plates made of typical silicon based materials, various initial tension and lateral pressure are considered, and different applied voltages up to a moderate magnitude are implemented. No edge effect was observed, in contrast to the cases of clamped plates in literature. In additions, varying the layer moduli seems to have an insignificant effect upon the structural responses of the layered plate. On the other hand, the piezoelectric effect tends to be apparent only in a low pretension condition. For a relatively large pretension, the effect of initial tension becomes dominant, yielding nearly unique solutions for the structural responses, regardless of the magnitudes of the applied voltage and the lateral pressure.
机译:研究了在初始张力下简单地支撑的压电层板的大偏转的非线性问题。该方法遵循von Karman板理论对对称层状各向同性壳体的大偏转,包括压电层。通过将相关联的线性分析解决方案作为初始猜测,使用数值有限差分法通过将相关的线性分析解决方案借助于迭代方案来求解用于横向斜坡和径向力和径向力的非线性控制。首先实施在压电层两端的非常低施加电压下几乎单片板的情况。发现结果对于在纯机械负载下的单层壳体的可用溶液中的相关溶液相关,因此验证了本方法。对于由典型的硅基材料制成的三个分层对称板,考虑了各种初始张力和横向压力,并且实现了不同的施加电压直至适度的幅度。与文献中夹紧板的情况相比,没有观察到边缘效应。另外,改变层模量似乎具有对层状板的结构响应的微不足道的影响。另一方面,压电效应趋于在低预留条件下显而易见。对于相对较大的预张力,初始张力的效果变得优势,不管施加的电压和横向压力的大小如何,产生近似独特的结构响应的解决方案。

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