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Deflection control of laminated composite beams with piezoceramic layers -- closed form solutions

机译：具有压电陶瓷层的层合复合梁的挠度控制-封闭形式的解决方案

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摘要

The three coupled equations of motion of a general non-symmetric piezolaminated composite beam subjected to axial and lateral tractions and its corresponding boundary conditions are derived using a variational approach. The displacement field is based on a first-order shear deformation theory. The static shape control is performed using either continuous piezoceramic layers or patches embedded or bonded to the surface of the beam structure. Closed form solutions for the bending angle and the axial lateral displacements along the beam are presented for various configurations of lay-up, boundary conditions and mechan- ical loading. A closed-loop approach is then applied to control the lateral deflection of an axially loaded piezolaminated beam based on the measurement of the average bending slope. The method yields good and consistent results.
机译：使用变分方法推导了一般非对称压电复合梁在轴向和横向牵引下的三个运动方程及其相应的边界条件。位移场基于一阶剪切变形理论。静态形状控制使用嵌入或结合到梁结构表面的连续压电陶瓷层或贴片来执行。给出了针对上叠，边界条件和机械载荷的各种配置的弯曲角度和沿梁的轴向横向位移的封闭形式解决方案。然后，基于平均弯曲斜率的测量，采用闭环方法来控制轴向加载的压电化梁的横向偏转。该方法产生了良好且一致的结果。

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