带剪切型压电激励器的板的高阶剪切变形理论

利用压电材料固有的正，逆压电效应可以对结构变形和振动进行控制。与外加电场与极化方向平行于板厚度的压电材料的拉伸作动机制相比，外加电场与极化方向垂直的压电材料的剪切作动机制可以在作动器内产生较小的应力，从而降低作动器边界产生分层破坏的危险。本文对于压电材料的剪切作动机制进行研究，应用三阶剪切变形理论建立带剪切型压电激励器的智能层合板模型。采用哈密顿原理导出带剪切型压电激励器的层合板的控制方程。采用空间法得到了各种边界条件组合条件下板的解析解。数值算例对一三层板采用高阶和一阶剪切变形理论进行计算，结果表明两种理论所得的变形曲线很相似。但对于厚度剪切型激励器而言，由于激励器是引起板的剪切变形，而高阶剪切变形理论比一阶剪切变形理论能更好地反映结构的剪切应变能，因此高阶剪切变形理论可以提供板变形的更为精确的解。因此，对于厚度剪切型激励器，剪切变形理论的选取对于板变形结果的好坏有重要的作用。

Higher Order Shear Deformation Theory for Smart Plates with Thickness-shear Piezoelectric Actuators

Due to the intrinsic direct and converse piezoelectric effects, piezoelectric materials have been widely used in engineering for the active shape or vibration control of structures. Compared with the extension actuation mechanism of piezoelectric materials when electric field and poling direction are along the piezoelectric layer thickness, the shear actuation mechanism of piezoelectric materials when applied e-lectric field and poling direction are perpendicular can induce lower stresses in actuators, which can reduce the possibility of debonding in actuators boundaries. The shear actuation mechanism of piezoelectric materials was researched in this paper and three-order shear deformation theory was used to model smart laminated plates with shear mode piezoelectric actuators. The governing equations were derived for laminated plates incorporating shear-mode piezoelectric actuators from Hamilton's principle. Analytical solutions for plates with various boundary conditions were developed using the state space approach. Using three-order and first-order shear deformation theory to calculate a three-layer laminated plate, the numerical results show that, the pattern of the curves is similar for the two theories. Yet for thickness shear actuators, due to the shear deformation dominates the plate deflection for shear actuation mechanism, the higher order shear theory can provide more accurate evaluation of the shear strain energy of the plate than the first-order one, higher order shear deformation theory can provide more accurate evaluation of the de- formation of the plate. Therefore, shear deformation theories play an important role in smart composites with thickness shear actuators.