层合板中压电作动器最优厚度和嵌入位置研究

研究了压电结构中压电片厚度和嵌入深度的优化问题。首先给出了压电层合板的高阶耦合分析模型;然后以不受约束的含压电铺层复合材料板为代表,在压电层厚度方向施加电场时板自由变形,假设板任意微元横截面上内力为零,以其弯(扭)曲曲率最大为优化目标,建立了求解压电片最优厚度和嵌入深度问题的约束优化模型。最后分别以各向同性板中嵌入各项同性压电片和复合材料板中嵌入各向异性压电片为例进行了分析,绘出了目标函数的三维曲面图及等高线图,结果表明压电片的作动效能与其厚度和嵌入位置密切相关,而最优厚度和嵌入位置是由压电片和基体的材料特性决定的。

THE OPTIMAL THICKNESS AND EMBEDDING POSITION OF PIEZOELECTRIC ACTUATOR IN COMPOSITE LAMINATES

The optimization of thickness and embedding position of a piezoelectric actuator in composite laminates is studied. First, a high order coupled model for piezoelectric laminates is presented. Then, a general laminate with a piezoelectric layer is selected as a typical representation, which has no constrains and can deform freely when an electric field is applied through the thickness of the piezoelectric layer. With that assumption that the internal forces on the cross sections of any plate element are zero, a constrained optimization problem is formulated by maximizing the bending or twisting curvature of the laminate. Finally, an isotropic plate with isotropic actuator and a composite plate with anisotropic actuator are analyzed. The three dimensional(3D) curved surface and contour graphs of the object function are given to visualize the results, which show that the effectiveness of the piezoelectric actuator is sensibly relative to its thickness and embedding position, and the optimal thicknenss and position are determined by the material properties of the actuator and the laminate.