Closed-form unified solutions using the distributed transfer functions (DTFs) method are presented for the first time for the static short/open-circuit sensing and voltage/charge actuation of moderately thick beam cantilevers with co-localized surface-bonded piezoelectric patches. For this purpose, the smart beam is divided into three segments, of which the clamp and free sides parts are elastic, while the middle one is made of an elastic core sandwiched between two electroded piezoelectric patches. The latter can be different in material properties and thickness but should have the same length, and their widths can be different from the host elastic beam. The theoretical formulation is based on Timoshenko’s first-order shear deformation theory for the kinematics and piezoelectric constitutive equations and the principle of virtual works for the variational equations. The latter integrate explicitly the physical equipotential constraints on the patches electrodes. The balance equations and boundary conditions are derived for the three segments independently and then connected at their interfaces by the equilibrium equations and continuity conditions. The unified static solutions for the resulting four problems are derived analytically in closed form using the DTF approach. These are validated against only open literature benchmarks having tabulated results or analytical formulas in order to avoid curves induced inherent additional deviations. Very good correlations were obtained in comparison with the found reference two-dimensional (2D) plane strain/stress analytical and 2D plane strain/stress and three-dimensional finite element results.

首次提出了使用分布式传递函数（DTF）方法的闭合形式统一解决方案，用于中等厚度的带有悬臂梁的压电悬臂梁的静态短路/开路传感和电压/电荷致动。为此，将智能梁分为三段，其中夹具和自由侧部分具有弹性，而中间部分由夹在两个电极压电片之间的弹性芯制成。后者的材料特性和厚度可以不同，但​​应具有相同的长度，并且它们的宽度可以与主体弹性梁不同。理论公式是基于蒂莫申科关于运动学和压电本构方程的一阶剪切变形理论以及关于变分方程的虚功原理。后者在贴片电极上明确集成了物理等电位约束。分别为这三个线段导出平衡方程和边界条件，然后通过平衡方程和连续性条件在它们的界面处进行连接。使用DTF方法以封闭形式分析得出针对所产生的四个问题的统一静态解决方案。仅针对具有制表结果或分析公式的开放文献基准进行了验证，以避免曲线引起固有的额外偏差。