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A mixed model for composite beams with piezoelectric actuators and sensors

机译：带有压电致动器和传感器的复合梁的混合模型

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摘要

A theoretical formulation to model composite smart structures in which the piezoelectric actuators and sensors are treated as constituent parts of the entire structural system is presented here. The mathematical model is based on a high order displacement field coupled with a layerwise linear electric potential. This model is developed for a composite beam structure using Hamilton's variational principle and is facilitated by the finite element (FE) formulation. The generic element implemented in the FE analysis is a two-noded Hermitian - 2(n + 1) layerwise noded element for an n-layered beam. The variational principle led to a derivation that could include dynamic analysis but the present work will only focus on the static beam structure. This formulation in general will enable the modeling of vibration and shape control applications. Comparison of numerical results from this formulation with previous works, including three configurations - non-piezoelectric, actuator and sensor configurations, showed a high to a reasonable degree of correlation. The effects of varying actuator locations and orientations on the deflection and curvature of the beam were also studied. Cantilever beam materials studied: aluminum honeycomb core sandwiched between two aluminum face sheets.
机译：本文介绍了对复合智能结构进行建模的理论公式，其中压电致动器和传感器被视为整个结构系统的组成部分。该数学模型基于与分层线性电势耦合的高阶位移场。此模型是使用汉密尔顿变分原理为复合梁结构开发的，并且通过有限元（FE）公式简化了该模型。在有限元分析中实现的通用元素是用于n层梁的两节点Hermitian-2（n +1）分层节点元素。变分原理导致了可以包括动态分析的推导，但是目前的工作仅集中在静态梁结构上。一般而言，该公式将能够对振动和形状控制应用程序进行建模。该公式的数值结果与以前的工作进行了比较，包括三种配置-非压电，执行器和传感器配置，显示出很高的相关度。还研究了致动器位置和方向的变化对梁的挠度和曲率的影响。研究的悬臂梁材料：铝蜂窝芯夹在两个铝面板之间。

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