Robust Optimal Control Applied to a Composite Laminated Beam

ABSTRACT: This paper proposes an active vibration control technique, which is based on linear matrix inequalities, that is applied to a piezoelectric actuator bonded to a composite structure, forming a so-called smart composite structure. Serendipity-type finite element, based on first-order shear deformation theory with rectangular shape, eight nodes, five mechanical degrees of freedom (DOF) per node and eight electrical DOF per piezoelectric layer, is established for the composite structural model. Additionally, a mixed theory that uses a single equivalent layer for the discretization of the mechanical displacement field and a layerwise representation of the electrical field is adopted. Temperature effects are neglected. Simulation results illustrate the effectiveness of the proposed vibration control methodology for composite structures.

摘要：本文提出一种基于线性矩阵不等式（Linear Matrix Inequalities）的主动振动控制技术，将其应用于粘接在复合材料结构上的压电驱动器（Piezoelectric Actuator），从而构建所谓的智能复合材料结构。针对该复合材料结构模型，本文建立了基于一阶剪切变形理论（First-order Shear Deformation Theory）的矩形serendipity型有限元（Serendipity-type Finite Element），该单元为八节点形式，每个节点具备5个力学自由度（Degrees of Freedom，DOF），每个压电层则包含8个电气自由度。此外，本文采用混合理论框架：对力学位移场采用单等效层进行离散化处理，而电场则采用分层表征形式。本研究未考虑温度效应的影响。仿真结果验证了所提主动振动控制方法在复合材料结构中的有效性。