主动板的正交性条件

ORTHOGONALITY CONDITIONS FOR ACTIVE PLATE

给出主动结构的伴随主动结构定义,将由离散主动结构的基本方程推导出来的互易定理推广应用于连续主动结构,具体研究分布作动和分布测量的主动板.通过引入作动和测量的位置函数,给出线性控制方程和测量方程,推导出用主动板振型和伴随主动板振型表示的模态正交性条件,并用数值模拟实例加以解释.应用这些正交性条件,可将主动板的运动微分方程解耦.

The adjoint structure of the active structure is denned, the reciprocity theorem, which is derived from the basic equations of the discrete active structure, is extended from the discrete active structures to the continuous active structures. The active plate with distributed sensor and actuator is studied. The control equation and the measurement equation are presented by using the functions locating actuation and measurement, respectively, and the orthogonality conditions are derived with the modal shapes of the active plate and its adjoint active plate. As a numerical example a rectangular plate is evaluated to give the notes about modes and orthogonality conditions of the active plate. The orthogonality conditions can be used to decouple the motion differential equations of the active plate.