含金属芯压电陶瓷纤维的本构方程(英文)

CONSTITUTIVE EQUATIONS OF METAL-CORE PIEZOELECTRIC FIBERS

含金属芯压电陶瓷纤维是一种新型的压电器件。为了研究压电纤维的压电和机械性能,本文推导了其本构方程。该方程用于描述压电纤维在受到外力和电压作用时的响应。在悬臂杆式压电纤维的电极上施加电压,并在自由端施加力,计算其在热平衡状态下的内能密度,并在整根纤维上积分,得到其整体能量。结果表明,自由端施加力作用时的广义位移为伸长量δ,电压的广义位移为电荷量Q。所建立的本构方程中的激励参量是作用力和施加的电压,而响应参量是自由端的伸长量和电极上的电荷量,两者之间由一个2×2的压电矩阵相联系。

Metal-core piezoelectric fibers （MPFs） are one of the new type piezoelectric devices. To investigate the piezoelectricity and the mechanical properties of the piezoelectric fibers, the constitutive equations are established. It can describe the response of piezoelectric fibers subject to an axial force and an external voltage. A cantilever bar subject to a tip axial force and an external voltage on the electrodes is considered. The internal energy density in thermodynamic equilibrium is obtained. The total internal energy is calculated by integrating over the entire volume of the bar. The generalized displacement of the tip axial force is the tip elongation δ, and the generalized displacement of the voltage is the electrical charge Q on the electrodes. In the established constitutive equations, the excitation （input） parameters are the axial force and the external voltage, the response （output） parameters are the tip elongation and the electric charge. And the response parameters are related to the excitation parameters by a 2× 2 piezoelectric matrix. Finally, two experiments using MPF as a sensor or an actuator are performed to verify the constitutive equations. And experimental results are compared with analytical ones.