含金属芯压电纤维的纵向振动研究

Longitudinal vibration of a metal core piezoelectric fiber

建立了悬臂杆结构含金属芯压电纤维的纵向振动模型和动态测试模型。基于第一类压电方程，推导了外加简谐激励电压时，悬臂杆结构含金属芯压电纤维的等效纵向外力；基于纵向振动理论，推导出纵向振动模型；并由电位移，得到表面电荷、电流、导纳，建立了动态测试模型，通过测量共振频率fr、反共振频率fa和低频电容CLF，计算出压电纤维的几个主要参数：弹性柔顺系数s11E、机电耦合系数k31、介电常数ε33和压电常数d31。详细叙述了纵向振动模型和动态测试模型的建立过程，并给出了具体的测试方法，提供了一个实际试样的测试结果。测试结果表明，根据纵向振动模型所建立的动态测试方法可以快速、准确地测量含金属芯压电纤维的主要参数。

A metal core piezoelectric fiber （MPF） is one of the new type piezoelectric devices for sensors and actuators. When an external harmonically varying voltage is applied on electrodes of a cantilevered MPF, it will cause longitudinal vibration. A force appears due to the strain caused by the electric field in the piezoelectric elements. Using the vibration theory of a cantilevered bar, the longitudinal vibration equations of the MPF were derived. The electric displacement was deduced by using the constitutive equations of the piezoelectric element. And the electric charges on the electrodes were given by integrating electric displacement. The total current flowing through the electrode surface and the admittance of the MPF was derived from the electric charges. Using the resonance frequency, the elastic coefficient at a constant electric field S11E was given from the admittance. And using the antiresonance frequency, the electromechanical r coupling factor R31 was obtained. The dielectric permittivity under a constant stress ε33T was extracted with the lower capacitance. Using above parameters, the piezoelectric coefficients d31 was calculated. One experiment was performed. The theoretical simulations and experimental results showed that this method is effective to measure the properties of MPF.