为了根据环境振动和电学负载的特点对悬臂梁式微型压电振动能采集器进行优化,本文考虑质量块质心与悬臂梁末端的位置差异,建立了在基础激励作用下采集器的运动微分方程和边界条件.通过引入常数,建立了对单压电层、双压电层并联和双压电层串联的3个悬臂梁式微型压电振动能采集器均适用的耦合电路方程,得到了采集器固有频率和振型的表达式,推导了简谐基础激励和任意基础激励作用下的输出电压表达式.实验结果显示,对于3个振动能采集器样机而言,以上固有频率和输出电压表达式的相对误差分别小于10％和20％,表明该模型基本满足微型压电振动能采集器优化设计的要求.%To optimize cantilevered piezoelectric vibration energy harvesters according to the characters of the environmental vibration and the electrical loads, a differential equation of motion and the boundary conditions for a cantilevered piezoelectric vibration energy harvester were established in consideration of the position difference between the center of proof mass and the free end of cantilever. A uniform coupled circuit equation applicable to the harvesters with one piezoelectric layer, two series connected piezoelectric layers and two parallel connected piezoelectric layers was developed by introducing several constants, and the expressions of the natural frequencies and corresponding mode shapes were obtained. Furthermore, the closed-form expressions of the output voltages were derived for harmonic base accelerometer excitations and arbitrary base accelerometer excitations. Experimental results indicate that the relative errors of the natural frequency expression and the output voltage expression are smaller than 10% and 20% respectively for three harvester prototypes, which shows that the model satisfies the requirements of optimizing harvesters.
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