By use of the concept of impedance, this paper establishes a random energy harvester output model of double-ended fixed beam piezoelectric energy harvester under random White Gaussian noise excitation, which is based on the discussion of the output characteristics influenced by changing vibration beam shape and piezoelectric sheet length under random excitation, while improving piezoelectric structure of double-ended fixed beam piezoelectric energy harvester. It also deduces the output voltage, current and power of energy harvester with Fokker–Planck equation, which are verified by Monte Carlo simulation and experimental testing. It can be found that improving vibration beam shape can reduce resonant frequency and increase average output power of the system. The optimal value of piezoelectric sheet length can be different corresponding to different structures, which proves that double-ended fixed beam piezoelectric energy harvester under random White Gaussian noise excitation can achieve maximum output with optimal piezoelectric sheet length. In addition, in order to further improve the output performance of piezoelectric energy harvester under random excitation, it is necessary to increase the acceleration spectral density under random excitation and set an optimal value of the piezoelectric loading resistance, which is more suitable for energy harvester applied under random low-frequency environment.

利用阻抗的概念，建立了在随机白高斯噪声激励下双端固定梁压电能量采集器的随机能量采集器输出模型，该模型在讨论振动梁形状和振动频率变化对输出特性的影响的基础上。压电片长度在随机激励下，同时改善了双端固定梁压电能量采集器的压电结构。它还通过Fokker-Planck方程推导出能量采集器的输出电压，电流和功率，并通过蒙特卡洛仿真和实验测试对其进行了验证。可以发现，改善振动束的形状可以降低谐振频率并增加系统的平均输出功率。压电片长度的最佳值可以根据不同的结构而有所不同，这证明在随机白高斯噪声激励下的双端固定梁压电能量采集器可以以最佳的压电片长度实现最大输出。另外，为了进一步提高压电激励器在随机激励下的输出性能，有必要增加随机激励下的加速度谱密度，并设置压电负载电阻的最佳值，这更适合应用在能量采集器上。在随机低频环境下。