We consider, from a mathematical perspective, the power generated by a contact-mode triboelectric nanogenerator, an energy harvesting device that has been thoroughly studied recently. We encapsulate the behaviour of the device in a differential equation, which although linear and of first order, has periodic coefficients, leading to some interesting mathematical problems. In studying these, we derive approximate forms for the mean power generated and the current waveforms, and describe a procedure for computing the Fourier coefficients for the current, enabling us to compute the power accurately and show how the power is distributed over the harmonics. Comparisons with numerics validate our analysis.

从数学的角度来看，我们认为接触式摩擦电纳米发电机是一种能量收集装置，最近已经对其进行了深入研究，它所产生的功率。我们将设备的行为封装在一个微分方程中，该方程虽然是线性的并且是一阶的，但具有周期性系数，从而导致一些有趣的数学问题。在研究这些过程中，我们推导了生成的平均功率和电流波形的近似形式，并描述了计算电流的傅立叶系数的过程，从而使我们能够准确地计算出功率并显示功率如何在谐波上分布。与数字的比较验证了我们的分析。