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.
Deane, J.H.B., Dharmasena, R.D.I.G., Gentile, G. (2018). Power computation for the triboelectric nanogenerator. NANO ENERGY, 54, 39-49 [10.1016/j.nanoen.2018.09.063].