A vibration energy harvester (VEH) converts the kinetic energy of a moving source into electrical energy. In this article, we consider a 1-D electromagnetic vibration energy harvester (1-D EMVEH) that consists of three coaxial cylindrical permanent magnets enclosed in a tube such that the middle magnet is levitating. The resulting movement of the middle magnet can then induce an electromotive force (EMF) in one or more surrounding coils. Using an analytical model, we derive expressions for the 1-D-EMVEHs characteristic frequency and output power by using the Fourier space approach. First, the magnetostatic energy of the system as a function of the position of the levitating magnet is calculated. Its spatial gradient gives the force acting on a magnet, which drives its dynamics. Next, more accurate magnetic flux and EMF expressions are obtained. The results are compared with experimental measurements, revealing an excellent agreement.

中文翻译：

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一维电磁振动能量收集器的解析力和磁通

振动能量收集器 (VEH) 将移动源的动能转换为电能。在本文中，我们考虑一维电磁振动能量采集器 (1-D EMVEH)，它由三个同轴圆柱形永磁体组成，这些永磁体封装在一个管子中，中间的磁铁悬浮。中间磁铁产生的运动然后会在一个或多个周围的线圈中感应出电动势 (EMF)。使用解析模型，我们通过傅立叶空间方法推导出一维电磁辐射的特征频率和输出功率的表达式。首先，计算作为悬浮磁体位置函数的系统的静磁能。它的空间梯度产生作用在磁铁上的力，从而驱动其动力学。接下来，获得更准确的磁通量和 EMF 表达式。