Abstract This paper presents a theoretical study on the scaling laws of electromagnetic and piezoelectric seismic vibration energy harvesters, which are assembled from discrete components. The scaling laws are therefore derived for the so called meso-scale range, which is typical of devices built from distinct elements. Isotropic scaling is considered for both harvesters such that the shape of the components and of the whole transducers do not change with scaling. The scaling analyses are restricted to the case of linearly elastic seismic transducers subject to tonal ambient vibrations at their fundamental natural frequency, where the energy harvesting is particularly effective. Both resistive-reactive and resistive optimal electric harvesting loads are considered. The study is based on equivalent formulations for the response and power harvesting of the two transducers, which employ the so called electromagnetic and piezoelectric power transduction factors, Π c m 2 and Π p e 2 . The scaling laws of the transduction coefficients and electrical and mechanical parameters for the two transducers are first provided. A comprehensive comparative scaling analysis is then presented for the harvested power, for the power harvesting efficiency and for the stroke of the two harvesters. Particular attention is dedicated to the scaling laws for the dissipative effects in the two harvesters, that is the Couette air losses and eddy currents losses that develop in the electromagnetic harvester and the material, air and dielectric losses that arise in the piezoelectric harvester. The scaling laws emerged from the study, are thoroughly examined and interpreted with respect to equivalent mechanical effects produced by the harvesting loads.

中文翻译：

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由分立元件构建的电磁和压电地震振动能量收集器的标度定律

摘要 本文对分立元件组装的电磁和压电地震振动能量采集器的标度规律进行了理论研究。因此，缩放定律是针对所谓的中尺度范围推导出来的，这是由不同元素构建的设备的典型特征。两个采集器都考虑了各向同性缩放，使得组件和整个换能器的形状不随缩放而改变。缩放分析仅限于线性弹性地震换能器在其基本自然频率下受到音调环境振动的情况，其中能量收集特别有效。电阻-电抗和电阻最佳电力采集负载都被考虑。该研究基于两个换能器的响应和功率收集的等效公式，它们采用所谓的电磁和压电功率换能因子 Π cm 2 和 Π pe 2 。首先提供了两个换能器的换能系数和电气和机械参数的标度定律。然后针对两个收割机的收获功率、功率收集效率和行程进行全面的比较缩放分析。特别关注两个采集器中耗散效应的缩放定律，即电磁采集器中产生的库埃特空气损耗和涡流损耗，以及压电采集器中产生的材料、空气和介电损耗。研究中出现了标度定律，