*Article* **System-Level Model and Simulation of a Frequency-Tunable Vibration Energy Harvester**

#### **Sofiane Bouhedma 1,\*, Yongchen Rao 1,2, Arwed Schütz 2, Chengdong Yuan 1,2, Siyang Hu 1,2, Fred Lange 1, Tamara Bechtold 1,2 and Dennis Hohlfeld 1**


Received: 10 December 2019; Accepted: 11 January 2020; Published: 14 January 2020

**Abstract:** In this paper, we present a macroscale multiresonant vibration-based energy harvester. The device features frequency tunability through magnetostatic actuation on the resonator. The magnetic tuning scheme uses external magnets on linear stages. The system-level model demonstrates autonomous adaptation of resonance frequency to the dominant ambient frequencies. The harvester is designed such that its two fundamental modes appear in the range of (50,100) Hz which is a typical frequency range for vibrations found in industrial applications. The dual-frequency characteristics of the proposed design together with the frequency agility result in an increased operative harvesting frequency range. In order to allow a time-efficient simulation of the model, a reduced order model has been derived from a finite element model. A tuning control algorithm based on maximum-voltage tracking has been implemented in the model. The device was characterized experimentally to deliver a power output of 500 μW at an excitation level of 0.5 g at the respected frequencies of 63.3 and 76.4 Hz. In a design optimization effort, an improved geometry has been derived. It yields more close resonance frequencies and optimized performance.

**Keywords:** piezoelectricity; vibration-based energy harvesting; multimodal structures; frequency tuning; nonlinear resonator; bistability; magnetostatic force
