# Vibration Energy Harvesting from Plates by Means of Piezoelectric Dynamic Vibration Absorbers
## 1 Introduction  
The present era, which is characterized by IoT and Industry 4.0, requires a lot of sensors to monitor industrial, urban and natural environments. The use of wiring to feed the sensors is sometimes unfeasible, e.g., this is the case of remote sensors installed in buoys in deep sea or in tall buildings and antennas. Nowadays, remote sensors nodes are fed by means of batteries, which are not eco-friendly and require complex and expensive replacement operations. Fortunately, the energy consumption of sensor nodes is constantly decreasing, and new technical solutions are possible. Vibration energy harvesting is a great opportunity since remote sensors can be fed by using existing sources of energy. Vibration energy harvesting can be performed by exploiting different physical phenomena to convert mechanical energy into electrical energy. In the scientific literature, piezoelectric [1], electromagnetic [2], electrostatic [3] and triboelectric [4; 5] harvesters have been proposed. Piezoelectric harvesters usually take the form of thin layers that are either bonded to a vibrating surface or are bonded to a cantilever beam to make a cantilever harvester. Piezoelectric harvesters generate high voltage, can be integrated with the vibrating structure and have small mass and encumbrance. For these reasons, they are adopted to feed sensors and other small electronic equipment in vehicles, industrial machinery, civil structures and biomedical devices. The vibrating plate is one of the most common vibrating structures and is a typical part of machines, domestic appliances, road vehicles, trains and aircraft [6; 7]. Vibrating plates can be found in buildings (panels of facades) and in other civil structures as well [8; 9]. Hence, harvesting vibration energy from plates is a very present research topic. Plates are sometimes excited by concentrated loads, but there are many cases in which this structure is excited by the distributed loads caused by wind, traffic or water flows. The simplest piezoelectric harvester for a vibrating plate is a piezoelectric layer directly bonded to theplate surface. It works in the bending mode (the 3-1 mode [10]) and exploits the strain caused by plate bending. The strain of the plate reaches the maximum value at the natural frequencies of the modes of vibrations that are excited by concentrated or distributed loads. A cantilever harvester with its tip mass tuned to the natural frequency of the most excited mode of vibration of the plate is a possible alternative that enables better exploitation of the resonance phenomenon. This cantilever harvester behaves as a dynamic vibration absorber (DVA) that is able to receive a large amount of energy from the plate. On the one hand, plate vibrations are strongly reduced [11]; on the other hand, the cantilever harvester experiences large-amplitude vibrations. It is worth noting that the principle of DVAs has been also adopted by several researchers to develop devices able to improve or extend the performance of simple harvesters. These devices include dynamic magnifiers [12; 13; 14], trimming oscillators [15] and inertial amplifiers [16; 17]. DVAs with piezoelectric layers have been studied in recent years both with the aim of suppressing the vibrations of the host structure and with the aim of scavenging energy. [PERSON] and [PERSON] in 2013 [18] proposed an energy harvesting DVA and analytically studied the coupling of this device with a one-degree-of-freedom (DOF) vibrating system. A lumped parameter 1-DOF model of the piezoelectric harvester was adopted. An analytical expression of the natural frequencies of the coupled system was given, the presence of two resonance peaks was demonstrated, and the influence of the piezoelectric layer on the damping of the DVA was highlighted. [PERSON] et al. in 2017 [19] studied the coupling of a cantilever harvester with a 1-DOF vibrating system. The cantilever harvester was modeled according to the modal expansion approach like in [20].