# Comprehensive Numerical Analysis of a Porous Piezoelectric Ceramic for Axial Load Energy Harvesting
###### Abstract  
In this paper, an axial-type piezoelectric energy generator with various porosities of piezoelectric ceramics is designed and analysed. A 3D finite element model is developed by using ANSYS software. The porosity of piezoelectric ceramic is varied from 0 to 80% through thickness or along the length of the duralumin beam. The axial type energy harvester consists of bimorph (d\({}_{31}\)) and cylinder (d\({}_{33}\)) piezoelectric patches with base excitation. The effects of various porosities, proof mass locations, and different applied acceleration are used to determine the output voltage and power generation. The maximum output voltage and power are obtained equal to 2.25 V and 51 uW, respectively. piezoelectric material; porous piezoelectric; energy harvesting +
Footnote †: journal: _Sciences_  
with the FE calculation [14]. The various piezoelectric materials and transducer configurations have been discussed by researchers. The operating parameters of various piezoelectric energy collection systems, as well as the scope of improvement of existing systems have been analysed. Individual examples of a push-type power generator, a stack-type generator, and a cantilever-type microgenerator have been considered. The piezoelectric materials have been used and the corresponding output power of such devices obtained [15]. Perovskite (CTO)-based polymetric (PVDF) composite film as a piezoelectric energy harvester have been developed with biocompatibility. Sensor accuracy has been increased with the help of artificial neural networks and digital signal processing techniques. The output power density of 0.19 uW/cm\({}^{2}\) at 10\({}^{8}\)\(\Omega\) was observed [16]. Biomass as value-added material was utilized in the fabrication of piezoelectric nanogenerators and piezospercapacitors for energy-oriented applications. The coconut husk-immobilized PVDF films were developed as piezoelectric films for the piezoelectric nanogenerator (PNG). The PNG has achieved a power density of 1.316 mW/cm\({}^{2}\) and an energy density of 76.33 mJ/cm\({}^{2}\)[17]. Researchers have optimized various parameters such as length, width, thickness, and position of piezoelectric materials. Various types of piezoelectric materials are used for energy harvesting, namely PZT5H, PZT5A, PZT19, PVDF, MFC, etc. An axial-type piezoelectric energy generator with effective elements at the base of the generator have been presented. A finite element simulations have been carried out and generator operated at a frequency of 70 Hz and produced a voltage of 6 V [18; 19; 20; 21]. The Gurtin-Murdoch model of surface stresses has been used to analyse nanoporous piezoelectric composites with stochastically scattered porosity using a cohesive approach to determine effective moduli [22]. The properties of porous piezoelectric ceramics have been analysed using the effective moduli method at the pore boundaries, and numerical simulations of porous piezoelectric ceramics have been performed in ANSYS software [23]. [PERSON] et al. have solved the problem for piezoceramic matrix with metal inclusions and mixed pores to determine the effective properties [24]. [PERSON] et al. have studied a numerical homogenization technique in piezocomposite system with metalized pores surfaces and developed random representative volume elements with random-size cubic inclusions [25]. Researches have studied various connectivity for porous piezoelectric ceramics including 3-0, 3-1, 3-2, 3-3, 0-3, 1-3, 2-2, and 2-3. Where the first notation indicates the connectivity of the electromechanically active phase and the second number signifies the electromechanically passive phase [26]. Porous ceramics are classified into two categories: (i) open cell (reticulated) and (ii) closed cell (foam). Pores are interconnected in open cell ceramics, whereas pores are generally isolated in a continuous ceramic matrix in a closed cell. Porous piezoelectric ceramics are composite materials made of two phases: (i) a porous (passive) phase and (ii) a piezoelectric cell (active) phase.