الفهرس 
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Abstract
This thesis aims to study harmonic energy harvesting behavior using analytical and theoretical methods. As well as verify the experimental output voltage by zinc oxide ceramics.
Firstly, the harmonic balance method (HBM) of linear and nonlinear piezoelectric vibration energy harvester (pVEH) based on Duffing type nonlinearity and Kirchhoff’s law are presented. The frequency response of the amplitudes of displacement, voltage, and power is studied based on the closed formula and numerically by the Wolfram Mathematica program. Also, Jacobian matrix is used to analyze the solutions’ stability. Runge-Kutta fourth order is used as a numerical method. The mentioned methods are used to study the sweeping up and down processes.
Secondly, Zinc oxide particles are synthesized by the precipitation method. The synthesized particles are compacted by uniaxial pressure and then annelid at 600° C and 700° C for 1 hour. X-ray diffraction (XRD) used in PDFgetx3 software and Broadening Microstructure Analysis Program (BMAP) software to study the bond length and microstructure characteristics of ZnO ceramics. Williamson Hall and modified Williamson Hall are discussed.
LCR meter is used to calculate dielectric and piezoelectric characteristics. Experimental energy harvester data extracted by ZnO ceramics are attached to the cantilever beam in operation mode 3-1. The comparison between HBM and experimental data is given.
Our work based on piezoelectric energy harvesting is divided into theoretical and experimental work as shown in the flowchart. In chapter one, an introduction to piezoelectric vibration energy harvesting is presented. Chapter two contains the theoretical part, and it discusses different theoretical methods and the effect of nonlinearity on the bandwidth, in addition to studying sweep-up and sweep-down processes. In the experimental part, chapter three provides the experimental techniques. Chapter four also contains the experimental results and discussion. A brief conclusion about this thesis is introduced in chapter five.