Study of electrical circuits using Runge Kutta method of order 4

In this paper, Runge Kutta method of order 4 is used to study the electrical circuits designs through past, intermediate and present voltages. When integrating differential equations with Runge Kutta method of order 4, a constant step size (ℎ) is used until a testing procedure confirms that the discontinuity occurs in the present integration interval. This step size function calculations would take place at the end of the functional calculations, but before the dependent variables were updated. Runge Kutta methods along with convolution are given by array interpretation (Butcher matrix) representation, this leads to identify the equilibrium state. The input parameters indicate the voltage coefficient controlled by current sources and measures it a random periodic time. The output parameters provide stable independent values and calculated from past voltage and current values. Finally solutions are compared with exact values and RK method of order 4 along with Heun, Midpoint and Taylors’s method with various ℎ values.

Enhancement of the Magnetoelectric Effect in PZT-Ni Ferrite Composites Using Post Sintering Thermal Treatment

In this chapter, the piezoelectric and magnetoelectric properties of Pb (Zr0.52T0.48)O3–X NiFe1.9Mn0.1O4 (PZT-NFM, where X ranges from 3 to 10%) were investigated along with SEM and TEM analysis. Post sintering thermal treatment (annealing and aging) was introduced to enhance the piezoelectric and magnetoelectric property of the composites. The density was found around 7.6–7.8 gm/cc. The piezoelectric constant d33 and the voltage constant were found to be decreased with increasing magnetic particle from 3–10%. Experimental results indicated that the magnetoelectric voltage coefficient (dE/dH) increases with increasing percentage of Nickel Ferrite (~35 for 3% NF to 140 mV/Oe. cm for 10% NF at 1125°C). The samples, which were annealed and aged after sintering show as high as 50% (140 to 220 mV/cm Oe) increase in dE/dH coefficient. This is due to the increase in resistivity due to better homogeneity. The H-M curve of the composite powders show that the PZT-NFM is a ferromagnetic material as well. The SEM investigation shows very compact structure with average grain size around 150 nm and some areas of the NF rich phase. The X-ray mapping shows that the NF is distributed in the big grains of the matrix and after annealing it homogenizes.

Strain-Mediated Magneto-Electric Effects in Coaxial Nanofibers of Y/W-Type Hexagonal Ferrites and Ferroelectrics

Nanofibers of Y- or W-type hexagonal ferrites and core–shell fibers of hexagonal ferrites and ferroelectric lead zirconate titanate (PZT) or barium titanate (BTO) were synthesized by electrospinning. The fibers were found to be free of impurity phases, and the core–shell structure was confirmed by electron and scanning probe microscopy. The values of magnetization of pure hexagonal ferrite fibers compared well with bulk ferrite values. The coaxial fibers showed good ferroelectric polarization, with a maximum value of 0.85 μC/cm2 and 2.44 μC/cm2 for fibers with BTO core–Co2W shell and PZT core–Ni2Y shell structures, respectively. The magnetization, however, was much smaller than that for bulk hexaferrites. Magneto-electric (ME) coupling strength was characterized by measuring the ME voltage coefficient (MEVC) for magnetic field-assembled films of coaxial fibers. Among the fibers with Y-type, films with Zn2Y showed a higher MEVC than films with Ni2Y, and fibers with Co2W had a higher MEVC than that of those with Zn2W. The highest MEVC of 20.3 mV/cm Oe was measured for Co2W–PZT fibers. A very large ME response was measured in all of the films, even in the absence of an external magnetic bias field. The fibers studied here have the potential for use in magnetic sensors and high-frequency device applications.

Magnetoelectric Response of Laminated Cantilevers Comprising a Magnetoactive Elastomer and a Piezoelectric Polymer, in Pulsed Uniform Magnetic Fields

The voltage response to pulsed uniform magnetic fields and the accompanying bending deformations of laminated cantilever structures are investigated experimentally in detail. The structures comprise a magnetoactive elastomer (MAE) slab and a commercially available piezoelectric polymer multilayer. The magnetic field is applied vertically and the laminated structures are customarily fixed in the horizontal plane or, alternatively, slightly tilted upwards or downwards. Six different MAE compositions incorporating three concentrations of carbonyl iron particles (70 wt%, 75 wt% and 80 wt%) and two elastomer matrices of different stiffness are used. The dependences of the generated voltage and the cantilever’s deflection on the composition of the MAE layer and its thickness are obtained. The appearance of the voltage between the electrodes of a piezoelectric material upon application of a magnetic field is considered as a manifestation of the direct magnetoelectric (ME) effect in a composite laminated structure. The ME voltage response increases with the increasing total quantity of the soft-magnetic filler in the MAE layer. The relationship between the generated voltage and the cantilever’s deflection is established. The highest observed peak voltage around 5.5 V is about 8.5-fold higher than previously reported values. The quasi-static ME voltage coefficient for this type of ME heterostructures is about 50 V/A in the magnetic field of ≈100 kA/m, obtained for the first time. The results could be useful for the development of magnetic field sensors and energy harvesting devices relying on these novel polymer composites.

A Systematic Review of Piezoelectric Materials and Energy Harvesters for Industrial Applications

In the last three decades, smart materials have become popular. The piezoelectric materials have shown key characteristics for engineering applications, such as in sensors and actuators for industrial use. Because of their excellent mechanical-to-electrical and vice versa energy conversion properties, piezoelectric materials with high piezoelectric charge and voltage coefficient have been tested in renewable energy applications. The fundamental component of the energy harvester is the piezoelectric material, which, when subjected to mechanical vibrations or applied stress, induces the displaced ions in the material and results in a net electric charge due to the dipole moment of the unit cell. This phenomenon builds an electric potential across the material. In this review article, a detailed study focused on the piezoelectric energy harvesters (PEH’s) is reported. In addition, the fundamental idea about piezoelectric materials, along with their modeling for various applications, are detailed systematically. Then a summary of previous studies based on PEH’s other applications is listed, considering the technical aspects and methodologies. A discussion has been provided as a critical review of current challenges in this field. As a result, this review can provide a guideline for the scholars who want to use PEH’s for their research.

Boosting Magnetoelectric Effect in Polymer-Based Nanocomposites

Polymer-based magnetoelectric composite materials have attracted a lot of attention due to their high potential in various types of applications as magnetic field sensors, energy harvesting, and biomedical devices. Current researches are focused on the increase in the efficiency of magnetoelectric transformation. In this work, a new strategy of arrangement of clusters of magnetic nanoparticles by an external magnetic field in PVDF and PFVD-TrFE matrixes is proposed to increase the voltage coefficient (αME) of the magnetoelectric effect. Another strategy is the use of 3-component composites through the inclusion of piezoelectric BaTiO3 particles. Developed strategies allow us to increase the αME value from ~5 mV/cm·Oe for the composite of randomly distributed CoFe2O4 nanoparticles in PVDF matrix to ~18.5 mV/cm·Oe for a composite of magnetic particles in PVDF-TrFE matrix with 5%wt of piezoelectric particles. The applicability of such materials as bioactive surface is demonstrated on neural crest stem cell cultures.

Large piezoelectric voltage coefficient in aluminate-sodalite-type improper ferroelectric oxide

Dielectric and piezoelectric properties of aluminate-sodalite-type oxides, (Ca1-xSrx)8[AlO2]12{MoO4}2 ((CS)AM-x) have been investigated in the present study. The variation of dielectric anomalies clarifies the phase diagram of (CS)AM-x over a composition...

Piezoelectric Properties of PVDF Modified 3-3 Type Cement-Based Piezoelectric Composites

In this study, 3-3 type cement-based piezoelectric composites were prepared by casting Portland cement paste in porous lead zirconate titanate (PZT) ceramics, then the Polyvinylidene fluoride (PVDF) of N-Methylpyrrolidone (NMP) solvent with concentration of 50-200 mg/ml was utilized to modify the PZT-PC composites. The influence of PVDF concentration on the density, microstructure, dielectric, piezoelectric and electromechanical properties were investigated. The results indicate that the density of PZT-PC composites increased gradually with PVDF concentration for the increasing combined weight of PVDF with the composites. The introduction of PVDF has also contributed to the reduction of leakage current during the poling and testing process, which led to increased relative permittivity εr and longitudinal piezoelectric strain coefficient d33, while the dielectric loss tanδ and longitudinal piezoelectric voltage coefficient g33 demonstrated an opposite changing trend. Both the thickness electromechanical coupling coefficient Kt and planar electromechanical coupling coefficient Kp of the PZT-PC composites increased with PVDF concentration. The acoustic impedance (Z) of PVDF modified PZT-PC composites ranged from 6.89 to 7.65 MRayls, making it suitable for applications in the health monitoring of civil engineering.