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Wireless sensor networks usually rely on internal permanent or rechargeable batteries as a power supply, causing high maintenance efforts. An alternative solution is to supply the entire system by harvesting the ambient energy, for example, by transducing ambient vibrations into electric energy by virtue of the piezoelectric effect. The purpose of this paper is to present a simple engineering approach for the bandwidth optimization of vibration energy harvesting systems comprising multiple piezoelectric cantilevers (PECs). The frequency tuning of a particular cantilever is achieved by changing the tip mass. It is shown that the bandwidth enhancement by mass tuning is limited and requires several PECs with close resonance frequencies. At a fixed frequency detuning between subsequent PECs, the achievable bandwidth shows a saturation behavior as a function of the number of cantilevers used. Since the resonance frequency of each PEC is different, the output voltages at a particular excitation frequency have different amplitudes and phases. A simple power-transfer circuit where several PECs with an individual full wave bridge rectifier are connected in parallel allows one to extract the electrical power close to the theoretical maximum excluding the diode losses. The experiments performed on two- and three-PEC arrays show reasonable agreement with simulations and demonstrate that this power-transfer circuit additionally influences the frequency dependence of the harvested electrical power.
Theoretical Modeling of Magnetoactive Elastomers on Different Scales: A State-of-the-Art Review
(2022)
A review of the latest theoretical advances in the description of magnetomechanical effects and phenomena observed in magnetoactive elastomers (MAEs), i.e., polymer networks filled with magnetic micro- and/or nanoparticles, under the action of external magnetic fields is presented. Theoretical modeling of magnetomechanical coupling is considered on various spatial scales: from the behavior of individual magnetic particles constrained in an elastic medium to the mechanical properties of an MAE sample as a whole. It is demonstrated how theoretical models enable qualitative and quantitative interpretation of experimental results. The limitations and challenges of current approaches are discussed and some information about the most promising lines of research in this area is provided. The review is aimed at specialists involved in the study of not only the magnetomechanical properties of MAEs, but also a wide range of other physical phenomena occurring in magnetic polymer composites in external magnetic fields.
Conventional calculations of the inertia tensor in undergraduate physics course are usually done for highly symmetrical bodies. Students might therefore get the impression that the moment of inertia about any axis through the center of mass is the same only for bodies with the highest degree of symmetry relative to this point, e.g., for spheres. A simple, seemingly counterintuitive example is presented, showing that the moment of inertia of a non-regular body, here an assembly of material points, can be the same about any axis passing through its center of mass.
The influence of an external magnetic field on the static shear strain and the effective shear modulus of a magnetoactive elastomer (MAE) is studied theoretically in the framework of a recently introduced approach to the single-particle magnetostriction mechanism [V. M. Kalita et al., Phys. Rev. E 93, 062503 (2016)]. The planar problem of magnetostriction in an MAE with magnetically soft inclusions in the form of a thin disk (platelet) having the magnetic anisotropy in the plane of this disk is solved analytically. An external magnetic field acts with torques on magnetic filler particles, creates mechanical stresses in the vicinity of inclusions, induces shear strain, and increases the effective shear modulus of these composite materials. It is shown that the largest effect of the magnetic field on the effective shear modulus should be expected in MAEs with soft elastomer matrices, where the shear modulus of the matrix is less than the magnetic anisotropy constant of inclusions. It is derived that the effective shear modulus is nonlinearly dependent on the external magnetic field and approaches the saturation value in magnetic fields exceeding the field of particle anisotropy. It is shown that model calculations of the effective shear modulus correspond to a phenomenological definition of effective elastic moduli and magnetoelastic coupling constants. The obtained theoretical results compare well with known experimental data. Determination of effective elastic coefficients in MAEs and their dependence on magnetic field is discussed. The concentration dependence of the effective shear modulus at higher filler concentrations has been estimated using the method of Pade approximants, which predicts that both the absolute and relative changes of the magnetic-field-dependent effective shear modulus will significantly increase with the growing concentration of filler particles.
The magnetic properties of a magnetoactive elastomer (MAE) filled with mu m-sized soft-magnetic iron particles have been experimentally studied in the temperature range between 150 K and 310 K. By changing the temperature, the elastic modulus of the elastomer matrix was modified, and it was possible to obtain magnetization curves for an invariable arrangement of particles in the sample and in the case when the particles were able to change their position within the MAE under the influence of magnetic forces. At low (less than 220 K) temperatures, when the matrix becomes rigid, the magnetization of the MAE does not show a hysteresis behavior, and it is characterized by a negative value of the Rayleigh constant. At room temperature, when the polymer matrix is compliant, a magnetic hysteresis exists where the dependence of the differential magnetic susceptibility on the magnetic field exhibits local maxima. The appearance of these maxima is explained by the elastic resistance of the matrix to the displacement of particles under the action of magnetic forces.
Magnetoactive elastomers (MAEs) are composite materials comprised of micrometer-sized ferromagnetic particles in a nonmagnetic elastomermatrix. Asingle-particle mechanism ofmagnetostriction in MAEs, assuming the rotation of a soft magnetic, mechanically rigid particle with uniaxial magnetic anisotropy in magnetic fields is identified and considered theoretically within the framework of an alternative model. In this mechanism, the total magnetic anisotropy energy of the filling particles in the matrix is the sum over single particles. Matrix displacements in the vicinity of the particle and the resulting direction of the magnetization vector are calculated. The effect of matrix deformation is pronounced well if the magnetic anisotropy coefficient K is much larger than the shear modulus mu of the elastic matrix. The feasibility of the proposed magnetostriction mechanism in soft magnetoactive elastomers and gels is elucidated. The magnetic-field-induced internal stresses in the matrix lead to effects of magnetodeformation and may increase the elastic moduli of these composite materials.
A magnetoelectric (ME) voltage transformer is fabricated on the basis of a ferromagnetic (FM)-piezoelectric (PE) heterostructure comprising two equally thick laminated layers of an amorphous FM alloy and a piezoceramic lead zirconate-titanate layer sandwiched between them. The structure, placed inside an excitation coil, is electrically poled and magnetized in the direction of the long axis. The primary voltage is applied to the coil and the secondary voltage is measured between the electrodes of the PE material. It is shown for the first time that the change in the total thickness of magnetic layers significantly influences the transformer ' s characteristics. At the largest total thickness of FM layers of 138 mu m, the open-circuit voltage transformation ratio K has a maximum value of about 20, and the power transfer efficiency eta at a matched resistive load of about 20 k omega reaches 45%. The variation of the control magnetic field in the range of 0-21.6 kA m(-1) makes it possible to change the voltage transformation ratio K from zero to the maximum value. A simple model allows one to calculate the dependence of the characteristics of the ME transformer on the frequency of the primary voltage, thickness of the FM layers, control magnetic field, and the load.
Ultra-small-angle neutron scattering (USANS) experiments are reported on isotropic magnetoactive elastomer (MAE) samples with different concentrations of micrometer-sized iron particles in the presence of an in-plane magnetic field up to 350 mT. The effect of the magnetic field on the scattering curves is observed in the scattering vector range between 2.5 x 10(-5) and 1.85 x 10(-4) angstrom(-1). It is found that the neutron scattering depends on the magnetization history (hysteresis). The relation of the observed changes to the magnetic-field-induced restructuring of the filler particles is discussed. The perspectives of employing USANS for investigations of the internal microstructure and its changes in magnetic field are considered.
A voltage transformer employing the magnetoelectric effect in a composite ceramic heterostructure with layers of a magnetostrictive nickel–cobalt ferrite and a piezoelectric lead zirconate–titanate is described. In contrast to electromagnetic and piezoelectric transformers, a unique feature of the presented transformer is the possibility of tuning the voltage transformation ratio K using a dc magnetic field. The dependences of the transformer characteristics on the frequency and the amplitude of the input voltage, the strength of the control magnetic field and the load resistance are investigated. The transformer operates in the voltage range between 0 and 112 V, and the voltage transformation ratio K is tuned between 0 and 14.1 when the control field H changes between 0 and 6.4 kA/m. The power at the transformer output reached 63 mW, and the power conversion efficiency was 34%. The methods for calculation of the frequency response, and the field and load characteristics of the transformer are proposed. The ways to improve performance characteristics of magnetoelectric transformers and their possible application areas are discussed.
It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the elastic and electro-conductive properties of a strongly inhomogeneous two-phase composite material, the steep rise of effective parameters occurs at different concentrations. To achieve the logical concordance between the cross-property relations, a modification of the effective medium theory of the elastic properties is introduced. It is shown that the qualitative conclusions of the theory do not change, while a possibility of describing a broader class of composite materials with various percolation thresholds arises. It is determined under what conditions there is an elasticity theory analogue of the Dykhne formula for the effective conductivity. The theoretical results are supported by known experiments and show improvement over the existing approach. The introduction of the theory with the variable percolation threshold paves the way for describing the magnetorheological properties of magnetoactive elastomers. A similar approach has been recently used for the description of magneto-dielectric and magnetic properties.