This paper is focused on presenting an accurate framework to describe frequency-dependent energy harvesting via magnetic shape memory alloys (MSMAs). Modeling strategy incorporates the phenomenological constitutive model developed formerly together with the magnetic diffusion equation. A hyperbolic hardening function is employed to define reorientation-induced strain hardening in the material, and the diffusion equation is used to add dynamic effects to the model. The MSMA prismatic specimen is surrounded by a pickup coil, and the induced voltage during martensite-variant reorientation is investigated with the help of Faraday's law of magnetic field induction. It has been shown that, in order to harvest the maximum RMS voltage in the MSMA-based energy harvester, an optimum value of bias magnetic field exists, which is the corresponding magnetic field for the start of pseudoelasticity behavior. In addition, to achieve a more compact energy harvester with higher energy density, a specimen with a lower aspect ratio can be chosen. As the main novelty of the paper, it is found that the dynamic effects play a major role in determining the harvested voltage and power, especially for high excitation frequency or specimen thickness.
In this paper, an analytical approach for free vibration analysis of moderately thick functionally graded rectangular plates coupled with piezoelectric layers is presented. The transverse distribution of electric potential satisfies the Maxwell equation as well as the electrical boundary conditions for both closed and open circuit piezoelectric layers. Based on the first order shear deformation plate theory and using both the Maxwell equation and Hamilton principle, the governing equations are obtained. These equations, which are six coupled partial differential equations, are decoupled through introducing four auxiliary functions. The decoupled equations are solved analytically for the Levy type of mechanical boundary condition, two opposite edges simply supported and arbitrary boundary conditions at the other edges. The numerical results for the plate natural frequency are established for various plate dimensions, power law indices and electrical and mechanical boundary conditions. Finally, the effect of piezoelectric layer thickness on the natural frequency is discussed for various plate parameters. It is found that the effect of the piezoelectric layer on the plate natural frequencies strongly depends on the mechanical and electrical boundary conditions.
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