A magnetoelastic strange attractor

Traditional vibration-based energy harvesters are designed for a specific base excitation frequency by matching its fundamental natural frequency. This work presents the modeling and analysis of a nonlinear, magnetically excited energy harvester that exhibits efficient broadband, frequency-independent performance utilizing a passive auxiliary structure that remains stationary relative to the base motion. This system is especially effective in the regime of driving frequencies well below its fundamental frequency, thus enabling a more compact design solution over traditional topologies. A model based on Euler–Bernoulli beam theory is coupled to a linear circuit and a model of the nonlinear, magnetic interaction to produce a distributed parameter magneto-electromechanical system. This model is used in both harmonic and stochastic base excitation case studies. The results of these simulations demonstrate multiple-order-of-magnitude power harvesting performance improvement at low driving frequencies and an insensitivity to time-varying base excitation. Furthermore, the proposed system is shown to outperform an optimally designed, standard energy harvester in the presence of broadband, random base excitation.

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Broadband vibration-based energy harvesting improvement through frequency up-conversion by magnetic excitation

In its simplest form the magnetoelastic buckling instability refers to the sudden bending transition of an elastic rod experiencing a uniform induction field applied at a normal angle with respect to its long axis. This fundamental physics phenomenon was initially documented in 1968, and, surprisingly, despite many refinements, a gap has always remained between the observations and the theoretical expectations. Here, we first renew the theory with a simple model based on the assumption that the magnetization follows the rod axis as soon as it bends. We demonstrate that the magnetoelastic buckling corresponds to a classical Landau second-order transition. Our model yields a solution for the critical field as well as the shape of the deformed rods which we compare with experiments on flexible ferromagnetic nickel rods at the centimeter scale. We also report this instability at the micrometer scale with specially designed rods made of nanoparticles. We characterized our samples by determining all of the relevant parameters (radius, length, Young modulus, magnetic susceptibility) and, using these values, we found that the theory fits extremely well the experimental results for both systems without any adjustable parameter. The superparamagnetic feature of the microrods also highlights the fact that ferromagnetic systems break the symmetry before the buckling. We propose a magnetic “stick–slip” model to explain this peculiar feature, which was visible in past reports but never detailed.

https://www.pnas.org/content/pnas/112/23/7135.full.pdf

A refined theory of magnetoelastic buckling matches experiments with ferromagnetic and superparamagnetic rods.

Magnet-polymer (Magpol) composites have an interesting ability to undergo large strains in response to an external magnetic field. The contraction behavior of composites of silicone and micron sized iron particles induced by an external magnetic field was studied. Simply by changing boundary conditions, Magpol can exhibit shape change from axial contraction to a novel coiling mechanism due to buckling. The analytically predicted magnetic fields for buckling agreed well with the measured values. The strain versus magnetic field relationship suggested that postbuckling behavior is a stable symmetric bifurcation, which is useful for continuous actuation. The coiling mode of Magpol exhibited high actuation strain (up to 60%) and actuation stress (up to 184 kPa), thus shows good potential for use in soft actuators.

Novel Coiling Behavior in Magnet‐Polymer Composites

The electromagnetic and thermal effects on the stress distribution around the crack tip in conducting materials due to electric current are investigated. Emphases are placed on quantifying the crack growth behavior affected by the interplay between these effects. A two-dimensional finite element analysis is conducted to examine the coupled problems. The results show that the compressive stress state around the crack tip plays a decisive role in preventing the crack from further growth. The resulting normal stress in front of the crack tip caused by the Joule heat generation tends to suppress the crack growth, while the stress induced by the electromagnetic forces provides a tensile normal stress with smaller magnitude in the vicinity of the crack tip, hence promotes the crack growth. Favorable agreements between numerical analysis results and existing experimental results are achieved. By utilizing these phenomena, the electric current may be used to actively control the damage propagation, hence catastrophic failure can be prevented.

Francis C. Moon

Papers

V – Problems in Magneto-solid Mechanics