# Encyclopedia Magnetica

Encyclopedia of magnetics and electromagnetics.

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magneto-elastic_resonance

# Magneto-elastic resonance

 Stan Zurek, Magneto-elastic resonance, Encyclopedia-Magnetica.com, {accessed 2019-06-16}

Magneto-elastic resonance1), magneto-mechanical resonance2) or magnetostrictive resonance3) - a resonance of a given structure magnetised at a frequency close to the frequency of its mechanical resonance.

Magnetoelastic resonance can influence the amount of loss dissipated in a magnetised core4)

by S. Zurek, E. Magnetica, CC-BY-3.0

Mechanical structures resonate in mechanical sense - they can amplify a certain frequency of mechanical vibrations. Such mechanical resonance frequency is dictated for instance by the shape, size, mechanical inertia and stiffness of a given structure.

Magnetic materials usually exhibit some level of magnetostriction, which causes mechanical vibrations. If the mechanical vibrations caused by the process of magnetisation have a frequency close to the mechanical resonance then the magneto-elastic resonance can occur.

## Practical significance

Such conditions lead to increased power loss5) and for brittle materials (like for instance ferrites) can cause cracks or even destruction of the core.6)

Power transformers generate acoustic noise mostly due to magnetostriction of electrical steel. They must be designed in such a way, as to avoid the magnetoelastic resonance, which would lead to exacerbated level of acoustic noise.7)

## Calculations

The frequency f of fundamental extensional mode of vibration of toroidal cores can be calculated as:8)

 $f = \frac{1}{2 · \pi · r} ·\sqrt{\frac{E}{\rho}}$ (Hz)

where: r - average radius of a ring core (m), E - Young's modulus of the core material (N/m²), ρ - specific density of the material (kg/m³).

For toroidal ferrite cores Ferroxcube gives the following equation. The result of the calculation is in kHz:9)

 $f = \frac{5700}{\pi · \frac{OD + ID}{2} }$ (kHz)

where: OD - outer diameter of the toroidal core (mm), ID - inner diameter (mm).

## References

2) Ramanan V.R.V., Smith C.H., Barberi L., Magnetomechanical resonant losses in metallic glasses, Journal of Applied Physics, Vol. 57 (8), Apr 1985, p. 3493, http://dx.doi.org/+10.1063/1.335038
4), 5), 8) Thottuvelil J.V., Wilson T.G., Owen, H.A. JR, Unusual high-frequency behaviour of some amorphous metallic-alloy tape-wound magnetic cores, IEEE Transactions on Magnetics, Vol. 20 (4), Jul, 1984, p. 570
7) T.P.P. Phway, A.J. Moses, Magnetisation-induced mechanical resonance in electrical steels, Journal of Magnetism and Magnetic Materials, Vol. 316 (2), Sep. 2007, p. 468