# Magneto-elastic resonance

**Magneto-elastic resonance**^{1)}, **magneto-mechanical resonance**^{2)} or **magnetostrictive resonance**^{3)} - 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 core

^{4)}
^{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 loss^{5)} 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).

## See also

## References

^{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