Damping of Oscillations by a Vibro-Impact System with Serial Magnetic Impact Pairs

Abstract

The body vibration damping process with a dynamic shock vibration damper containing a system of successive shock pairs in which the colliding elements are magnets is considered. The projected parameters’ effect of the vibration damper on the body oscillations is considered. The features of setting up the system in the mode of wideband vibration damping are described.

Appendix

Analytical function for magnetic characteristic was found according to Biot–Savart–Laplace principle and current circuit interaction principle (for more details, see [16]). Following expression is obtained:

$$ F\left( X \right) = \frac{3}{2}\frac{{\pi B_{M}^{2} r^{4} h^{2} X}}{{\mu_{0} \left( {r^{2} + X^{2} } \right)^{5/2} }}, $$

where

• B_M—remanence of material [T],

• r—magnet radius, [m],

• h—magnet height, [m],

• $\mu_{0}$—magnetic constant, [$m\, \cdot \,{\text{kg}}\, \cdot \,s^{ - 2} A^{ - 2}$],

• X—distance between magnets, [m].

After some manipulations, one obtains:

$$ F\left( z \right) = \frac{{F_{0} z}}{{\left( {1 + \left( z \right)^{2} } \right)^{5/2} }}F_{0} = \frac{3}{2}\frac{{\pi B_{M}^{2} h^{2} }}{{\mu_{0} }}z = \frac{X}{r} $$

(25.9)

The best match with the experiment for specific magnets shows the following function:

$$ F\left( z \right) = \frac{{F_{0} \left( {z - \frac{h}{{\left( {2r} \right)}}} \right)}}{{\left( {1 + \left( {z - \frac{h}{{\left( {2r} \right)}}} \right)^{2} } \right)^{3} }} $$

This one was used in the numerical simulation of the device.