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Small-scale magnetorheological dampers for vibration mitigation ...

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Proofs<br />

Introduction<br />

Hysteretic models<br />

Identification methodology<br />

Future work<br />

Experimental identification<br />

Summary<br />

Proof.<br />

Demonstration of alternative to shear-mode MR damper<br />

Previous considerations<br />

Overparametrized → per<strong>for</strong>m normalization<br />

Ikhouane and Dyke<br />

The fact that lim ρ−→∞ ψ σ,n(¯x tp) = −1 is independent from σ and n <strong>for</strong> large values of ρX max<br />

Proof<br />

Conclusion → <strong>for</strong> large values of ρX max, the values of the parameters σ and n are irrelevant.<br />

After considering the previous alternatives a new model is suggested<br />

F(T) = k vẋ(t) + k vF c(ẋ)<br />

k x and k w are voltage dependent, and F c is the Coulomb dry friction <strong>for</strong>ce representation<br />

F c(ẋ) = 1 <strong>for</strong> ẋ > 0<br />

F c(ẋ) = −1 <strong>for</strong> ẋ < 0<br />

Disadvantage → discontinuity at zero velocity or numerical instability when the ẋ of the damper is<br />

close to 0<br />

Return<br />

Arturo Rodríguez Tsouroukdissian<br />

<strong>Small</strong>-<strong>scale</strong> MR <strong>dampers</strong> <strong>for</strong> <strong>vibration</strong> <strong>mitigation</strong>

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