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Small-scale magnetorheological dampers for vibration mitigation ...

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Proofs (Cont’d)<br />

Introduction<br />

Hysteretic models<br />

Identification methodology<br />

Future work<br />

Experimental identification<br />

Summary<br />

Proof.<br />

Step 3 θ(x) demonstration<br />

Then its derivative<br />

dθ(x)<br />

= k wρ(1 − w(x))<br />

dx<br />

Defining a = k wρ and b = ρ, the derivative can be rewritten as<br />

dθ(x)<br />

= a − ρθ(x)<br />

dx<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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