## Critical Loss Factor in 2-Dof in-Series System with Hysteretic Friction and Its Use for Vibration Control

**Authors:** Roman Vinokur

Although the classical theory of lumped mechanical systems employs the viscous friction mechanisms (dashpots), the loss factors of most solid structures are largely controlled by hysteresis. This paper presents new relationships for the dynamics of 2-DOF in-series systems with hysteresis damping. The most important among them is a close-form equation for the critical loss factor that was derived as the marginal condition for the degenerate case where the higher-frequency resonance peak fully vanishes in the vibration spectrum of the second mass. The critical loss factor can take values between 0 and 2-3/2 ≈ 0.354 and depends on the ratio of the natural frequencies of 2-DOF system: the closer the undamped natural frequencies, the lower the critical loss factor. The equation may help to interpret the vibration spectra for the second mass in the real 2-DOF systems, in particular on sweep-sine shaker tests. The single resonance peak in the degenerate case for a 2-DOF grows up notably as the natural frequencies get close to each other. By a formal analogy with 1-DOF systems, the peak magnitude can be reduced by increasing the loss factor. But in 2-DOF systems, the vibration can be effectively attenuated for the same loss factor by making the natural frequencies more different from each other (in particular, via increasing the stiffness of the second spring).

**Comments:** 17 Pages.

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### Submission history

[v1] 2016-12-02 19:09:43

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