The energy dissipated in hysteresis damping per cycle under harmonic excitation can be expressed in the general form

where \(\gamma\) is an exponent \((\gamma=2\) was considered in Eq. (2.150)), and \(\beta\) is a coefficient of dimension (meter \()^{2-\gamma}\). A spring-mass system having \(k=60 \mathrm{kN} / \mathrm{m}\) vibrates under hysteresis damping. When excited harmonically at resonance, the steady-state amplitude is found to be \(40 \mathrm{~mm}\) for an energy input of \(3.8 \mathrm{~N}-\mathrm{m}\). When the resonant energy input is increased to \(9.5 \mathrm{~N}-\mathrm{m}\), the amplitude is found to be \(60 \mathrm{~mm}\). Determine the values of \(\beta\) and \(\gamma\) in Eq. (E.1).

Transcribed Image Text:

AW = kXY (E.1)