( ) ( ) ( ) ( ) 2, 2 2 2 21 2, 2 1, 1 2, 2 1 1 1 1 ζ ζ ζ ζ ⋅ Ω Ω − ⋅Ω ⋅ Ω Ω ⋅ = K G H H H F k X , (5a) ( ) ( ) ( ) ( ) 2, 2 2 2 21 2, 2 1, 1 2, 2 1 1 2 1 ζ ζ ζ ζ ⋅ Ω Ω − ⋅Ω ⋅ Ω Ω ⋅ = K G H H G F k X , (5b) where ( ) 2 1 21 / K k k = is the stiffness ratio and ( ) / , 1,2 = Ω = i i i ω ω is a normalized angular frequency. The symbols ( ) i i H ζ , Ω and ( ) i i G ζ , Ω are functions of the normalized angular frequency and the damping ratio: ( ) i i i i j GΩ = + Ωζ ζ , 1 2 (6a) ( ) i i i i i j H Ω = −Ω + Ωζ ζ 2 , 1 2 (6b) where 1,2 =i . 0 20 40 60 80 100 10-8 10-7 10-6 10-5 10-4 Frequency(Hz) |FRF| 1st model 2 nd model 8.4 8.45 8.5 8.55 8.6 -4 -2 0 2 4 x 10-5 Time(sec) Displacement of m1 1 st model 2nd model Fig. 2 Comparison of the 1st model and the 2nd model: (a) Frequency response functions at 1m ; and (b) time responses at 1m . cf is an excitation force frequency. If the damping ratios iζ are much less than one, the response in Fig. 2a is extremely high when the excitation force frequency ( cω) coincides with the natural 276
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