frequency ( 1ω) of the 1 st model: ( ) c c ω ω / 1Ω =Ω = . This phenomenon is called ‘resonance’. To avoid the resonance, an additional one-degree-of freedom mass-spring-damper system is attached to the original system as shown in Fig. 1b, and the natural frequency 2Ω of the additional system is adjusted to that of the original system: 2 1Ω =Ω =Ω c . The reason why the physical treatment can reduce the vibration magnitude is that the additional system modifies the frequency response function of 1 1 / X F as shown in Eq. (5a): an anti-resonance frequency is created at the excitation force frequency due to natural frequency adjustment for the additional system as shown in Fig. 2. In many engineering environments, however, a forced vibration response is disregarded as resonance phenomenon or incorrectly simplified models are used for theoretical vibration analysis and reduction. That is, the natural frequency adjustment always does not yield an anti-resonance frequency at an excitation frequency resulting in response reduction at the excitation frequency. To point out these errors, in the following subsection, some equations are developed for two-degree-offreedom mass-spring-damper system. Dynamic Absorber Design for Two-degree-of-freedom Systems The 3rd model is a simplified vibration model representing low-frequency vibration characteristics of linear compressors, and the 4th model is considered to reduce high level vibration response due to resonance phenomenon. As a similar way in the previous subsection, two frequency response functions for the 3rd and 4th models are derived respectively as follows: ( ) ( ) ( ) ( ) 2, 2 2 2 21 2, 2 1, 1 2, 2 21 2 2 1 1 ζ ζ ζ ζ ⋅ Ω Ω − ⋅Ω ⋅ Ω ⋅ Ω ⋅ = K G H H K G F k X (7a) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2, 2 3, 3 2 3 31 3, 3 2, 2 2 2 21 3, 3 2, 2 1, 1 3, 3 2, 2 21 2 2 1 1 ζ ζ ζ ζ ζ ζ ζ ζ ζ ⋅ ⋅ − ⋅Ω⋅Ω Ω − ⋅Ω⋅Ω Ω ⋅ ⋅ Ω Ω Ω ⋅ ⋅ Ω Ω ⋅ = K G H K G H H H H K G H F k X (7b) If an extremely high response happens due to * 2 ω ω = c , only frequency adjustment ( 3 * 2 Ω =Ω =Ω c ) can yield vibration reduction as shown in Fig. 3a. How277
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