Conceptual Design Strategy of Dynamic Absorber The dynamic elements denoted by subscripts ‘2’ in Fig. 1b consist of an additional harmonic mechanical system connected to the 1st model in Fig. 1a to reduce the extremely high response displacement when the excitation force frequency coincides with natural frequency of the 1st model. For the two simple models in Fig. 1a and 1b, frequency response functions are derived with basic equations of motion to explain the concept of dynamic absorber design The vibration displacement ( ) x t i of the 1 st model excited by an external force ( ) f t i in Fig. 1a is governed by ( ) ( ) ( ) ( ) f t m x t c x t k x t i i i i i i i ⋅ + ⋅ + ⋅ = & && , (1) where im, ic , and ik are mass, damping coefficient and spring constant. Assuming the harmonic motion of the external force and the displacement ( ( ) j t i if t F e ω = ⋅ , ( ) j t i ix t X e ω ⋅ = ), Eq. (1) is converted to the following equation: { } i i i i ik m j c X F ⋅ = ⋅ + − ω ω 2 , (2) where ω is an angular frequency. The frequency response function of the 1st model is ( ) i i i i i i j F k X ω ω ω ω ζ ⋅ + − = 2 / / 1 1 1 2 , (3) where i i i k m/ =ω and i i i i c k/ 1/2⋅ ⋅ = ζ ω are the natural frequency and the damping ratio of the 1st model, respectively. Assuming the harmonic motions of vibration displacements and the external force ( ( ) j t x t X e ω ⋅ = 1 1 , ( ) j t x t X e ω ⋅ = 2 2 , ( ) j t f t F e ω = ⋅ 1 1 ) in Fig. 1b, the vibration equation for the 2nd model is expressed in a matrix form: ( ) = − + − − − − + − + + 0 1 2 1 2 2 2 2 2 2 2 2 1 2 2 1 2 1 F X X j c k m k j c k j c j c c k k m ω ω ω ω ω ω . (4) In this system, one can obtain the following two frequency response functions: 275
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