Lecture 6 CK - MECHANICAL VIBRATIONS BMM3553 LECTURE 6 CHE...

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MECHANICAL VIBRATIONS BMM3553 LECTURE 6 CHE KU EDDY NIZWAN BIN CHE KU HUSIN
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Today’s Objectives Students will be able to: Determine the Response of damped system under harmonic motion Solve the problem related to damped SDOF Force vibration
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Response of a Damped System Under Harmonic Force The equation of motion for damped system is t F kx x c x m cos 0 t X t x p cos solution particular the Let, t X t x t X t x p p cos and sin 2 t F t kX t cX t mX cos cos sin cos 0 2
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Response of a Damped System Under Harmonic Force The equation of motion The solution gives and t F t c t m k X cos sin cos 0 2 0 cos sin sin cos 2 0 2 c m k X F c m k X 2 / 1 2 2 2 2 0 c m k F X 2 1 tan m k c
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The figure shows typical plots of the forcing function and steady-state) response. Substituting the following, ; m k n ; 2 n m c  ; 0 k F st n r
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and We obtain 2 2 2 2 / 1 2 2 2 ) 2 ( ) 1 ( 1 2 1 1 r r X n n st 2 1 2 1 1 2 tan 1 2 tan r r n n
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The following characteristics of the magnification factor (M) can be noted from figure and as follows: c n st C c X M r ,
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1. For a undamped system, Reduces to (undamped system) And 0 2 2 2 2 / 1 2 2 2 ) 2 ( ) 1 ( 1 2 1 1 r r X n n st ) 1 ( 1 1 1 2 2 r X M n st  M r r n then, 1 i.e. 1
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2. Any amount of damping ( ) reduces M for all values of F ( t ) 3. For any specified value of r , a higher value of damping reduces value of M 4. In the degenerate case of a constant force ( when r = 0), the value of M = 1.
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