Unformatted text preview: Summary – FRFs and Time History for a Two
DOF System The transfer function for block 1 for the two
DOF shown below: +
+
x1
x2
K
k
f(t)
M
m
C
c
has been shown to have the form (for M = m , C = c and K = k ): X1 ( s )
ms 2 + cs + k
G (s) =
=
2
F (s)
ms 2 + 2 cs + 2 k ms 2 + cs + k − ( cs + k ) ( )( ) For harmonic input f ( t ) = F0 sinω t , the steady
state response for block 1 can be written in terms of its amplitude and phase frequency response functions (FRFs) as: x1, ss ( t ) = F0 G ( jω ) sin (ω t + ∠G ( jω )) The movie that follows presents the amplitude FRF G ( jω ) vs. ω (shown as a log log plot) and the time history x1, ss ( t ) over a range of excitation frequencies ω . As you view this movie consider the following three frequencies and the response near those frequencies: • The amplitude FRF G ( jω ) demonstrates peaks for two frequencies. These two peaks occur at two frequencies (known as the resonant frequencies) that are near the imaginary parts of the poles of the transfer function. The time history shows a large amplitude of response around the resonant frequencies. • The amplitude FRF G ( jω ) demonstrates a minimum for a frequency (known as the anti
resonant frequency) between the two resonant frequencies. This anti
resonant frequency is near the imaginary part of the zeros of the transfer function. The time history shows very small amplitude of response near the anti
resonance. ...
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 Fall '10
 Meckle
 Trigraph, Tier One, the00

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