***INVESTIGATING ON THE POWER SPECTRAL
DENSITY OF DUFFING’S EQUATION
BY EQUIVALENT LINEARIZATION METHOD
By CO .
H .
TRAN .
Faculty of Mathematics & Informatics , University of Natural Sciences – VNU-HCM
Abstract :
We consider the non-linear...
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***INVESTIGATING ON THE POWER SPECTRAL
DENSITY OF DUFFING’S EQUATION
BY EQUIVALENT LINEARIZATION METHOD
By CO .
H .
TRAN .
Faculty of Mathematics & Informatics , University of Natural Sciences – VNU-HCM
Abstract :
We consider the non-linear random vibration model demonstrated by the Duffing’s differential
equation :
)( 2" 32
00 tfxxxx =+++ μβωξω
(*)
The stationary random process is f( t) which is satisfied < f(t) > = 0
with the spectral density function Sf ( ω ) .
To find the solution Sx ( ω ) of (*) we use the
equivalent linearization method .
1/.
Model Definition :
The non-linear random vibration model includes the mass (m) - dashpot (c) -spring (k)
( fig.
1 ) .
This model moves on the rough surface which is described by the random variable y(s)
with the constant velocity v .
If we have the relation s = vt and the mass m is also
influenced under the non-linear stimulating force , then the vibration differential equation
of the mass m can be rewritt
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