7/23/2019 Estimation of Damping by Logdecrement

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How do you f in d the log decrement and how i s it related to the damping ratio?

The logarithmic decrement represents the rate at which the amplitude of a free damped vibration decreases. It isdefined as the natural logarithm of the ratio of any two successive amplitudes. It is found from the time response of

underdamped vibration (oscilloscope or real-time analyzer).

Response of damped free vibration

)cos()( = tAetxd

tn

11

tnAeX = , ( )dnn Ttt AeAeX + == 122

( )dn

dn

nT

Tt

t

e

Ae

Ae

X

X

== +

1

1

2

1

222

1

1

2

1

2

ln

TX

X

n

ndn

====

If 12