Logarithmic Decrement 2

[SKJoe]

Hi,

i need to perform transient dynamic analysis of railway bridge and results compare with measurement. But in this field i am a new one. I have already studied some stuff in ansys help. I want to include some damping via alpha and beta coefficients of Rayleigh Damping formulation. To compute alpha and beta i need to know logarithmic decrement to comtute damping ratio... I have studied "VM72" from ansys manual and realized that some value c = 0.12 lb-sec/in is applied. The problem is that i dont know where to pick this value up from. The worst thing is that i acctually even dont know its meaning - may be some structural damping ? But how to calculate it ?

Can someone help ?
Regards,
lubo

 

[meshparts]

Hello,

The damping constant c is the velocity multiplier in the equation of motion of a freely vibrating spring-mass-viscous damping system:

m*x(t)''+c*x(t)'+k*x(t)=0

You can divide the equation of motion by the mass m:

x(t)''+c/m*x(t)'+k/m*x(t)=0

The coefficient of x(t) is the square root of the undamped eigen frequency:

k/m=omega^2

leading to

omega=sqrt(k/m)

The damping ratio is defined as

zeta=c/(2*m*omega)

So the coefficient of x(t)' can also be written as

c/m=2*zeta*omega

The logarithmic decrement is defined as

Lambda=2*pi*zeta/sqrt(1-zeta^2)

For small damping you can approximate the logarithmic decrement by

Lambda=2*pi*zeta

If you know the logarithmic decrement from measurements, then you can compute the damping constant c by:

c=1/pi*m*omega*Lambda

But: You don't know the mass m. This is no problem, since you can define the modal damping by using the command MDAMP. The modal daming is the zeta factor. So

zeta=Lambda/(2*pi)

mdamp,,zeta

So in my opinion it a better way to simulate damping by modal damping. This is a far better method than the Rayleigh Damping, if you know the log decrements from measurements.

Hope it helps!

Regards,
Alex

 

[SKJoe]

Hi,

Thank you for your exhausting answer. I have a measurement but, i am afraid that i am not able to get logarithmic decrement from it. The bridge is relatively short (24m only, an engine has 11.5m from the first axle to the last). The weight of the engine is relatively small compare to weight of the bridge. Furthermore there is railway ballast (it means granular material) on it. So i can not see any sine wave after engine is behind the bridge - there is almost straight line of record. I think I will perform only static anylisis first, and if the there is big discrepancy between fem results/measurement I will perform transient analysis without damping as a second alternative. If still the fem results are not as desired i will try to find some empirical formulae to calculate the decrement, or i do a trial-and-error analysis with various zeta values as a third alternative.
But thank you anyway - if i am able to get this logarithmic decrement somehow i will try this modal damping instead Rayleigh damping.

Regards,
lubo

 

[meshparts]

Hello,

What kind of measurements do you have: frequency or time range.

If you have the frequency response of the bridge, you can directly get your modal damping factors from the measurements using the very simple but effective Half Bandwidth Method.

If you have the time response of the freely vibrating bridge,then you can get the logarithmic decrement also very easy from the amplitude of two Peaks of the time response and the Period of the vibration. The Formula is:

Lambda=ln(A1/A2)

where A1 and A2 are the amplitudes two by one period separated peaks.

Regards,
Alex

 

[SKJoe]

Hi,

ok, when i wrote that i am a new one i didnt mean that i dont have any theoretical basics. Before i wrote this thread i have recalled the basics. So i know the formula for logarithmic decrement. As i wrote previously the problem is that when the engine has left the bridge (the time response of the freely vibrating bridge) there is almost linear record. Ok, there are some sine waves but values are in tolerance range of strain gauges...
i have time response - each 1/50 s is recorded one value.

Regards,
lubo