Damping constant in General flexible Beam

Hi.

I'm using the General flexible Beam model given in Simscape Multibody. In which you can define the "Damping constant (beta)" in s.

My problem is that I don't know a damping coeffizient with seconds as the unit. I want to implement results from real life experiments out of which I calculated the logarithmic decrement in s^-1.

So my main question is, what kind of damping coefficient is used in the simscape model as I want to implement my test results?

Thanks and best regards

Answer 1

[Steve Miller]

The logarithmic decrement lets you calculate the damping ratio. That would be easiest to use if you set the damping type to "Uniform Modal" where you can enter the Damping Ratio directly.

The Proportional Damping model needs coefficients to multiply by the K and M terms. Since the damping, C is calculated according to this formula:

[C]=α[M]+β[K],

you need to provide alpha with units of 1/s and beta with units of seconds to yield a damping coefficient of N*s/m or kg/s.

--Steve

[SARTHAK]

@Steve Miller

Hi Steve,

Thank you very much for your earlier response.

I’ve been working with flexible beams in Simscape Multibody for about six months now, and I had a follow-up question regarding damping modeling.

From my experiments, I have an estimated damping ratio for the beam. Instead of specifying a uniform modal damping ratio in the Flexible Beam block, would it be more appropriate to use proportional (Rayleigh) damping in this case?

Specifically, is there a systematic way to relate an experimentally identified damping ratio to the Rayleigh damping coefficients α (mass-proportional) and β (stiffness-proportional)? For example, can we determine α and β using two known natural frequencies and their corresponding damping ratios?

I would be grateful if you could elaborate on best practices for transitioning from experimentally measured damping ratios to proportional damping parameters in Simscape.