Determine critical damping of multimass system

[tiljoachim]

Hi

I have a spring mass damper system with multiple masses. Is there any way I can calculate the magnitude of the damping in order to get a critical damped system?

I have the scaling of the dampers(c1/c2) and they are connected in series.
c_eq=c1+c2...

I tried with the formula:

ζ=1=c_eq/(2*m_eq*ω_n)

ω_n=√(k/m)

But it doesn't give the correct results so I did a FFT of the response to find the most dominating frequency and put in this new omega but without succes. Is it possible at all to determine a damping that satisfies this if the scaling(c1/c2) is to large?

 

[Achy47]

Hi there,

Thank you for reaching out with your question about calculating the magnitude of damping in a spring mass damper system. The critical damping coefficient for a system with multiple masses can be calculated using the following formula:

ζ_crit = 1 / (2 * √(m1/m_eq + m2/m_eq + ... + mn/m_eq) * ω_n)

Where m_eq is the equivalent mass of the system and ω_n is the natural frequency. The equivalent mass, m_eq, can be calculated by summing the individual masses in the system.

In order to calculate the natural frequency, ω_n, you can use the formula you mentioned:

ω_n = √(k / m_eq)

Where k is the spring constant of the system.

Once you have calculated the critical damping coefficient, you can then use this value to determine the damping ratio for the individual dampers in the system. The damping ratio, ζ, can be calculated using the following formula:

ζ = c / (2 * √(m * k))

Where c is the damping coefficient and m is the mass of the individual damper.

If the scaling of the dampers (c1/c2) is too large, it may not be possible to achieve critical damping in the system. In this case, you may need to adjust the scaling of the dampers or consider using a different type of damping system.

I hope this helps and please let me know if you have any further questions.