I’m familiar with the experimental methods to determine the damping ratio of a material, but I’m wondering if there’s an alternative way to calculate it using mechanical properties alone.

For example, stiffness (K) can be derived using the formula K= (A*E)/L, where A is the area, E is the modulus of elasticity, and L is the length. I’m curious if there’s a similar approach for damping ratio? Assume we don’t know the Damping Co-efficient or factor.

The damping ratio is more of a global property of a particular system. You can think of it as a callibration knob for linear dynamic structural models (such as those using FEA), to make them match the actual dynamics of a system.

It is in general measured by experimental methods because there are so many factors that can affect it, that it is not practical to deduct it from analytical models. For example:

Dynamics of the structure (natural modes of vibration and frequencies)

Friction between the parts (materials, surface finish, lubrication, etc)

Internal material dissipation (molecular forces, friction)

So the common practice is to use experimental data to estimate the damping ratio(s), then infer material properties such as the loss modulus. The other way around is not usually done.

Another usual approach is to use values of similar systems or materials, which can be found in tabulated data.

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