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modal damping ratio for viscoelastic material
Mon, 2010-07-19 12:59 - huangyun99
Hi, I am wondering if anyone can give me suggestion on the following problem.
I would like to do Frequency response study on a viscoelastic material. The frequency response computation usually takes a modal damping ratio. However the viscoelatic material is defined by K (elastic bulk modulus), G0 (short-time shear modulus), Gi (long-time shear modulus) and Beta (decay constant).
Is there a way to find the modal damping ratio from the time domain viscoelastic material parameters (K, G0, Gi and Beta)? E.g. in a FEM environment?
Thanks.
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modal damping ratio for viscoelastic material
Instead of doing a mode-based frequency response analysis, consider a more general subspace based analysis where the nonlinear stiffness and damping matrices are calculated as in a full harmonic analysis, and then projected onto a reduced subspace. That way, the storage and loss moduli associated with the Prony series time-domain viscoelastic parameters (G0, Gi, beta_i) will be handled automatically.
Abaqus has one called "Subspace-based steady state dynamic analysis". It is similar to the mode-based analysis in one key issue: it solves on the projected modal degrees of freedom rather than the nodal ones, so it involves a small system of equations. The equations are not diagonal however as in the mode-based analysis, but it still computationally efficient. Ansys has a "Reduced Method" for harmonic response analysis. I haven't used it but it seems a little different.
Also, if you stick with mode-based frequency response analysis, then one way to get an approximate modal damping from other forms of damping, including viscoelastic materials, is the "Modal Strain Energy Method".
Nagi Elabbasi