We all know that damping can represent by Damping ratio and Natural frequency .
We can represent the damping in terms of ( ''Linear stiffness - The first term in the nonlinear stiffness ) Under small deflection conditions. However, It is not reasonable to use this method under the condition of large displacement .
Please help me to solve this problem, or provide some relevant literature .thanks
Dear Dong
The problem of using classical damping is that the damping forces will be calculated based on the structure initial (elastic) stiffness matrix, while the actual damping should be calculated using the updated one (nonlinear). Therefore when hinges are formed at the vicinity of joints, the moment remains relatively constant (Mp) while the damping forces will increase linearly and result in unbalanced moments that are developed at the joints and will over damp the structure (decreases the displacement demands and increases columns force demands).
To eliminate this, you have some options:
1- Using tangent stiffness: there are some methods for that, and all have pros and cons (visit OpenSees wiki).
2- implementing modal damping, which provides a diagonal damping matrix. Thus no extra force exists in the rotational degree of freedoms (location of plastic hinges). This method is suitable for MRFs, but for BFs, there are some serious questions. (Please see Chopra and Mckenna)
3- Employing Zareian and Medina model that modifies the Rayleigh stiffness matrix by eliminating the rotational DOFs damping forces. This model is also accurate for modeling MRFs.
All the mentioned methods are available in OpenSees.
Good Luck
Hi DR DONG: The classical time domain and frequency domain methods of damping identification are not be suitable to the structures with nonlinear stiffness. https://www.jvejournals.com/article/14835
I hope the input helps. Regards--
Dear Dong
The problem of using classical damping is that the damping forces will be calculated based on the structure initial (elastic) stiffness matrix, while the actual damping should be calculated using the updated one (nonlinear). Therefore when hinges are formed at the vicinity of joints, the moment remains relatively constant (Mp) while the damping forces will increase linearly and result in unbalanced moments that are developed at the joints and will over damp the structure (decreases the displacement demands and increases columns force demands).
To eliminate this, you have some options:
1- Using tangent stiffness: there are some methods for that, and all have pros and cons (visit OpenSees wiki).
2- implementing modal damping, which provides a diagonal damping matrix. Thus no extra force exists in the rotational degree of freedoms (location of plastic hinges). This method is suitable for MRFs, but for BFs, there are some serious questions. (Please see Chopra and Mckenna)
3- Employing Zareian and Medina model that modifies the Rayleigh stiffness matrix by eliminating the rotational DOFs damping forces. This model is also accurate for modeling MRFs.
All the mentioned methods are available in OpenSees.
Good Luck
Dear Dong,
Damping ratio can be set to less than 0.5 or equal in case of critical or under damped condition. Ansys workbench for non linear analysis with either large deformation or large rotation or stress stiffening or stress tensioning there is an option called damping coefficient where in the value can be fed. So you can explore the option...
Virtually all damping properties you can find in literature is modal damping coefficients. They can be used in time domain through a Rayleigh damping model, but that demands linearity. If your non-linearity is due to elastic buckling, then a Rayleigh damping model based on modal damping coefficients may still be ok, but, if your non-linearities are caused by plastification, then such an approach will not be good enough. In that case you will have to use a stepwis update of damping as well as stiffness, together with incremental control of equilibrium between internal and external forces. Some information may be found in literature, it has briefly been touched upon in my textbook «Structural dynamics», Springer Verlag, 2014, but you may have to dig deeper, because in the plastic domain damping hysteresis is strongly material as well as system dependent.
Thank you so much to everyone for your efforts and sharing. Thanks to professor Ijaz, the document you provided was particularly useful. But, the Methods in the literature depends on the accuracy of the experiment and we can't really parse this damping very well. Thanks to professor Arun, The finite element method may be useful but we lack the relevant skills and experience. I'm more interested in what professor Shayan and Einar suggested. I hope to find the relationship between damping and nonlinear stiffness change and wish that through the updated stiffness matrix to solve my problem.
Thank you again.
- Badges
- Science topic
- Similar topics
- Philosophy
- Philosophy Of Science
- Reasoning