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Mode decomposition method for non-classically damped structures using acceleration responses

By: J.-S. Hwang, S.-H. Shin and H. Kim

all methods of defining damping are based on observed external phenomena and have little to no microstructural relevance. Damping in a structure can be caused by many physical responses (as simple as plasticity or hysteresis for example). Therefore, classical or non-classical are just ways to capture those in a broader sense. As long as it is used correctly, it'll give reasonable results.

Modal Analysis of Generally Damped Linear Structures Subjected to Seismic Excitations:

http://mceer.buffalo.edu/publications/catalog/reports/Modal-Analysis-of-Generally-Damped-Linear-Structures-Subjected-to-Seismic-Excitations-MCEER-08-0005.html

Modal Analysis of Arbitrarily Damped Three-Dimensional Linear Structures Subjected to Seismic Excitations:

http://mceer.buffalo.edu/publications/catalog/reports/Modal-Analysis-of-Arbitrarily-Damped-Three-Dimensional-Linear-Structures-Subjected-to-Seismic-Excitations-MCEER-09-0001.html

In some special cases that we have Non-uniform distribution of damping in different parts of a system, we need to use non-classical damping matrix of the system. For example interaction of soil-structure or interaction of fluid (water) and structure (Dam).

The 11th chapter of Chopra (maybe) can help you more.

The damping model selection is highly dependent on the structure itself. In case of structures having inconsistency in damping distribution, such as the cases of dams, soil-structure interaction models, or controlled structures (i.e. supplemental damping is utilized), in these cases, non-classical damping model is more appropriate for several reasons as follows:

Firstly,

If classical viscous damping model (for example Rayleigh model) is used, it may underestimate the response of the system in some cases and fail to capture the nonlinearity in the system (Val, V.D & Segal, F. (2005).

Secondly,

The main advantage of classical viscous damping model (for example Rayleigh model) is that the orthogonality of the modes is preserved; based on that the classical modal analysis will be, to some extent, similar to the un-damped vibration and easier in analysis. In the case of controlled structures (with dampers), due to the addition of dampers, damping becomes non-classical and the orthogonality of the modes will not be applicable. This means that using the classical damping model (Rayleigh model) will give inaccurate results, Adhikari S. (2000).

Thirdly,

The other main issue with this classical damping model (e.g. Rayleigh model) is the strong dependence on the frequency of the structure as the constants (Alpha and Beta) are evaluated as a function of the frequency. There have been a large number of studies investigating the frequency dependence of the analytical model used in practice, and interestingly the majority of these studies emphasize that material level damping highly dependent on the displacement rather than the angular frequency (Adhikari 2000).

A couple of famous non-classical damping models are “non-viscous damping models” and “frequency independent damping models”. More details can be found in Puthanpurayil etal, (2012).

The issue of simplicity needs comparative analysis study, which I do not have. This may need further investigation. I think it is better to search the more suitable damping model to your system rather than searching for the simplest one.

Ref.

Val, V.D & Segal, F. (2005). Effect of damping model on pre-yielding earthquake response of structures. Engineering Structures 27, 1968-1980.)

Adhikari S. (2000). Damping models for structural vibration. PhD Dissertation, University of Cambridge

Puthanpurayil etal, (2012), Optimal Passive Damper Positioning Techniques: State-of-the-Art”, book: Design Optimization of Active and Passive Structural Control Systems Chapter: 4