I am trying to do some harmonic analysis , I have to select the most effective natural modes. I have the modal matrix (natural modes eigen vectors), but I am confused between many techniques. some techniques depend on selection of modes based on orthogonality of modes. while some techniques depend on independency of the modes like (Modal Independence Factor (MIF), Modal Independence Index (MII), and Modal Assurance Criterion (MAC)).
Are there any other techniques ? and which of them consider the most effective and feasible technique ? and if it is possible to include a literature for such method ?
Seyed Reza Jafari
this step is already done to select the primary set of " natural modes" .
I am now trying to select the most independent modes to minimize the computational effort ( since it is possible to have two modes with high mass participation factor but dependent on each other , so rejecting one of them will not affect the results)
I do not know the details of the different methodes you mention, but i know that the matematics behind vibration modes, requires them to be orthogonal, otherwise they would not be modes. If orthogonality is skipped, it will be ODS-analysis.
The success of a measurement (modal analysis) or a calculation (FEA, you do not state what you do of these) is probably more dependant of other factors than these details in the modal fitting porocedure. On intuition I‘d guess it does not matter which method you choose, or just try the different ones and see what you get. Both measurements and calculations is much about doing a «good handicraft» and, as stated above, is likely to be more dependant on other factors than the exact methodes in the routines. If the data «suck» and routine will «suck», if the measurements are very good, they will be pretty robust in the analysis.
The modes shapes of a system are orthogonal to each other but with respect to mass and stiffness matrix of the system. Therefore, they are not directly orthogonal to each other. MAC or other approaches do not determine whether the modes are independent from each other. They only give how close the one vector (mode shape vector) to another vector (mode shape vector). MAC value clsoe to 1 means that they the two vectors (in this case modes) are very close to each other; hence, they can be treated as the same modes. MAC value close to 0 means that they are different modes. Therefore, these approaches are used to identify whether a mode obtained from two different approaches (two different programs, analytical versus experimental, etc.) are the same modes or not. However, they do not give any idea about whether the mode shapes are orthogonal or not, since orthogonality is defined based on the mass and stiffness matrices of the system.
There two things to be considered for the determination of which modes will participate in the response.
1) First is the frequency range of the excitation acting on the system. Neglecting the damping the system consider the 1/(wr^2-w^2) term for each mode r for the frequency range of interest. You can eliminate the modes which have very small values (use threshold value) from your solution.
2) Second is the forcing itself. Where it is applied and which modes it can excite. You can simply calculate the modal forcing term i.e. Phi_r^T*F as if the force is constant. Eliminate the modes selected based on the first criteria if modal forcing is very small (use threshold value). Then use the remaining modes in your analysis.
If you want, you can combine them to get a simple expression.
Prof Ender Cigeroglu has nicely detailed it. Most of the times, people get trapped under the auspices of modal participation / effective modal mass from FEA software, which are applicable only for base excitation problems (like seismic excitations). However I am not sure whether the softwares can provide a effective modes / effectiveness for forcing excitation types of problems.
Murugan Jeyaselvan
many thanks for your help, I could now have a clear vision, would you please help me with some references, researches, or papers around this crucial issue to cite them in my research work ?
Regards
- Badges
- Science topic