Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List

ETD Abstract Container

Abstract Header

Developing a correlation criterion(spaceMAC) for repeated and pseudo-repeated modes

Vinze, Pranjal Makarand

Abstract Details

2019, MS, University of Cincinnati, Engineering and Applied Science: Mechanical Engineering.
One of the most important factors in the validation of a finite element model is whether the modal vectors obtained from the finite element solution match sufficiently with the modal analysis results of the part or a test prototype. Modal assurance criterion(MAC) is usually a very effective way to check this condition. However, in case of repeated modes, MAC can give misleading results. A low MAC value could indicate that the finite element model suffers from some deficiencies or in case of closely spaced modes it could mean that these modes are repeated modes. Hence, there is a need for a method that could indicate how well the finite element method based estimates for the repeated modes correlate with the modal analysis modes. This thesis work is an attempt to develop a correlation criterion between a set of repeated roots from a finite element method solution and a experimental modal analysis solution. Building on a low dimensional modal vector example a vector subspace based approach was identified to help properly define the solution to a characteristic equation with repeated roots. This analogy was extended to higher dimension modal vector cases and vector subspace or hyper planes were identified as a way to model a repeated mode case. Similar to MAC, consistency of the solution was considered an ideal way to establish correlation. But in this case the consistency of the solution subspace was found to be more important than that of normalized modal vectors. The smallest principal angle between the two solution subspace was identified as a way of measuring the consistency. The criterion, called spaceMAC, was developed as a function of this angle such that the range of the criterion is 0 to 1, similar to MAC. SpaceMAC was defined as 1 − sin(θ) where θ is the principal angle between the two solution subspaces. The performance of this criterion was tested with experimental data sets from two different symmetric structures known to exhibit the repeated mode condition.
Randall Allemang, Ph.D. (Committee Chair)
Allyn Phillips, Ph.D. (Committee Member)
Yongfeng Xu, Ph.D. (Committee Member)
70 p.

Recommended Citations

Citations

  • Vinze, P. M. (2019). Developing a correlation criterion(spaceMAC) for repeated and pseudo-repeated modes [Master's thesis, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1553614020008611

    APA Style (7th edition)

  • Vinze, Pranjal. Developing a correlation criterion(spaceMAC) for repeated and pseudo-repeated modes. 2019. University of Cincinnati, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1553614020008611.

    MLA Style (8th edition)

  • Vinze, Pranjal. "Developing a correlation criterion(spaceMAC) for repeated and pseudo-repeated modes." Master's thesis, University of Cincinnati, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1553614020008611

    Chicago Manual of Style (17th edition)