Dynamic Eigen Decomposition II: Applications

Shan Siddiqui
Shan Siddiqui
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Published 2021-09-22
Video 2 in a series about dynamic eigen decomposition (DED) theory and applications. Here we cover applications of the DED including a finite element aeroelastic wing model and an Euler equation CFD solver. Higher Order Modally Equivalent Perturbed Systems (HOMEPS) is developed to handle global parameter variations.

Review video 1 for basic theory.

   • Dynamic Eigen Decomposition I: Parame...  

Review the following publications to get ahead of the video content.

1. Kim, T., “Finding Characteristically Rich Nonlinear Solution Space: a Statistical Mechanics Approach”, International Journal of Numerical Methods in Engineering, 10.1002/nme.6310, 2020.
2. Kim T, “Flutter Prediction Based on Dynamic Eigen Decomposition and Frequency-Domain Stability”, Journal of Fluids and Structures 86 (2019) 0-13, authors.elsevier.com/a/1Yiir3..., 2019.
3. Kim, T., “Higher order modal transformation for reduced‐order modeling of linear systems undergoing global parametric variations,” International Journal for Numerical Methods in Engineering, 2018;1–22. doi.org/10.1002/nme.5905.
4. Lee, S., Kim, T., Shashank, S., “Efficiency enhancement of aeroelastic optimization process using parametric reduced order modelling”, Journal of Aerospace Engineering 2018; 31 (2): 04018004.
5. Kim, T., “Parametric model reduction for aeroelastic systems: Invariant aeroelastic modes,” Journal of Fluids and Structures, 2016, 65: 196-216.
6. Kim, T., “Surrogate model reduction for linear dynamic systems based on a frequency domain modal analysis”, Computational Mechanics, 2015, 56 (4), 709-723.
All Comments (4)
  • @johnkim3840
    Correction: Part 3. which is out already is about applications to flutter prediction and linear time-varying systems. Part 4. will be about applications to nonlinear systems.
  • @johnkim3840
    The Higher-Order MEPS is not to account for a big magnitude of Delta A but to account for a high rank of Delta A. Higher order or not, there's no limit on how big ||Delta A|| can be in the formulation.
  • @johnkim3840
    Gauge Modal Invariance (or Symmetry) = no matter what ICs, BCs, Inputs are the same set of modes can span all the solutions. In this sense, the modes are invariant to (or symmetric with respect to) the ICs, BCs, Inputs.