MATLAB codes accompanying the article "An Energy Closure Criterion for Model Reduction of a Kicked Euler-Bernoulli Beam"

**MATLAB source code accompanying the forthcoming research article in the Journal of vibration and acoustics:

Bhattacharyya, S., and Cusumano, J. P. (November 2, 2020). "An Energy Closure Criterion for Model Reduction of a Kicked Euler–Bernoulli Beam." ASME. J. Vib. Acoust. August 2021; 143(4): 041001.

https://doi.org/10.1115/1.4048663

**Code description: This MATLAB code generates Figs. 5c, 5d, and Figs. 7 of the Paper, for the set of parameter values mentioned in the paper.

The code also calculates the energy balance error and modeling errors for the Euler-Bernoulli beam in various situations, with different parameter values.

**Contact: Suparno Bhattacharyya (suparno.bhattacharyya@gmail.com), Penn State University.

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Work Title MATLAB codes accompanying the article "An Energy Closure Criterion for Model Reduction of a Kicked Euler-Bernoulli Beam"
Access
Open Access
Creators
  1. Suparno Bhattacharyya
Keyword
  1. energy closure analysis
  2. structural vibrations
  3. reduced order model (ROM)
  4. dynamical systems
  5. proper orthogonal decomposition (POD)
  6. model order reduction
License Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)
Work Type Article
Publisher
  1. ASME
Publication Date November 2, 2020
DOI doi:10.26207/2g7h-hd43
Publisher Identifier (DOI)
  1. https://doi.org/10.1115/1.4048663
Deposited September 11, 2020

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Version 2
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  • Updated Description Show Changes
    Description
    • Abstract: Reduced order models (ROMs) can be simulated with lower computational cost while being more amenable to theoretical analysis. Here, we examine the performance of the proper orthogonal decomposition (POD), a data-driven model reduction technique. We show that the accuracy of ROMs obtained using POD depends on the type of data used and, more crucially, on the criterion used to select the number of proper orthogonal modes (POMs) used for the model. Simulations of a simply supported Euler-Bernoulli beam subjected to periodic impulsive loads are used to generate ROMs via POD, which are then simulated for comparison with the full system. We assess the accuracy of ROMs obtained using steady-state displacement, velocity, and strain fields, tuning the spatiotemporal localization of applied impulses to control the number of excited modes in, and hence the dimensionality of, the system's response. We show that conventional variance-based mode selection leads to inaccurate models for sufficiently impulsive loading, and that this poor performance is explained by the energy imbalance on the reduced subspace. Specifically, the subspace of POMs capturing a fixed amount (say, 99.9%) of the total variance underestimates the energy input and dissipated in the ROM, yielding inaccurate reduced-order simulations. This problem becomes more acute as the loading becomes more spatio-temporally localized (more impulsive). Thus, energy closure analysis provides an improved method for generating ROMs with energetics that properly reflect that of the full system, resulting in simulations that accurately represent the system's true behavior. MATLAB source code accompanying the forthcoming research article in the Journal of vibration and acoustics: Bhattacharyya Suparno, Cusumano, Joseph P., 2020, "An Energy Closure Criterion for Model Reduction of a Kicked Euler-Bernoulli Beam", Journal of vibration and acoustics. Contact: Bhattacharyya Suparno (sxb1086@psu.edu), Penn State University Code description: This MATLAB code generates Figs. 5c, 5d, and Figs. 7 of the Paper, for the set of parameter values mentioned in the paper. The code also calculates the energy balance error ($e_W$) and modeling errors ($\widehat{e}_d$) and ($\widehat{e}_v$) for the Euler-Bernoulli beam in various situations, with different parameter values.
    • **MATLAB source code accompanying the forthcoming research article in the Journal of vibration and acoustics:
    • Bhattacharyya, S., and Cusumano, J. P. (November 2, 2020). "An Energy Closure Criterion for Model Reduction of a Kicked EulerBernoulli Beam." ASME. J. Vib. Acoust. August 2021; 143(4): 041001.
    • https://doi.org/10.1115/1.4048663
    • --------------------
    • **Code description: This MATLAB code generates Figs. 5c, 5d, and Figs. 7 of the Paper, for the set of parameter values mentioned in the paper.
    • The code also calculates the energy balance error and modeling errors for the Euler-Bernoulli beam in various situations, with different parameter values.
    • --------------------
    • **Contact: Suparno Bhattacharyya (suparno.bhattacharyya@gmail.com), Penn State University.
  • Updated Work Title Show Changes
    Work Title
    • An Energy Closure Criterion for Model Reduction of a Kicked Euler-Bernoulli Beam
    • MATLAB codes accompanying the article "An Energy Closure Criterion for Model Reduction of a Kicked Euler-Bernoulli Beam"
  • Updated Creator Suparno Bhattacharyya
  • Updated License, Publisher, Publisher Identifier (DOI), and 1 more Show Changes
    License
    • https://creativecommons.org/licenses/by-nc-nd/4.0/
    • https://creativecommons.org/licenses/by-nc/4.0/
    Publisher
    • ASME
    Publisher Identifier (DOI)
    • https://doi.org/10.1115/1.4048663
    Publication Date
    • 2020-11-02
  • Published