Browse > Article
http://dx.doi.org/10.6109/jkiice.2022.26.11.1586

DMD based modal analysis and prediction of Kirchhoff-Love plate  

Shin, Seong-Yoon (School of Computer Information & Communication Engineering, Kunsan National University)
Jo, Gwanghyun (Department of Mathematics, Kunsan National University)
Bae, Seok-Chan (School of Computer Information & Communication Engineering, Kunsan National University)
Publication Information
Journal of the Korea Institute of Information and Communication Engineering / v.26, no.11, 2022 , pp. 1586-1591 More about this Journal
Abstract
Kirchhoff-Love plate (KLP) equation is a well established theory for a description of a deformation of a thin plate under certain outer source. Meanwhile, analysis of a vibrating plate in a frequency domain is important in terms of obtaining the main frequency/eigenfunctions and predicting the vibration of plate. Among various modal analysis methods, dynamic mode decomposition (DMD) is one of the efficient data-driven methods. In this work, we carry out DMD based modal analysis for KLP where thin plate is under effects of sine-type outer force. We first construct discrete time series of KLP solutions based on a finite difference method (FDM). Over 720,000 number of FDM-generated solutions, we select only 500 number of solutions for the DMD implementation. We report the resulting DMD-modes for KLP. Also, we show how DMD can be used to predict KLP solutions in an efficient way.
Keywords
Dynamic mode decomposition; Kirchhoff-Love plate; Modal analysis; Data-driven simulation;
Citations & Related Records
연도 인용수 순위
  • Reference
1 E. Enferad, C. Giraud-Audine, F. Giraud, M. Amberg, and B. L. Semail, "Generating controlled localized stimulations on haptic displays by modal superimposition," Journal of Sound and Vibration, vol. 449, pp. 196-213, Jun. 2019.   DOI
2 P. J. Schmid, "Dynamic mode decomposition of numerical and experimental data," Journal of fluid mechanics, vol. 656 pp. 5-28, Jul. 2010.   DOI
3 P. J. Schmid, L. Li, M. P. Juniper, and O. Pust, "Applications of the dynamic mode decomosition," Theoretical and Computational Fluid Dynamics, vol. 25, pp. 249-259, Aug. 2010.   DOI
4 G. Jo, Y. -J. Lee, and I. Ojeda-Ruiz, "2D and 3D image reconstruction from slice data based on a constrained bilateral smoothing and dynamic mode decomposition," Applied Mathematics and Computation, vol. 420, no. 126877, May 2022.
5 D. N. Arnold, A. L. Madureira, and S. Zhang, "On the Range of Applicability of the Reissner-Mindlin and Kirchhoff-Love Plate Bending Models," Journal of elasticity and the physical science of solids, vol. 67, no. 3, pp. 171-185, Jun. 2002.   DOI
6 D. Kropiowska, L. Mikulski, and P. Szeptynski, "Optimal design of a Kirchhoff-Love plate of variable thickness by application of the minimum principle," Structural and Multidisciplinary Optimization, vol. 59, no. 5, pp. 1581-1598, Nov. 2018.   DOI
7 P. Hansbo and M. G. Larson, "A posteriori error estimates for continuous/discontinuous Galerkin approximations of the Kirchhoff-Love plate," Computer Methods in Applied Mechanics and Engineering, vol. 200, no. 47-48, pp. 3289-3295, Nov. 2011.   DOI
8 D. Mora and I. Velasquez, "Virtual element for the buckling problem of Kirchhoff-Love plates," Computer Methods in Applied Mechanics and Engineering, vol, 360, no. 112687, Mar. 2020.