Journal of the Korea Institute of Information and Communication Engineering (한국정보통신학회논문지)

The Korea Institute of Information and Commucation Engineering (한국정보통신학회)
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DMD based modal analysis and prediction of Kirchhoff-Love plate

DMD기반 Kirchhoff-Love 판의 모드 분석과 수치해 예측

  • 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)
  • Received : 2022.09.30
  • Accepted : 2022.10.12
  • Published : 2022.11.30
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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.

Kirchhoff-Love 판 (KLP) 방정식은 특정 외력이 얇은 막에 끼치는 변형을 기술하는 잘 알려진 이론이다. 한편, frequency 도메인에서 진동하는 판을 해석하는 것은 주요 진동 주파수와 고유함수들을 구하는 것과 판의 진동을 예측하는데 중요하다. 다양한 모드 분석 방법들 중 dynamic mode decomposition (DMD)는 효율적인 data 기반 방법이다. 이 논문에서 우리는 DMD를 기반으로 sine 유형 외력의 영향력 안에 있는 KLP의 모드 분석을 수행한다. 우리는 먼저 유한차분법을 사용하여 이산적으로 표현된 시계열 형식의 KLP 해를 구한다. 720,00개의 FDM으로 생성된 해중에서, 오직 500개의 해만을 DMD의 구현을 위해 선택한다. 우리는 결과적으로 얻어진 DMD-mode를 보고한다. 또한, DMD를 통하여 KLP의 해를 예측하는 효율적인 방법을 소개한다.

Keywords

Acknowledgement

The second author is supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (NO. 2020R1C1C1A01005396).

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