数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (2): 511-526.doi: 10.1016/S0252-9602(17)30018-8

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NONLINEAR ANALYSIS ON THE VIBRATION OF ELASTIC PLATES

丁敏, 龚胜波   

  1. 1. Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070, China;
    2. School of Mathematical Science and School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
  • 收稿日期:2016-03-14 修回日期:2016-05-23 出版日期:2017-04-25 发布日期:2017-04-25
  • 作者简介:Min DING,E-mail:minding@whut.edu.cn;Shengbo GONG,E-mail:jiaoda20064154@sjtu.edu.cn
  • 基金资助:

    Min Ding was supported in part by Innovation Award by Wuhan University of Technology under a project Grant 20410771; Shengbo Gong was supported in part by China Scholarship Council under Grant 201306230035.

NONLINEAR ANALYSIS ON THE VIBRATION OF ELASTIC PLATES

Min DING, Shengbo GONG   

  1. 1. Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070, China;
    2. School of Mathematical Science and School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2016-03-14 Revised:2016-05-23 Online:2017-04-25 Published:2017-04-25
  • Supported by:

    Min Ding was supported in part by Innovation Award by Wuhan University of Technology under a project Grant 20410771; Shengbo Gong was supported in part by China Scholarship Council under Grant 201306230035.

摘要:

We consider the vibration of elastic thin plates under certain reasonable assump-tions. We derive the nonlinear equations for this model by the Hamilton Principle. Under the conditions on the hyperbolicity for the initial data, we establish the local time well-posedness for the initial and boundary value problem by Picard iteration scheme, and obtain the estimates for the solutions.

关键词: Vibration of elastic plates, Hamilton principle, well-posedness, Picard iteration

Abstract:

We consider the vibration of elastic thin plates under certain reasonable assump-tions. We derive the nonlinear equations for this model by the Hamilton Principle. Under the conditions on the hyperbolicity for the initial data, we establish the local time well-posedness for the initial and boundary value problem by Picard iteration scheme, and obtain the estimates for the solutions.

Key words: Vibration of elastic plates, Hamilton principle, well-posedness, Picard iteration