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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (9): 1143-1151.doi: https://doi.org/10.1007/s10483-009-0908-2

• Articles • 上一篇    下一篇

A convolution-type semi-analytic DQ approach to transient response of rectangular plates

彭建设1,2 杨杰3 袁玉全4 罗光兵1   

  1. 1. School of Physics and Electronic Information, China West Normal University,Nanchong 637002, Sichuan Province, P. R. China;
    2. Chengdu University, Chengdu 610106, P. R. China;
    3. School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University,P. O. Box 71, Bundoora, VIC 3083 Australia;
    4. School of Science, Sichuan University of Science & Engineering, Zigong 643000,Sichuan Province, P. R. China
  • 收稿日期:2009-01-05 修回日期:2009-08-05 出版日期:2009-09-01 发布日期:2009-09-01

A convolution-type semi-analytic DQ approach to transient response of rectangular plates

PENG Jian-She1,2, YANG Jie3, YUAN Yu-Quan4, LUO Guang-Bing1   

  1. 1. School of Physics and Electronic Information, China West Normal University,Nanchong 637002, Sichuan Province, P. R. China;
    2. Chengdu University, Chengdu 610106, P. R. China;
    3. School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University,P. O. Box 71, Bundoora, VIC 3083 Australia;
    4. School of Science, Sichuan University of Science & Engineering, Zigong 643000,Sichuan Province, P. R. China
  • Received:2009-01-05 Revised:2009-08-05 Online:2009-09-01 Published:2009-09-01

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摘要： The convolution-type Gurtin variational principle is known as the only variational principle that is, from the mathematics point of view, totally equivalent to the initial value problem system. In this paper, the equation of motion of rectangular thin plates is first transformed to a new governing equation containing initial conditions by using a convolution method. A convolution-type semi-analytical DQ approach, which involves differential quadrature (DQ) approximation in the space domain and an analytical series expansion in the time domain, is proposed to obtain the transient response solution. This approach offers the same advantages as the Gurtin variational principle and, at the same time, is much simpler in calculation. Numerical results show that it is very accurate yet computationally efficient for the dynamic response of plates.

关键词: convolution, transient response, differential quadrature method, semianalytical method

Abstract: The convolution-type Gurtin variational principle is known as the only variational principle that is, from the mathematics point of view, totally equivalent to the initial value problem system. In this paper, the equation of motion of rectangular thin plates is first transformed to a new governing equation containing initial conditions by using a convolution method. A convolution-type semi-analytical DQ approach, which involves differential quadrature (DQ) approximation in the space domain and an analytical series expansion in the time domain, is proposed to obtain the transient response solution. This approach offers the same advantages as the Gurtin variational principle and, at the same time, is much simpler in calculation. Numerical results show that it is very accurate yet computationally efficient for the dynamic response of plates.

Key words: convolution, transient response, differential quadrature method, semianalytical method

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