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The Thin Plate Equation

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Boundary Element Methods with Applications to Nonlinear Problems

Part of the book series: Atlantis Studies in Mathematics for Engineering and Science ((ASMES,volume 7))

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Abstract

The dynamic thin plate equation

$$\rho w_{tt}(x,t)+D\Delta^2w(x,t)=0,\quad x\in\Omega\subseteq {\rm R}^2, t>0,$$
(8.1)

was first proposed by Kirchhoff [112] to model the vibration of a thin plate subject to pure bending with small deflection. It is an important mathematical model in structural mechanics and seismology.

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Authors and Affiliations

  1. Mathematics and Aerospace Engineering, Texas A&M University, College Station, Texas, 77843, USA

    Goong Chen (Professor)

  2. Mathematics and Aerospace Engineering, Texas A&M University, Taipei, Taiwan, Republic of China

    Goong Chen (Distinguished Professor)

  3. Mathematics Texas A&M University, College Station, Texas, 77843, USA

    Jianxin Zhou (Professor of Mathematics)

Authors
  1. Goong Chen
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  2. Goong Chen
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  3. Jianxin Zhou
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© 2010 Atlantis Press/World Scientific

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Chen, G., Chen, G., Zhou, J. (2010). The Thin Plate Equation. In: Boundary Element Methods with Applications to Nonlinear Problems. Atlantis Studies in Mathematics for Engineering and Science, vol 7. Atlantis Press. https://doi.org/10.2991/978-94-91216-27-5_8

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