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The Schrödinger equation in theory of plates and shells with orthorhombic anisotropy

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Abstract

This work is the continuation of the discussion of Refs. [1–5]. In this paper:

  1. [A]

    The Love-Kirchhoff equations of vibration problem with small deflection for orthorhombic anisotropic thin shells or orthorhombic anisotropic thin plates on Winkler's base are classified as several of the same solutions of Schödinger equation, and we can obtain the general solutions for the two above-mentioned problems by the method in Refs. [1] and [3–5].

  2. [B]

    The, von KármánVlasov equations of large deflection problem for shallow shells with orthorhombic anisotropy (their special cases are the von Kármán equations of large deflection problem for thin plates with orthorhombic anisotropy) are classified as the solutions of AKNS equation or Dirac equation, and we can obtain the exact solutions for the two abovementioned problems by the inverse scattering method in Refs. [4–5]

.

The general solution of small deflection problem or the exact solution of large deflection problem for the corrugated or ribreinforced plates and shells as special cases is included in this paper.

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  1. University of Science and Technology of China, Hefei

    Shen Hui-chuan

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Communicated by Chien Wei-zang

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Hui-chuan, S. The Schrödinger equation in theory of plates and shells with orthorhombic anisotropy. Appl Math Mech 8, 367–376 (1987). https://doi.org/10.1007/BF02015257

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