Unsteady Elastic-Diffusion Oscillations of a Simply Supported Kirchhoff Plate Under the Distributed Transverse Load Action

  • O. A. Afanasieva
  • A. V. ZemskovEmail author
Conference paper
Part of the Structural Integrity book series (STIN, volume 16)


We study unsteady vibrations of a isotropic Kirchhoff plate considering mass transfer. In the general case, the plate is subjected to tensile and shear forces as well as bending moments and torque. Densities of diffusion fluxes are also defined. For the problem formulation, we use the coupled elastic diffusion continuum model in a rectangular Cartesian coordinate system. Further, the unsteady model of an elastodiffusive Kirchhoff plate is obtained using the d’Alembert variational principle. The solution is sought in integral form. To find the Green’s functions, we use the Laplace integral transform and Fourier series expansion.


Elastic diffusion Coupled problem Unsteady problem Integral transformation Multicomponent continuum Kirchhoff plate Green’s function 


  1. 1.
    Zemskov, A.V., Tarlakovskii, D.V.: Model nestatsionarnykh uprugodiffuzionnykh kolebaniy plastiny Kirchhoffa. XII Vserossiyskiy syezd po fundamentalnym problemam teoreticheskoy i prikladnoy mekhaniki: sbornik trudov v 4 tomakh. T. 3: Mekhanika deformiruyemogo tverdogo tela, pp. 906–909, Ufa, RITs BashGU (2019). In Russian).

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Moscow Aviation Institute (National Research University)MoscowRussia
  2. 2.Institute of MechanicsLomonosov Moscow State UniversityMoscowRussia

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