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Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 539.3
I.T. Selezov1

DEVELOPMENT AND APPLICATION OF THE CAUCHY–POISSON METHOD
TO ELASTODYNAMICS OF LAYER

Abstract. We consider a generalization of the Cauchy–Poisson method to an n-dimensional Euclidean space and its application to the construction of hyperbolic approximations. In Euclidean space, constraints on derivatives are introduced. The principle of hyperbolic degeneracy in terms of parameters is formulated and its implementation in the form of necessary and sufficient conditions is given. As a particular case of a 4-dimensional space with preserving operators up to the 6th order and dimensioning, a generalized hyperbolic equation is obtained for bending vibrations of plates with coefficients depending only on the Poisson number. As special cases, this equation includes all the well-known equations of Bernoulli–Euler, Kirchhoff, Rayleigh, and Timoshenko. As a development of Maxwell’s and Einstein’s research on the propagation of perturbations with finite velocity in a continuous medium, the Tymoshenko’s non-trivial construction of the equation for bending vibrations of a beam is noted.

Keywords: Cauchy–Poisson method, Euclidean space, elastodynamics, elastic layer.



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1 Institute of Hydromechanics, National Academy of Sciences of Ukraine, Kyiv, Ukraine,
e-mail: igor.selezov@gmail.com.

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