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Coupled Systems Mechanics
  Volume 9, Number 1, February 2020, pages 77-89

Non-stationary mixed problem of elasticity for a semi-strip
Viktor Reut, Natalya Vaysfeld and Zinaida Zhuravlova

    This study is dedicated to the dynamic elasticity problem for a semi-strip. The semi-strip is loaded by the dynamic load at the center of its short edge. The conditions of fixing are given on the lateral sides of the semistrip. The initial problem is reduced to one-dimensional problem with the help of Laplace\'s and Fourier\'s integral transforms. The one-dimensional boundary problem is formulated as the vector boundary problem in the transform\'s domain. Its solution is constructed as the superposition of the general solution for the homogeneous vector equation and the partial solution for the inhomogeneous vector equation. The matrix differential calculation is used for the deriving of the general solution. The partial solution is constructed with the help of Green\'s matrix-function, which is searched as the bilinear expansion. The case of steady-state oscillations is considered. The problem is reduced to the solving of the singular integral equation. The orthogonalization method is applied for the calculations. The stress state of the semi-strip is investigated for the different values of the frequency.
Key Words
    semi-strip; dynamic problem; steady-state oscillation; singular integral equation; Green matrix-function
Viktor Reut, Natalya Vaysfeld and Zinaida Zhuravlova: Faculty of Mathematics, Physics and Informational Technologies, Odessa I.I. Mechnikov National University,
Dvoryanska Str., 2, Odessa, Ukraine

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