Boundary value problems of integrodifferential equations under boundary conditions taking into account physical nonlinearity
Физикалық бейсызықты негiзiндегi шекаралық шарттардағы интегралдық-дифференциалдық теңдеулердiң шеттiк есептерi
Краевые задачи интегро–дифференциальных уравнений при граничных условиях с учетом физической нелинейности
Seitmuratov A.Zh. Medeubaev N.K. Kozhoshov T.T. Medetbekov B.R.
2023E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2023#110Issue 2131 - 141 pp.
When solving integrodifferential equations under boundary conditions, taking into account physical nonlinearity, a broad class of boundary-value problems of oscillations arises associated with various boundary conditions at the edges of a flat element. When taking into account non-stationary external influences, the main parameters is the frequency of natural vibrations of a flat component, taking into account temperature, prestressing, and other factors. The study of such problems, taking into account complicating factors, reduces to solving rather complex problems. The difficulty of solving these problems is due to both the type of equations and the variety. We analyze the results of previous works on the boundary problems of vibrations of plane elements. Possible boundary conditions at the edges of a flat element and the necessary initial conditions for solving particular problems of self-oscillation and forced vibrations, and other problems are considered. The set of equations, boundaries, and initial conditions make it possible to formulate and solve various boundary value problems of vibrations for a flat element. The oscillation equations for a flat element in the form of a plate given in this paper contain viscoelastic operators that describe the viscous behavior of the materials of a flat component. In studying oscillations and wave processes, it is advisable to take the kernels of viscoelastic operators regularly, since only such operators describe instantaneous elasticity and then viscous flow.
approximate equation , boundary value problems , integrodifferential equation , isotropic plates , nonlinear operators , oscillations , physical nonlinearity , plates , wave process
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Korkyt Ata Kyzylorda University, Kyzylorda, Kazakhstan
Karagandа University of the name of academician E.A. Buketov, Karaganda, Kazakhstan
Kyrgyz State Technical University, Bishkek, Kyrgyzstan
Academy of Civil Aviation (AGA), Almaty, Kazakhstan
Korkyt Ata Kyzylorda University
Karagandа University of the name of academician E.A. Buketov
Kyrgyz State Technical University
Academy of Civil Aviation (AGA)
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