Oscillation modeling of viscoelastic elements of thin-walled structures

Abstract The paper presents the results of an oscillation process study of thin-walled structures viscoelastic elements, taking into account the static pressure drop. When studying the oscillations of thin-walled structure elements in a gas flow, a model in the form of a cylindrical panel was used. To describe the viscoelastic properties, the hereditary Boltzmann-Volterra theory of viscoelasticity was applied. When realizing the physicomechanical properties of the object material, the systems of integro-differential equations (IDE) in partial derivatives with corresponding initial and boundary conditions are the mathematical model of the problems under consideration. The obtained nonlinear partial differential equations using the Bubnov-Galerkin method were reduced to the solution of nonlinear ordinary differential equations with constant or variable coefficients with respect to the time function. The integration of the equations obtained using the polynomial approximation of deflections was carried out numerically. Based on this method, an algorithm for the numerical solution of the problem was developed fit for all viscoelastic elements of thin-walled structures of panel type.

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