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Tarasyuk I.A., Kravchuk A.S. Axisymmetric viscoelastoplastic oscillations of the round composite membrane, isotropic on the average. Modern technologies. System analysis. Modeling, 2018, Vol. 57, No. 1, pp. 109-117. DOI: 10.26731 / 1813-9108.2018.1 (57). 109-117.

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The work focuses on the generalization of the equation of axisymmetric oscillations of a circular composite membrane, isotropic on the average, in case of a nonlinearly deformable rheologically active material. The nonlinear behavior of the composite membrane is modeled by considering the Rabotnov equations of nonlinear creep and relaxation in hereditary theory as the defining relationships of its components. In this case, the bilinear Prandtl diagrams are used as the curves of instant elastic-plastic deformation of the material components. To study the vibrations of the composite membrane, the equation of state is homogenized. For this, an estimative delta of effective viscoelastoplastic characteristics is constructed using the Voigt hypothesis on the homogeneity of deformations and the Reuss hypothesis on the uniformity of stresses in the volume of the composite body. With the help of the method of homogenization proposed by the authors, the obtained range of effective parameters of deformation of a composite, on the average isotropic membrane, is reduced. According to this technique, the effective equations of state are determined by the rule of the mixture for effective creep and relaxation Voigt-Reuss equations. Analytic expressions are obtained for the effective Young's modulus, hardening modulus, Poisson's ratio, yield point, creep and relaxation nuclei, as well as frequencies of free axisymmetric oscillations of the circular membrane as functions of these viscoelastoplastic characteristics. The results obtained can be used in the design and vibration analysis of membrane structural elements, since they make it possible to trace the change in the characteristics of deformation when structural, mechanical and geometric parameters of the composite membrane change.

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