Wydział Mechaniczny / Faculty of Mechanical Engineering / W1

Stały URI zbioruhttp://hdl.handle.net/11652/1

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Filtry

2007 - 200912010 - 201932020 - 20211

Ustawienia

Autorsearch.filters.applied.operator.equals: search.filters.author.Andrianov, Igor V.

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Teraz wyświetlane 1 - 5 z 5
  • Pozycja
    Thermal waves in composite membrane with circular inclusions in hexagonal lattice structures
    (Wydawnictwo Politechniki Łódzkiej, 2021) Andrianov, Igor V.; Awrejcewicz, Jan; Starushenko, G.A.; Kvitka, S.A.
    Non-stationary heat conduction in the fibre composite materials is studied. 2D сomposite media consists of matrix with circular inclusions in hexagonal lattice structures. The perfect contact between different materials is assumed on the boundary of the fibres. The local temperature field in the unit cell is modeled by the heat equation. Time variable excludes from the original boundary value problem using of Laplace transform. Asymptotic homogenization method allows to reduce original problem for multiply-connected domain to the sequence of boundary value problems in simply-connected domains. Composite material is supposed densely-packed with a high-contrast. In this case, the local boundary value problem includes a small parameter equal to the ratio of the distance between the inclusions to the characteristic cell size. Using of additional small parameter and thin layer asymptotics allows to solve local problem analytically. Closed form expression for effective heat conductivity is obtained.
  • Pozycja
    On the vibrations of a composite structure with hexagonal structure of a circular inclusions.
    (Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki., 2015) Andrianov, Igor V.; Awrejcewicz, Jan; Markert, Bernd; Starushenko, Galina A.
    One of the major advantages of homogenization is a possibility of the generalization of the obtained results. Namely, if a solution to the local problem is found, then without principal problems one may solve not only the analyzed problem, by also a series of related static and dynamic problems, including: linear, quasilinear, the eigenvalue problems, etc. The mentioned approach has been applied to the eigenvalue problems regarding the perforated structures and periodically nonhomogenous 2D constructions with a square mesh of inclusions. In this work we have used theory of averaging to solve the vibrations problem regarding stiffly clamped rectangular membrane with periodically located circular inclusions creating a hexagonal mesh. The relations governing eigenvalues (frequencies) and eigenfunctions have been derived. The derivation of analytical formulas governing membrane eigenforms and frequencies consists of three parts. In the first part the local problem regarding a cell (inclusion) of the composite is studied. Second part is focused on finding main terms of the averaged problem. The third part is aimed at an estimation of the first improvement term with respect to the membrane fundamental frequency.
  • Pozycja
    Internal resonances in nonlinear vibrations of a continuous rod with microstructure.
    (Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki., 2015) Andrianov, Igor V.; Awrejcewicz, Jan; Danishevskyy, Vladyslav V.; Markert, Bernd
    Nonlinear longitudinal vibrations of a periodically heterogeneous rod are considered. Geometrical nonlinearity is described by the Cauchy–Green strain tensor. Physical nonlinearity is modelled expressing the energy of deformation as a series expansion in powers of the strains. The governing macroscopic dynamical equation is obtained by the higher-order asymptotic homogenization method. An asymptotic solution is developed by the method of multiple time scales. The effects of internal resonances and modes coupling are predicted. The specific objective of the paper is to analyse how the presence of the microstructure influences on the processes of mode interactions. It is shown that depending on a scaling relation between the amplitude of the vibrations and the size of the unit cell different scenarios of the modes coupling can be realised.
  • Pozycja
    Strain analysis and structural optimization of functionally graded rod with small concentration of inclusions.
    (Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki., 2015) Andrianov, Igor V.; Diskovsky, Alexander A.; Awrejcewicz, Jan
    The homogenization procedure is applied to strain analysis and optimal design of a Functionally Graded (FG) rod in the case when the inclusion size is essentially less than a distance between them. The method is illustrated using an example of the rod longitudinal strain. We considered separately the cases of FG inclusion sizes and FG steps between inclusions. Two particular problems of optimal design are discussed in some details.
  • Pozycja
    Asymptotic study of elastic half-plane with embedded punch.
    (Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2007) Andrianov, Igor V.; Awrejcewicz, Jan; Kirichek, Yurii A.; Koblik, Steve G.
    A contact problem for an elastic half-plane and an embedded rigid punch is studied. The employed mathematical model describes the behavior of a soil with embedded foundation. The analytical solution geverning the stress field behaviour is derived. Singular perturbation and complex analysis techniques are used.