Wydział Mechaniczny / Faculty of Mechanical Engineering / W1

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

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20153

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Autorsearch.filters.applied.operator.equals: search.filters.author.Andrianov, Igor V.Tematsearch.filters.applied.operator.equals: search.filters.subject.dynamical systems - conference

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Teraz wyświetlane 1 - 3 z 3
  • 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.