Awrejcewicz, J.Andrianov, I.I.Diskovsky, A.A.2021-12-032021-12-032021Awrejcewicz J., Andrianow I.I., Diskovsky A.A., Higher order asymptotic homogenization for dynamical problems. W: DSTA-2021 Conference Books – Abstracts (16th International Conference : Dynamical Systems Theory and Applications DSTA 2021 ABSTRACTS), Awrejcewicz J. (red.), Kaźmierczak M. (red.), Olejnik P. (red.), Mrozowski J. (red.), Wydawnictwo Politechniki Łódzkiej ; Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki, Łódź 2021, s. 723-724, ISBN 978-83-66741-20-1.978-83-66741-20-1http://hdl.handle.net/11652/4138In general, asymptotic homogenization methods are based on the hypothesis of perfect scale separation. In practice, this is not always the case. The problem arises of improving the solution in such a way that it becomes applicable if inhomogeneity parameter is not small. Our study focuses on the higher order asymptotic homogenization for dynamical problems. Systems with continuous and piecewise continuous parameters, discrete systems, and also continuous systems with discrete elements are considered. Both low-frequency and highfrequency vibrations are analyzed. For low-frequency vibrations, several approximations of the asymptotic homogenization method are constructed. The influence of the boundary conditions, the system parameters is investigated.enAll rights reservedFair use conditionWszystkie prawa zastrzeżoneDla wszystkich w zakresie dozwolonego użytkuperiodically nonhomogeneous structuresdynamicshomogenizationscale separationstruktury okresowo niejednorodnedynamikahomogenizacjapodział skaliAbstractLUT LicenseLicencja PŁLodz University of Technology. Faculty of Mechanical Engineering. Department of Automation, Biomechanics and Mechatronics.Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki.