Nonlinear vibrations of a slender beam interacting with a periodic viscoelastic subsoil

• Autorzy: Świątek M. , Jędrysiak J. , Domagalski Ł.
• Języki publikacji: EN

Abstrakty

EN

The paper describes nonlinear vibrations of Euler-Bernoulli beams interacting with a periodic viscoelastic foundation. The original model equations with highly oscillating periodic coefficients are transformed using the tolerance modelling technique. Newly delivered equations have constant coefficients and describe macro-dynamics of the beam including the effect of the microstructure size. The main purpose of this paper is to propose an equivalent approximate model describing the nonlinear vibrations of a beam interacting with a periodic viscoelastic subsoil.

Słowa kluczowe

EN

periodic beams; Euler-Bernoulli beam

PL

belka o strukturze periodycznej; belka Bernoulliego-Eulera

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2018
• Tom: Vol. 29
• Strony: art. no. 2018030
• Opis fizyczny: Bibliogr. 15 poz., il., wykr.

Twórcy

autor

Świątek M.

• Department of Structural Mechanics, Łódź University of Technology, al. Politechniki 6, 90-924 Łódź, Poland

autor

Jędrysiak J.

• Department of Structural Mechanics, Łódź University of Technology, al. Politechniki 6, 90-924 Łódź, Poland

autor

Domagalski Ł.

• Department of Structural Mechanics, Łódź University of Technology, al. Politechniki 6, 90-924 Łódź, Poland

Bibliografia

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• 3. A. Bensoussan, J. L. Lions, G. Papanicolaou, Asymptotic analysis for periodic structures, NorthHolland, Amsterdam 1978.
• 4. T. Chen, Investigations on flexural wave propagation of a periodic beam using multi-reflection method, Archive of Applied Mechanics 83, 2 (2013) 315 - 329.
• 5. Ł. Domagalski, J. Jędrysiak, Nonlinear vibrations of periodic beams, Journal of Theoretical and Applied Mechanics, 54 (2016) 1095 - 1108.
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• 9. V. V. Jikov, S. M. Kozlov, O. A. Oleinik, Homogenization of differential operators and integral functionals, Springer Verlag, Berlin-Heidelberg-New York 1994.
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• 11. K. Mazur-Śniady, Macro-dynamics of micro-periodic elastic beams, Journal of Theoretical and Applied Mechanics, 31 (1993) 781 - 793.
• 12. Y. Z. Wang, F. M. Li, Nonlinear primary resonance of nano beam with axial initial load by nonlocal continuum theory, International Journal of Non-Linear Mechanics, 61 (2014) 74 - 79.
• 13. C. Woźniak et al (eds.), Mathematical modelling and analysis in continuum mechanics of microstructured media, Silesian University of Technology Press, Gliwice 2010.
• 14. H. J. Xiang, Z. F. Shi, Analysis of flexural vibration band gaps in periodic beams using differential quadrature method, Computers and Structures, 87 (2009) 1559 - 1566.
• 15. D. L. Yu, J. H. Wen, H. J. Shen, Y. Xiao, X. S. Wen, Propagation of flexural wave in periodic beam on elastic foundations, Physics Letters A, 376 (2012) 626 - 630.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).