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Vibrations of microstructured beams with axial force

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Języki publikacji
EN
Abstrakty
EN
In this contribution there are considered vibrations of microstructured periodic slender beams, with axial force. In order to analyse the effect of the microstructure size of the beams on their vibrations the tolerance modelling method is applied. Using this method there are derived governing equations of two tolerance models - general and standard, base on two various concepts - weakly-slowly-varying functions and slowly-varying functions. These models are applied to obtain formulas of lower order and higher order frequencies with influence of the axial force. To evaluate these results of the modelling the formula of lower order frequencies in the framework of the asymptotic model (neglecting the effect of the microstructure size) is also derived.
Rocznik
Strony
art. no. 2020208
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
  • Department of Structural Mechanics, Łódź University of Technology, al. Politechniki 6, 90-924 Łódź, Poland
Bibliografia
  • 1. S.J. Matysiak, W. Nagórko, Microlocal parameters in the modelling of microperiodic plates, Ing. Arch., 59 (1989) 434-444.
  • 2. A. Kolpakov, Application of homogenization method to justification of 1-D model for beam of periodic structure having initial stresses, Int. J. Solids Struct., 35 (1998) 2847-2859.
  • 3. M. Grygorowicz, E. Magnucka-Blandzi, Mathematical modeling for dynamic stability of sandwich beam with variable mechanical properties of core, Appl. Math. Mech., 37 (2016) 361-1374.
  • 4. T. Strek, H. Jopek, A. Fraska, Torsion of elliptical composite beams with auxetic phase, Phys. Status Solidi Basic Res., 253 (2016) 1359-1368.
  • 5. H. Jopek, T. Stręk, Torsion of a two-phased composite bar with helical distribution of constituents, Phys. Status Solidi, 254 (2017) 1700050.
  • 6. L. Brillouin, Wave propagation in periodic structures, Dover Pub. Inc., Dover, UK, 1953.
  • 7. C.W. Robinson, G.W. Leppelmeier, Experimental verification of dispersion relations for layered composites, J. Appl. Mech., 41 (1974) 89-91.
  • 8. H.-J. Xiang, Z.-F. Shi, Analysis of flexural vibration band gaps in periodic beams using differential quadrature method, Comp. Struct., 87 (2009) 1559-1566.
  • 9. Z.B. Cheng, Y.G. Xu, L.L. Zhang, Analysis of flexural wave bandgaps in periodic plate structures using differential quadrature element method, Int. J. Mech. Sci., 100 (2015) 112-125.
  • 10. D. Yu, J. Wen, H. Shen, Y. Xiao, X. Wen, Propagation of flexural wave in periodic beam on elastic foundations, Physics Letters A, 376 (2012) 626-630.
  • 11. Y. Xu, X. Zhou, W. Wang, L. Wang, F. Peng, B. Li, On natural frequencies of non-uniform beams modulated by finite periodic cells, Physics Letters A, 380 (2016) 3278-3283.
  • 12. T. Chen, Investigations on flexural wave propagation of a periodic beam using multi-reflection method, Arch. Appl. Mech., 83 (2013) 315-329.
  • 13. C. Woźniak, E. Wierzbicki, Averaging techniques in thermomechanics of composite solids. Tolerance averaging versus homogenization, Techn. Univ. of Czestochowa Press, Częstochowa, Poland, 2000.
  • 14. C. Woźniak, J. Jędrysiak, B. Michalak, Thermomechanics of heterogeneous solids and structures, tolerance averaging approach, Lodz Univ. of Techn., Łódź, Poland, 2008.
  • 15. C. Woźniak (eds.), Mathematical Modelling and Analysis in Continuum Mechanics of Microstructured Media, Silesian Univ. Press, Gliwice, Poland 2010.
  • 16. K. Mazur-Śniady, Macro-dynamic of micro-periodic elastic beams, J. Theor. Appl. Mech., 31 (1993) 781-793.
  • 17. B. Michalak, The meso-shape functions for the meso-structural models of wavy-plates, ZAMM, 81 (2001) 639-641.
  • 18. W. Nagórko, C. Woźniak, Nonasymptotic modelling of thin plates reinforced by a system of stiffeners, Electr. J. Polish Agric. Univ. - Civil Engineering, 5 (2002).
  • 19. E. Baron, On dynamic behaviour of medium-thickness plates with uniperiodic structure, Arch. Appl. Mech., 73 (2003) 505-516.
  • 20. J. Jędrysiak, Free vibrations of thin periodic plates interacting with an elastic periodic foundation, Int. J. Mech. Sci., 45 (2003) 1411-1428.
  • 21. B. Tomczyk, Dynamic stability of micro-periodic cylindrical shells, Mech. Mech. Eng., 14 (2010) 137-150.
  • 22. Ł. Domagalski, J. Jędrysiak, Nonlinear vibrations of periodic beams, J. Theor. Appl. Mech., 54 (2016) 1095-108.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
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