Influence of substructure properties on natural vibrations of periodic Euler-Bernoulli beams

• Autorzy: Świątek M. , Jędrysiak J. , Domagalski Ł.
• Konferencja: Symposium Vibrations In Physical Systems (27 ; 09-13.05.2016 ; Będlewo koło Poznania ; Polska)
• Języki publikacji: EN

Abstrakty

EN

In this paper there are considered vibrations of Euler-Bernoulli beams with geometrical and material properties periodically varying along the axis. The basic exact equations with highly oscillating periodic coefficients are replaced by the system of averaged equations with constant coefficients. The new model is based on the tolerance modelling technique, which describes macro-dynamics of the beam including the effect of the microstructure size. The purpose of this paper is to present an approximately equivalent model, which describe vibrations of periodic beams taking into account length of the periodicity cell.

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: 2016
• Tom: Vol. 27
• Strony: 377--384
• Opis fizyczny: Bibliogr. 12 poz., rys., wykr.

Twórcy

autor

Świątek M.

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

autor

Jędrysiak J.

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

autor

Domagalski Ł.

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

Bibliografia

• 1. N. S. Bakhvalov, G. P. Panasenko, Averaging of processes in periodic media, Nauka, Moskwa 1984 (in Russian).
• 2. A. Bensoussan, J. L. Lions, G. Papanicolaou, Asymptotic analysis for periodic structures, NorthHolland, Amsterdam 1978.
• 3. T. Chen, Investigations on flexural wave propagation of a periodic beam using multi-reflection method, Archive of Applied Mechanics, 83(2) (2013) 315 – 329.
• 4. M. Hajianmaleki, M.S. Quatu, Vibrations of straight and curved composite beams: A review, Composite Structures, 100 (2013) 218 – 232.
• 5. W. M. He, W. Q. Chen, H. Qiao, Frequency estimate and adjustment of composite beams with small periodicity, Composites: Part B, 45 (2013) 742 – 747.
• 6. J. Jędrysiak, Modelling of dynamic behaviour of microstructured thin functionally graded plates, Thin-Walled Structures, 7 (2013) 71 – 102.
• 7. V. V. Jikov, S. M. Kozlov, O. A. Oleinik, Homogenization of differential operators and integral functionals, Springer Verlag, Berlin-Heidelberg-New York 1994.
• 8. K. Mazur-Śniady, C. Woźniak, E. Wierzbicki, On the modelling of dynamic problems for plates with a periodic structure, Archive of Applied Mechanics, 74 (2004) 179 – 190.
• 9. K. Mazur-Śniady, Macro-dynamics of micro-periodic elastic beams, Journal of Theoretical and Applied Mechanics, 31 (1993) 781 – 793.
• 10. Cz. Woźniak et al (eds.), Mathematical modelling and analysis in continuum mechanics of microstructured media, Silesian University of Technology Press, Gliwice 2010.
• 11. 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.
• 12. 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 ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.