A study on natural frequencies of Timoshenko beam with rapidly varying stiffness

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

Abstrakty

EN

Vibrations of Timoshenko beams with properties periodically varying along the axis are under consideration. The tolerance method of averaging differential operators with highly oscillating coefficients is applied to obtain the governing equations with constant coefficients. The dynamics of Timoshenko beam with the effect of the cell length is described. A asymptotic model is then constructed, which is further studied in analysis of the low order natural frequencies. The proposed model is able to describe dynamics of beams made of non-slender cells.

Słowa kluczowe

EN

beam vibrations; periodic beams; tolerance modelling

PL

drgania belki; belka o strukturze periodycznej; modelowanie tolerancyjne

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2016
• Tom: Vol. 27
• Strony: 369--376
• Opis fizyczny: Bibliogr. 10 poz., 1 rys., wykr.

Twórcy

autor

Świątek M.

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

autor

Domagalski Ł.

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

autor

Jędrysiak J.

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

Bibliografia

• 1. N. S. Bakhvalov, G. P. Panasenko, Averaging of processes in periodic media, Nauka, Moskwa 1984.
• 2. A. Bensoussan, J. L. Lions, G. Papanicolaou, Asymptotic analysis for periodic structures, North-Holland, Amsterdam 1978.
• 3. Ł. Domagalski, J. Jędrysiak, Geometrically nonlinear vibrations of slender meso-periodic beams. The tolerance modelling approach, Comp. Struct., 136 (2016) 270 – 277.
• 4. S. M. Han, H. Benaroya, T. Wei, Dynamics of transversely vibrating beams using four engineering theories, Journal of Sound and Vibration, 225(5) (1999) 935 – 988.
• 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, 71 (2013) 102 – 107.
• 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, Macro-dynamics of micro-periodic elastic beams, J. Theor. Appl. Mech., 31 (1993) 34 – 46.
• 9. C. Wozniak et al (eds.), Mathematical modelling and analysis in continuum mechanics of microstructured media, Silesian University of Technology Press, Gliwice 2010.
• 10. Cz. Woźniak, E. Wierzbicki, Averaging techniques in thermomechanics of composite solids, Wydawnictwo Politechniki Częstochowskiej, Częstochowa 2000.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.