An analytical-numerical approach to analysis of large amplitude vibrations of slender periodic beams

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

Abstrakty

EN

The paper is devoted to analysis of geometrically nonlinear vibrations of beams with geometric and material properties periodically varying along the axis. The 1-D Euler-Bernoulli theory of beams with von Kármán nonlinearity is applied. An analytical-numerical model based on non-asymptotic tolerance modelling approach and Galerkin method is applied. The linear natural frequencies and mode shapes are determined and the results are confirmed by comparison with a finite element model. Forced damped vibrations analysis in the large deflection range is performed to illustrate complex behaviour of the system.

Słowa kluczowe

EN

nonlinear vibrations; periodic beams; averaging; tolerance modelling

PL

drgania nieliniowe; belka o strukturze periodycznej; uśrednianie; modelowanie tolerancyjne

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2016
• Tom: Vol. 27
• Strony: 99--106
• Opis fizyczny: Bibliogr. 6 poz., rys., wykr.

Twórcy

autor

Domagalski Ł.

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

Bibliografia

• 1. A. Bensoussan, J. L. Lions, G. Papanicolaou, Asymptotic analysis for periodic structures, North-Holand, Amsterdam 1978.
• 2. Ł. Domagalski, M. Gajdzicki, Moderately large deflections of thin densely ribbed plates, in: W. Pietraszkiewicz, J. Górski (eds.), Shell Structures: Theory and Applications, Taylor & Francis Group, London, 3 (2014) 77 – 80.
• 3. Ł. Domagalski, J. Jędrysiak, Nonlinear vibrations of periodic beams, Vibrations in Physical Systems, 26 (2014) 73 – 78.
• 4. A. G. Kolpakov, The governing equations of a thin elastic stressed beam with a periodic structure, Journal of Applied Mathematics and Mechanics, 63(3) (1999) 495 – 504.
• 5. B. Tomczyk, C. Woźniak, Tolerance models in elastodynamics of certain reinforced thin-walled structures, in: Z. Kołakowski, K. Kowal-Michalska (eds.), Statics, Dynamics and stability of Structural Elements and Systems, TUL PRESS, Łódź, 2 (2012) 123 – 153.
• 6. C. Woźniak et al. (eds.), Mathematical modeling and analysis in continuum mechanics of microstructured media, Wydawnictwo Politechniki Śląskiej, Gliwice 2010.

Uwagi

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