On the combined asymptotic-tolerance modelling of dynamic problems for thin biperiodic cylindrical shells

• Autorzy: Tomczyk B. , Litawska A.
• Języki publikacji: EN

Abstrakty

EN

The objects of consideration are thin linearly elastic Kirchhoff-Love-type circular cylindrical shells having a periodically microheterogeneous structure in circumferential and axial directions (biperiodic shells). The aim of this contribution is to formulate and discuss a new averaged general asymptotic-tolerance model for the analysis of selected dynamic problems for the shells under consideration. This model is derived by applying the combined modelling which includes two techniques: the asymptotic modelling procedure and a certain extended version of the known tolerance non-asymptotic modelling technique based on a new notion of weakly slowly-varying function. Contrary to the starting exact shell equations with highly oscillating, non-continuous and periodic coefficients, governing equations of the averaged combined model have constant coefficients depending also on a cell size. The differences between the general combined model proposed here and the corresponding known standard combined model derived by means of the more restrictive concept of slowly-varying functions are discussed.

Słowa kluczowe

EN

micro-periodic cylindrical shells; dynamics; tolerance modelling; length-scale effect

PL

mikroperiodyczne powłoki cylindryczne; dynamika; modelowanie tolerancyjne; efekt skali

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2018
• Tom: Vol. 29
• Strony: art. no. 2018020
• Opis fizyczny: Bibliogr. 9 poz., 1 rys.

Twórcy

autor

Tomczyk B.

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

autor

Litawska A.

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

Bibliografia

• 1. I. V. Andrianov, J. Awrejcewicz, L. Manevitch, Asymptotical mechanics of thinwalled structures, Springer, Berlin 2004.
• 2. C. Woźniak, et al. (eds.), Mathematical modelling and analysis in continuum mechanics of microstructured media, Silesian Technical University Press, Gliwice 2010.
• 3. B. Tomczyk, Length-scale effect in dynamics and stability of thin periodic cylindrical shells, Bulletin of the Lodz University of Technology, No. 1166, series: Scientific Dissertations, Lodz University of Technology Press, Lodz 2013.
• 4. M. Kaźmierczak, J. Jędrysiak, Tolerance modelling of vibrations of thin functionally graded plates, Thin Walled Structures, 49 (2011) 1295 - 1303.
• 5. B. Tomczyk, P. Szczerba, Tolerance and asymptotic modelling of dynamic problems for thin microstructured transversally graded shells, Composite Structures, 162 (2017) 365 - 373.
• 6. 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 structures, Lodz University of Technology Press, Lodz 2012, 123 - 153.
• 7. B. Tomczyk, A. Litawska, A new tolerance model of vibrations of thin microperiodic cylindrical shells, Journal of Civil Engineering, Environment and Architecture, 64 (2017) 203 - 216.
• 8. B. Tomczyk, A. Litawska, A new asymptotic-tolerance model of dynamics of thin uniperiodic cylindrical shells, In: J. Awrejcewicz et al. (eds.), Mathematical and numerical aspects of dynamical system analysis, ARSA-Press, Lodz 2017, 519 - 532.
• 9. B. Tomczyk, A. Litawska, Tolerance modelling of dynamic problems for thin biperiodic shells. In: W. Pietraszkiewicz, W. Witkowski (eds.), Shell structures. Theory and applications, CRC Press/Balkema, London 2018, 341 - 344.

Uwagi

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