Linear vibrations of periodic Timoshenko and Rayleigh beams

• Autorzy: Świątek M. , Jędrysiak J. , Domagalski Ł.
• Języki publikacji: EN

Abstrakty

EN

Elastic periodic structures with variable material and geometrical properties exhibit dynamic characteristics that are investigated in this contribution. The paper is devoted to analysis of geometrically linear vibrations of Rayleigh and Timoshenko beams with cross-sections and material properties periodically varying along the longitudinal axis. The period of inhomogeneity is assumed to be sufficiently small when compared to the beam length. Equations of motion in both beam theories under consideration have highly-oscillating coefficients. In order to derive the averaged model equations with constant coefficients for vibrations, the tolerance averaging approach is applied. The method of averaging differential operators with rapidly varying coefficients is applied to obtain averaged governing equations with constant coefficients. An assumed tolerance and indiscernibility relations and the definition of slowly varying function found the applied technique. Numerical results from the tolerance Rayleigh and Timoshenko beam model equations are compared.

Słowa kluczowe

EN

periodic beams; Timoshenko beams; Rayleigh beam

PL

belka o strukturze periodycznej; belka Timoshenki; belka Rayleigha

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2018
• Tom: Vol. 29
• Strony: art. no. 2018035
• Opis fizyczny: Bibliogr. 13 poz., 1 il. kolor., wykr.

Twórcy

autor

Świątek M.

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

autor

Jędrysiak J.

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

autor

Domagalski Ł.

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

Bibliografia

• 1. Ł. Domagalski, J. Jędrysiak, Geometrically nonlinear vibrations of slender mesoperiodic beams. The tolerance modeling approach, Composite Structures, 136 (2016) 270 - 277.
• 2. Ł. Domagalski, J. Jędrysiak, Nonlinear vibrations of periodic beams, Journal of Theoretical and Applied Mechanics, 54 (2016) 1095 - 1108.
• 3. J. Jędrysiak, Tolerance modelling of free vibration frequencies of thin functionally graded plates with one-directional microstructure, Composite Structures, 161 (2017) 453 - 468.
• 4. J. Jędrysiak, Modelling of dynamic behaviour of microstructured thin functionally graded plates, Thin-Walled Structures, 71 (2013) 102 - 107.
• 5. L. Majkut, Free and forced vibrations of Timoshenko beams described by single difference equation, Journal of Theoretical and Applied Mechanics, 47 (2009) 193 - 210.
• 6. J. Marczak, J. Jędrysiak, Tolerance modelling of vibrations of periodic three-layered plates with inert core, Composite Structures, 134 (2015) 854 - 861.
• 7. K. Mazur-Śniady, Macro-dynamic of micro-periodic elastic beams, Journal of Theoretical and Applied Mechanics, 31 (1993) 781 - 793.
• 8. G. G. Sheng, X. Wang, The geometrically nonlinear dynamic responses of simply supported beams under moving loads, Applied Mathematical Modelling, 48 (2017) 183 - 195.
• 9. B. Tomczyk, On the modelling of thin uniperiodic cylindrical shells, Journal of Theoretical and Applied Mechanics, 41 (2003) 755 - 774.
• 10. A. Wirowski, J. Jędrysiak, M. Kaźmierczak, Vibrations of thin tolerance-periodic plates. PAMM 10 (2010).
• 11. C. Woźniak, E. Wierzbicki, Averaging techniques in thermomechanics of composite solids. Tolerance averaging versus homogenization, Technical University of Czestochowa Press 2000.
• 12. C. Woźniak (eds.). Mathematical Modelling and Analysis in Continuum Mechanics of Microstructured Media, Silesian University Press, 2010.
• 13. C. Woźniak, J. Jędrysiak, B. Michalak, Thermomechanics of heterogeneous solids and structures, tolerance averaging approach, Lodz University of Technology, 2008.

Uwagi

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