Free vibrations of microstructured functionally graded plate band with clamped edges

• Autorzy: Kaźmierczak-Sobińska Magda , Jędrysiak Jarosław

Identyfikatory

DOI

10.21008/j.0860-6897.2021.2.16

• Języki publikacji: EN

Abstrakty

EN

In this paper there are presented free vibrations of thin functionally graded plate band. This kind of plates has tolerance-periodic microstructure on the microlevel in planes parallel to the plate midplane. Dynamic problems of plates of this kind are described by partial differential equations with highly oscillating, tolerance-periodic, non-continuous coefficients. Thus, there are proposed here two models describing these plates by equations with smooth, slowly-varying coefficients. As an example there are analyses of free vibration frequencies for thin functionally graded plate band clamped on both edges. Using the known Ritz method the frequencies are obtained in the framework of proposed two models - the tolerance model and the asymptotic model.

Słowa kluczowe

EN

thin functionally graded plate band; microstructure; free vibrations; tolerance modelling

PL

pasmo płytowe; płyty cienkie o funkcyjnej gradacji własności; mikrostruktura; drgania własne; modelowanie tolerancyjne

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2021
• Tom: Vol. 32, nr 2
• Strony: art. no. 2021216
• Opis fizyczny: Bibliogr. 23 poz., rys., wykr.

Twórcy

autor

Kaźmierczak-Sobińska Magda

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

autor

Jędrysiak Jarosław

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

Bibliografia

• 1. S. Suresh, A. Mortensen. Fundamentals of Functionally Graded Materials. The University Press, Cambridge, 1998.
• 2. R.V. Kohn, M. Vogelius. A new model of thin plates with rapidly varying thickness. Int. J. Solids Struct., 20:333-350, 1984.
• 3. M. Grygorowicz, E. Magnucka-Blandzi. Mathematical modeling for dynamic stability of sandwich beam with variable mechanical properties of core. Applied Mathematics and Mechanics, 37: 361-374, 2016.
• 4. N. Fantuzzi, F. Tornabene. Strong Formulation Isogeometric Analysis (SFIGA) for laminated composite arbitrarily shaped plates. Composites Part B: Engineering, 96: 173-203, 2016.
• 5. B. Liu, A.J.M. Ferreira, Y.F. Xing, A.M.A. Neves. Analysis of composite plates using a layerwise theory and a differential quadrature finite element method. Compos. Struct., 156: 393-398, 2016.
• 6. H. Jopek, T. Strek. Torsion of a two-phased composite bar with helical distribution of constituents. Phys. Status Solidi B, 254(12):1700050, 2017.
• 7. C. Woźniak, B. Michalak, J. Jędrysiak. Thermomechanics of Heterogeneous Solids and Structures. Publishing House of Lodz University of Technology, Łódź, 2008.
• 8. C. Woźniak, et al. Mathematical Modelling and Analysis in Continuum Mechanics of Microstructure Media. Publishing House of Silesian University of Technology, Gliwice, 2010.
• 9. E. Baron. On modelling of periodic plates having the inhomogeneity period of an order of the plate thickness. JTAM, 44:3-18, 2006.
• 10. Ł. Domagalski, J. Jędrysiak. On the elastostatics of thin periodic plates with large deflections. Meccanica, 47:1659-1671, 2012.
• 11. J. Jędrysiak. Dynamics of thin periodic plates resting on a periodically inhomogeneous Winkler foundation. Arch. Appl. Mech., 69:345-356, 1999.
• 12. B. Tomczyk. A non-asymptotic model for the stability analysis of thin biperiodic cylindrical shells. Thin-Walled Struct., 45:941-944, 2007.
• 13. Ł. Domagalski, J. Jędrysiak. Nonlinear vibrations of periodic beams. J. Theor. Appl. Mech., 54: 1095-1108, 2016.
• 14. J. Jędrysiak, B. Michalak. On the modelling of stability problems for thin plates with functionally graded structure. Thin-Walled Struct., 49:627-635, 2011.
• 15. M. Kaźmierczak, J. Jędrysiak. A new combined asymptotic-tolerance model of vibrations of thin transversally graded plate. Eng. Struct., 46:322-331, 2013.
• 16. J. Jędrysiak, M. Kaźmierczak-Sobińska. On free vibration of thin functionally graded plate bands resting on an elastic foundation. J. Theor. Appl. Mech., 53:629-642, 2015.
• 17. J. Jędrysiak. Tolerance modelling of free vibration frequencies of thin functionally graded plates with one-directional microstructure. Compos. Struct., 161:453-468, 2017.
• 18. P. Ostrowski, B. Michalak. The combined asymptotic-tolerance model of heat conduction in a skeletal micro-heterogeneous hollow cylinder. Compos. Struct., 134:343-352, 2015.
• 19. E. Pazera, J. Jędrysiak. Effect of microstructure in thermoelasticity problems of functionally graded laminates. Compos. Struct., 202:296-303, 2018.
• 20. B. Tomczyk. P. Szczerba. Tolerance and asymptotic modelling of dynamic problems for thin microstructured transversally graded shells. Compos. Struct., 162:365-373, 2017.
• 21. B. Tomczyk. P. Szczerba. Combined asymptotic-tolerance modelling of dynamic problems for functionally graded shells. Compos. Struct., 183:176-184, 2018.
• 22. B. Tomczyk. P. Szczerba. A new asymptotic-tolerance model of dynamic and stability problems for longitudinally graded cylindrical shells. Compos. Struct., 202:473-481, 2018.
• 23. J. Jędrysiak. Thermomechanics of Laminates, Plates and Shells with Functionally Graded Structure. Publishing House of Lodz University of Technology, Łódź, 2010.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).