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Abstrakty
This paper is devoted to the analysis of ambient temperature influence on harmonic vibrations of von Kármán geometrically non-linear plates. The time-temperature superposition and the Williams-Landel-Ferry formula for the horizontal shift are used to modify the viscosity properties in the fractional Zener material model of viscoelasticity. The non-linear amplitude equation is obtained from the time-averaged principle of virtual work and the harmonic balance method. It is then solved after the finite element (FE) discretization using the continuation method to get the response curves in the frequency domain. Several numerical examples are solved and a significant influence of temperature on the resonance properties of the analysed plates is observed.
Czasopismo
Rocznik
Tom
Strony
159--176
Opis fizyczny
Bibliogr. 27 poz., rys., tab., wykr.
Twórcy
autor
- Institute of Structural Analysis Poznan University of Technology Piotrowo 5, 60-965 Poznan
autor
- Institute of Structural Analysis Poznan University of Technology Piotrowo 5, 60-965 Poznan
Bibliografia
- 1. Alavi S.H., Eipakchi H., An analytical approach for free vibrations analysis of viscoelastic circular and annular plates using FSDT, Mechanics of Advanced Materials and Structures, 27(3): 250–264, 2018, doi: 10.1080/15376494.2018.1472348.
- 2. Amabili M., Nonlinear damping in nonlinear vibrations of rectangular plates: derivation from viscoelasticity and experimental validation, Journal of the Mechanics and Physics of Solid, 118: 275–292, 2018, 10.1016/j.jmps.2018.06.004.
- 3. Amabili M., Nonlinear Mechanics of Shells and Plates: Composite, Soft and Biological Materials, Cambridge University Press, New York, 2018.
- 4. Amabili M., Nonlinear vibrations of viscoelastic rectangular plates, Journal of Sound and Vibration, 362: 142–156, 2010, doi: 10.1016/j.jsv.2015.09.035.
- 5. Atanackovic T.M., A modified Zener model of a viscoelastic body, Continuum Mechanics and Thermodynamics, 14(2): 137–148, 2002, doi: 10.1007/s001610100056.
- 6. Bagley R.L., Torvik P.J., A theoretical basis for the application of fractional calculus to viscoelasticity, Journal of Rheology, 27(3): 201–210, 1983, doi: 10.1122/1.549724.
- 7. Bagley R.L., Torvik P.J., On the fractional calculus model of viscoelastic behaviour, Journal of Rheology, 30(1): 133–155, 1986, doi: 10.1122/1.549887.
- 8. Brinson H.F., Brinson L.C., Polymer Engineering Science and Viscoelasticity. An Introduction, Springer, New York, 2008.
- 9. Eldred L.B., Baker W.P., Palazotto A.N., Kelvin-Voigt versus fractional derivative model as constitutive relations for viscoelastic materials, AAIA Journal, 33(3): 547–550, 1995, doi: 10.2514/3.12471.
- 10. Eshmatov B.K., Nonlinear vibrations and dynamic stability of viscoelastic orthotropic rectangular plates, Journal of Sound and Vibration, 300(3–5): 709–726, 2007, doi: 10.1016/j.jsv.2006.08.024.
- 11. Gopalan V., Suthenthiraveerappa V., Pragasam V., Experimental and numerical investigation on the dynamic characteristics of thick laminated plant fiber-reinforced polymer composite plates, Archive of Applied Mechanics, 89(2): 363–384, 2019, doi: 10.1007/s00419-018-1473-8.
- 12. Lewandowski R., Influence of temperature on the dynamic characteristics of structures with viscoelastic dampers, Journal of Structural Engineering, 145(2): 04018245, 2019, doi: 10.1061/(ASCE)ST.1943-541X.0002238.
- 13. Lewandowski R., Przychodzki M., Approximate method for temperature-dependent characteristics of structures with viscoelastic dampers, Archive of Applied Mechanics, 88(10): 1695–1711, 2018, doi: 10.1007/s00419-018-1394-6.
- 14. Li H., Gomez D., Dyke S.J., Xu Z., Fractional differential equation bearing models for base-isolated buildings: framework development, Journal of Structural Engineering, 146(2): 04019197, 2020, doi: 10.1061/(ASCE)ST.1943-541X.0002508.
- 15. Lijun Y., Xueliang J., The natural transverse vibration of rectangular thick plates with viscoelastic on viscoelastic foundation, Electronic Journal of Geotechnical Engineering, 19: 3173–3179, 2014.
- 16. Litewka P., Lewandowski R., Nonlinear harmonically excited vibrations of plates with Zener material, Nonlinear Dynamics, 89(1): 691–712, 2017, doi: 10.1007/s11071-017-3480-7.
- 17. Litewka P., Lewandowski R., Steady-state non-linear vibrations of plates using Zener material with fractional derivative, Computational Mechanics, 60(2): 333–354, 2017, doi: 10.1007/s00466-017-1408-1.
- 18. Makris N., Constantinou M.C., Fractional-derivative Maxwell model for viscous dampers, Journal of Structural Engineering, 117(9): 2708–2724, 1991, doi: 10.1061/(ASCE)0733-9445(1991)117:9(2708).
- 19. Morin B., Legay A., Deü J-F., Reduced order models for dynamic behavior of elastomer damping devices, Finite Elements in Analysis and Design, 143: 66–75, 2018, doi: 10.1016/j.finel.2018.02.001.
- 20. Permoon M.C., Haddadpour H., Javadi M., Nonlinear vibration of fractional viscoelastic plate: primary, subharmonic, and superharmonic response, International Journal of Non-Linear Mechanics, 99: 154–164, 2018, doi: 10.1016/j.ijnonlinmec.2017.11.010.
- 21. Pirk R., Rouleau L., Desmet W., Pluymers B., Validating the modeling of sandwich structures with constrained layer damping using fractional derivative models, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38(7): 1959–1972, 2016, doi: 10.1007/s40430-016-0533-7.
- 22. Podlubny I., Fractional Differential Equations, Academic Press, 1998.
- 23. Salehi M., Aghaei H., Dynamic relaxation large deflection analysis of non-axisymmetric circular viscoelastic plates, Computers and Structures, 83(23–24): 1878–1890, 2005, doi: 10.1016/j.compstruc.2005.02.023.
- 24. Shaw M.T., Introduction to Polymer Rheology, Wiley, New Jersey, 2012.
- 25. Touati D., Cederbaum G., Dynamic stability of nonlinear viscoelastic plates, International Journal of Solids and Structures, 31(17): 2367–2376, 1994, doi: 10.1016/0020-7683(94)90157-0.
- 26. Trogdon S.A., Small amplitude vibration of viscoelastic plates, Acta Mechanica, 53(3): 233–243, 1984, doi: 10.1007/BF01177953.
- 27. Xu X., Gao S., Zhang D., Niu S., Jin L., Ou Z., Mechanical behavior of liquid nitrile rubber-modified epoxy resin: experiments, constitutive model and application, International Journal of Mechanical Sciences, 151: 46–60, 2019, doi: 10.1016/j.ijmecsci.2018.11.003.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-cde442dd-49c4-4d0d-bd16-706011e12532