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Erschienen in: Acta Mechanica 12/2020

06.10.2020 | Original Paper

Nonlinear instability of a thin laminated composite circular plate subjected to a tensile periodic load

verfasst von: Khaled M. Elmorabie, Kadry Zakaria, Magdy A. Sirwah

Erschienen in: Acta Mechanica | Ausgabe 12/2020

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Abstract

In this work, we have investigated the nonlinear instability behavior of a thin laminated composite circular plate subjected to a tensile periodic load. A nonlinear system with quadratic and cubic nonlinear terms, referred to the effect of large deflection, is obtained. The method of multiple time scales is used to obtain periodic solutions for the second- and third-order systems, which directly leads to the solvability conditions of the two orders including the nonlinearity terms. Different cases of resonance with the instability criteria are taken into account. For the numerical application, the effect of the tensile periodic load was studied on a plate of graphite fabric-carbon material.
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Literatur
1.
Zurück zum Zitat Bert, C.W., Birman, V.: Dynamic instability of shear deformable antisymmetric angle-ply plates. Int. J. Solids Struct. 23(7), 1053–1061 (1987)CrossRef Bert, C.W., Birman, V.: Dynamic instability of shear deformable antisymmetric angle-ply plates. Int. J. Solids Struct. 23(7), 1053–1061 (1987)CrossRef
2.
Zurück zum Zitat Darabi, M., Darvizeh, M., Darvizeh, A.: Non-linear analysis of dynamic stability for functionally graded cylindrical shells under periodic axial loading. Compos. Struct. 83, 201–211 (2008)CrossRef Darabi, M., Darvizeh, M., Darvizeh, A.: Non-linear analysis of dynamic stability for functionally graded cylindrical shells under periodic axial loading. Compos. Struct. 83, 201–211 (2008)CrossRef
3.
Zurück zum Zitat Bolotin, V.V.: The Dynamic Stability of Elastic Systems. Holden-Day, San Francisco (1964)MATH Bolotin, V.V.: The Dynamic Stability of Elastic Systems. Holden-Day, San Francisco (1964)MATH
4.
Zurück zum Zitat Sahu, S.K., Datta, P.K.: Research advances in the dynamic stability behavior of plates and shells: 1987–2005 part I: Conservative systems. Appl. Mech. Rev. 60(2), 65–75 (2007)CrossRef Sahu, S.K., Datta, P.K.: Research advances in the dynamic stability behavior of plates and shells: 1987–2005 part I: Conservative systems. Appl. Mech. Rev. 60(2), 65–75 (2007)CrossRef
5.
Zurück zum Zitat Srinivasan, R.S., Chellapandi, P.: Dynamic stability of rectangular laminated composite plates. Comput. Struct. 24(2), 233–238 (1986)CrossRef Srinivasan, R.S., Chellapandi, P.: Dynamic stability of rectangular laminated composite plates. Comput. Struct. 24(2), 233–238 (1986)CrossRef
6.
Zurück zum Zitat Bert, C.W., Birman, V.: Dynamic instability of shear deformable antisymmetric angle-ply plates. Int. J. Solids Struct. 23(7), 1053–1061 (1987)CrossRef Bert, C.W., Birman, V.: Dynamic instability of shear deformable antisymmetric angle-ply plates. Int. J. Solids Struct. 23(7), 1053–1061 (1987)CrossRef
7.
Zurück zum Zitat Reddy, J.N.: Mechanics of laminated composite plates and shells: theory and analysis,2nd ed., CRC Press (2003) Reddy, J.N.: Mechanics of laminated composite plates and shells: theory and analysis,2nd ed., CRC Press (2003)
8.
Zurück zum Zitat Moorthy, J., Reddy, J.N., Plaut, R.H.: Parametric instability of laminated composite plates with transverse shear deformation. Int. J. Solids Struct. 26(7), 801–811 (1990)CrossRef Moorthy, J., Reddy, J.N., Plaut, R.H.: Parametric instability of laminated composite plates with transverse shear deformation. Int. J. Solids Struct. 26(7), 801–811 (1990)CrossRef
9.
Zurück zum Zitat Sridhar, S., Mook, D.T., Nayfeh, A.H.: Nonlinear resonances in the forced responses of plates. Part I: Symmetric responses of circular plates. J. Sound Vib. 41, 359–373 (1975) Sridhar, S., Mook, D.T., Nayfeh, A.H.: Nonlinear resonances in the forced responses of plates. Part I: Symmetric responses of circular plates. J. Sound Vib. 41, 359–373 (1975)
10.
Zurück zum Zitat Sridhar, S., Mook, D.T., Nayfeh, A.H.: Nonlinear resonances in the forced responses of plates. Part II: Asymmetric responses of circular plates. J. Sound Vib. 59, 159–170 (1978) Sridhar, S., Mook, D.T., Nayfeh, A.H.: Nonlinear resonances in the forced responses of plates. Part II: Asymmetric responses of circular plates. J. Sound Vib. 59, 159–170 (1978)
11.
12.
Zurück zum Zitat Walker, M.: Multiobjective design of laminated plates for maximum stability using the finite element method. Comput. Struct. 54(2), 389–393 (2001)CrossRef Walker, M.: Multiobjective design of laminated plates for maximum stability using the finite element method. Comput. Struct. 54(2), 389–393 (2001)CrossRef
13.
Zurück zum Zitat Hu, H.T., Tzeng, W.L.: Buckling analysis of skew laminate plates subjected to uniaxial inplane loads. Thin-Walled Struct. 38(1), 53–77 (2000)CrossRef Hu, H.T., Tzeng, W.L.: Buckling analysis of skew laminate plates subjected to uniaxial inplane loads. Thin-Walled Struct. 38(1), 53–77 (2000)CrossRef
14.
Zurück zum Zitat Baltaci, A., Sarikanat, M., Yildiz, H.: Static stability of laminated composite circular plates with holes using shear deformation theory. Finite Elem. Anal. Des. 43(11–12), 839–846 (2007)CrossRef Baltaci, A., Sarikanat, M., Yildiz, H.: Static stability of laminated composite circular plates with holes using shear deformation theory. Finite Elem. Anal. Des. 43(11–12), 839–846 (2007)CrossRef
15.
Zurück zum Zitat Powmya, A., Narasimhan, M.C.: Free vibration analysis of axisymmetric laminated composite circular and annular plates using Chebyshev collocation. Int. J. Adv. Struct. Eng. (IJASE) 7(2), 129–141 (2015)CrossRef Powmya, A., Narasimhan, M.C.: Free vibration analysis of axisymmetric laminated composite circular and annular plates using Chebyshev collocation. Int. J. Adv. Struct. Eng. (IJASE) 7(2), 129–141 (2015)CrossRef
16.
Zurück zum Zitat Coman, C.D., Haughton, D.M.: Localized wrinkling instabilities in radially stretched annular thin films. Acta Mech. 185(3–4), 179–200 (2006)CrossRef Coman, C.D., Haughton, D.M.: Localized wrinkling instabilities in radially stretched annular thin films. Acta Mech. 185(3–4), 179–200 (2006)CrossRef
17.
Zurück zum Zitat Coman, C.D., Haughton, D.M.: On some approximate methods for the tensile instabilities of thin annular plates. J. Eng. Math. 56(1), 79–99 (2006)MathSciNetCrossRef Coman, C.D., Haughton, D.M.: On some approximate methods for the tensile instabilities of thin annular plates. J. Eng. Math. 56(1), 79–99 (2006)MathSciNetCrossRef
18.
Zurück zum Zitat Popov, A.A.: Parametric resonance in cylindrical shells: a case study in the nonlinear vibration of structural shells. Eng. Struct. 25, 789–799 (2003)CrossRef Popov, A.A.: Parametric resonance in cylindrical shells: a case study in the nonlinear vibration of structural shells. Eng. Struct. 25, 789–799 (2003)CrossRef
19.
Zurück zum Zitat Amabili, M.: Nonlinear Vibrations and Stability of Shells and Plates. Cambridge University Press, New York (2008)CrossRef Amabili, M.: Nonlinear Vibrations and Stability of Shells and Plates. Cambridge University Press, New York (2008)CrossRef
20.
Zurück zum Zitat Fung, Y.C.: Foundation of Solid Mechanics. Prentice-Hall, Englewood Cliffs (1965) Fung, Y.C.: Foundation of Solid Mechanics. Prentice-Hall, Englewood Cliffs (1965)
21.
Zurück zum Zitat Nayfeh, A.H.: Introduction to perturbation techniques. Wiley, Hoboken (2011)MATH Nayfeh, A.H.: Introduction to perturbation techniques. Wiley, Hoboken (2011)MATH
22.
Zurück zum Zitat Zakaria, Kadry, Sirwah, Magdy A., Alkharashi, Sameh: Instability through porous media of three layers superposed conducting fluids. Eur. J. Mech. B Fluids 28, 259–270 (2009)MathSciNetCrossRef Zakaria, Kadry, Sirwah, Magdy A., Alkharashi, Sameh: Instability through porous media of three layers superposed conducting fluids. Eur. J. Mech. B Fluids 28, 259–270 (2009)MathSciNetCrossRef
23.
Zurück zum Zitat Allaire, G., Delgado, G.: Stacking sequence and shape optimization of laminated composite plates via a level-set method. J. Mech. Phys. Solids 97, 168–196 (2016)MathSciNetCrossRef Allaire, G., Delgado, G.: Stacking sequence and shape optimization of laminated composite plates via a level-set method. J. Mech. Phys. Solids 97, 168–196 (2016)MathSciNetCrossRef
Metadaten
Titel
Nonlinear instability of a thin laminated composite circular plate subjected to a tensile periodic load
verfasst von
Khaled M. Elmorabie
Kadry Zakaria
Magdy A. Sirwah
Publikationsdatum
06.10.2020
Verlag
Springer Vienna
Erschienen in
Acta Mechanica / Ausgabe 12/2020
Print ISSN: 0001-5970
Elektronische ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-020-02783-8

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