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Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method

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Abstract

This research deals with the nonlocal dynamic buckling analysis of embedded microplates reinforced by single-walled carbon nanotubes (SWCNTs). The material properties of structure are assumed viscoelastic based on Kelvin–Voigt model. Agglomeration effects are considered based on Mori–Tanaka approach. The elastic medium is simulated by orthotropic visco-Pasternak medium. The motion equations are derived applying higher-order shear plate model based on sinusoidal kinematic in which the size effects are considered using Eringen’s nonlocal theory. The Navier method in conjunction with the Bolotin’s methods is applied for calculating resonance frequency and dynamic instability region of structure. The effects of different parameters such as volume percent of SWCNTs, agglomeration, volume percent of SWCNTs in volume, nonlocal parameter and structural damping on the dynamic instability of visco-system are shown. The results are compared with other published works in the literature. Results indicate that the agglomeration effects have an important role in dynamic stability of structure. In addition, increasing volume percent of SWCNTs leads to higher resonance frequency.

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References

  1. Mori, T., Tanaka, K.: Average Stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. Mater. 21, 571–574 (1973)

    Article  Google Scholar 

  2. Alibeigloo, A.: Free vibration analysis of nano-plate using three-dimensional theory of elasticity. Acta Mech. 222, 149–159 (2011)

    Article  MATH  Google Scholar 

  3. Ghorbanpour, Arani A., Kolahchi, R., Vossough, H.: Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory. Physica B 407, 4458–4465 (2012)

    Article  Google Scholar 

  4. Ramezani, Sh: Nonlinear vibration analysis of micro-plates based on strain gradient elasticity theory. Nonlinear Dyn. 73, 1399–1421 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Thai, C.H., Kulasegaram, S., Tran, L.V., Nguyen-Xuan, H.: Generalized shear deformation theory for functionally graded isotropic and sandwich plates based on isogeometric approach. Comput. Struct. 141, 94–112 (2014)

    Article  Google Scholar 

  6. Nguyen, N.T., Hui, D., Lee, J., Nguyen-Xuan, H.: An efficient computational approach for size-dependent analysis of functionally graded nanoplates. Comput. Methods Appl. Mech. Eng. 297, 191–218 (2015)

    Article  MathSciNet  Google Scholar 

  7. Ghorbanpour Arani, A., Kolahchi, R., Zarei, M.Sh: Visco-surface-nonlocal piezoelasticity effects on nonlinear dynamic stability of graphene sheets integrated with ZnO sensors and actuators using refined zigzag theory. Compos. Struct. 132, 506–526 (2015)

    Article  Google Scholar 

  8. Ghorbanpour Arani, A., Fereidoon, A., Kolahchi, R.: Nonlinear surface and nonlocal piezoelasticity theories for vibration of embedded single-layer boron nitride sheet using harmonic differential quadrature and differential cubature methods. J. Intell. Math. Syst. Struct. 26, 1150–1163 (2015)

    Article  Google Scholar 

  9. Phung-Van, P., Tran, L.V., Ferreira, A.J.M., Nguyen-Xuan, H., Abdel-Wahab, M.: Nonlinear transient isogeometric analysis of smart piezoelectric functionally graded material plates based on generalized shear deformation theory under thermo-electro-mechanical loads. Nonlinear Dyn. (2016). doi:10.1007/s11071-016-3085-6

    Google Scholar 

  10. Nguyen, H.X., Nguyen, T.N., Abdel-Wahab, M., Bordas, S.P.A., Nguyen-Xuan, H., Vo, T.P.: A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory. Comput. Methods Appl. Mech. Eng. 313, 904–940 (2017)

    Article  MathSciNet  Google Scholar 

  11. Wang, ZhX, Shen, H.S.: Nonlinear dynamic response of nanotube-reinforced composite plates resting on elastic foundations in thermal environments. Nonlinear Dyn. 70, 735–754 (2012)

    Article  MathSciNet  Google Scholar 

  12. Ghorbanpour Arani, A., Kolahchi, R., Mosallaie Barzoki, A.A., Mozdianfard, M.R., Noude Farahani, S.M.: Elastic foundation effect on nonlinear thermo-vibration of embedded double layered orthotropic graphene sheets using differential quadrature method. Proc. IMechE Part C. J. Mech. Eng. Sci. 227, 862–879 (2013)

    Article  Google Scholar 

  13. Natarajan, S., Haboussi, M., Manickam, G.: Application of higher-order structural theory to bending and free vibration analysis of sandwich plates with CNT reinforced composite facesheets. Compos. Struct. 113, 197–207 (2014)

    Article  Google Scholar 

  14. Abdollahzadeh Shahrbabaki, E., Alibeigloo, A.: Three-dimensional free vibration of carbon nanotube-reinforced composite plates with various boundary conditions using Ritz method. Compos. Struct. 111, 362–370 (2014)

    Article  Google Scholar 

  15. Heydari, M.M., Hafizi Bidgoli, A., Golshani, H.R., Beygipoor, Gh, Davoodi, A.: Nonlinear bending analysis of functionally graded CNT-reinforced composite Mindlin polymeric temperature-dependent plate resting on orthotropic elastomeric medium using GDQM. Nonlinear Dyn. 79, 1425–1441 (2015)

    Article  Google Scholar 

  16. Phung-Van, P., Abdel-Wahab, M., Liew, K.M., Bordas, S.P.A., Nguyen-Xuan, H.: Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory. Compos. Struct. 123, 137–149 (2015)

    Article  Google Scholar 

  17. Kolahchi, R., Rabani Bidgoli, M., Beygipoor, Gh, Fakhar, M.H.: A nonlocal nonlinear analysis for buckling in embedded FG-SWCNT-reinforced microplates subjected to magnetic field. J. Mech. Sci. Tech. 29, 3669–3677 (2015)

    Article  Google Scholar 

  18. Phung-Van, P., Nguyen, L.B., Tran, L.V., Dinh, T.D., Thai, C.H., Bordas, S.P.A., Abdel-Wahab, M., Nguyen-Xuan, H.: An efficient computational approach for control of nonlinear transient responses of smart piezoelectric composite plates. Int. J. Nonlinear Mech. 76, 190–202 (2015)

    Article  Google Scholar 

  19. Phung-Van, P., Abdel-Wahab, M., Liew, K.M.: Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory. Compos. Struct. 123, 137–149 (2015)

    Article  Google Scholar 

  20. Kolahchi, R., Moniri Bidgoli, A.M., Heydari, M.M.: Size-dependent bending analysis of FGM nano-sinusoidal plates resting on orthotropic elastic medium. Struct. Eng. Mech. 55, 1001–1014 (2015)

    Article  Google Scholar 

  21. Kolahchi, R., Safari, M., Esmailpour, M.: Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium. Compos. Struct. 150, 255–265 (2016)

    Article  Google Scholar 

  22. Ghorbanpour Arani, A., Jamali, M., Mosayyebi, M., Kolahchi, R.: Wave propagation in FG-CNT-reinforced piezoelectric composite micro plates using viscoelastic quasi-3D sinusoidal shear deformation theory. Compos. Part B Eng. 95, 209–224 (2016)

    Article  Google Scholar 

  23. Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703–10 (1983)

    Article  Google Scholar 

  24. Lei, Y., Adhikari, S., Friswell, M.I.: Vibration of nonlocal Kelvin-Voigt viscoelastic damped Timoshenko beams. Int. J. Eng. Sci. 66–67, 1–13 (2013)

    Article  MathSciNet  Google Scholar 

  25. Reddy, J.N.: Analysis of functionally graded plates. Int. J. Numer. Methods Eng. 47, 663–684 (2000)

    Article  MATH  Google Scholar 

  26. Touratier, M.: An efficient standard plate theory. Int. J. Eng. Sci. 29, 901–916 (1991)

    Article  MATH  Google Scholar 

  27. Benyoucef, S., Mechab, I., Tounsi, A., Fekrar, A., Ait Atmane, H., Adda Bedia, E.A.: Bending of thick functionally graded plates resting on Winkler-Pasternak elastic foundations. Mech. Compos. Mater. 46, 425–434 (2010)

    Article  Google Scholar 

  28. Mantari, J.L., Oktem, A.S., Guedes Soares, C.: Bending response of functionally graded plates by using a new higher order shear deformation theory. Compos. Struct. 94, 714–723 (2012)

    Article  MATH  Google Scholar 

  29. Thai, H.T., Vo, T.P.: A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates. Appl. Math. Model. 37, 3269–3281 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  30. Kolahchi, R., Moniribidgoli, A.M.: Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes. Appl. Math. Mech. 37, 265–274 (2016)

    Article  MathSciNet  Google Scholar 

  31. Mosharrafian, F., Kolahchi, R.: Nanotechnology, smartness and orthotropic nonhomogeneous elastic medium effects on buckling of piezoelectric pipes. Struct. Eng. Mech. 58, 931–947 (2016)

    Article  Google Scholar 

  32. Bolotin, V.V.: The dynamic stability of elastic systems. In: The Dynamic Stability of Elastic Systems. Holden-Day, San Francisco (1964)

  33. Lanhe, W., Hongjun, W., Daobin, W.: Dynamic stability analysis of FGM plates by the moving least squares differential quadrature method. Compos. Struct. 77, 383–394 (2007)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Meymeh Branch, Islamic Azad University, Meymeh, Iran

    Reza Kolahchi & Ali Cheraghbak

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  1. Reza Kolahchi
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  2. Ali Cheraghbak
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Correspondence to Reza Kolahchi.

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Kolahchi, R., Cheraghbak, A. Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method. Nonlinear Dyn 90, 479–492 (2017). https://doi.org/10.1007/s11071-017-3676-x

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  • DOI: https://doi.org/10.1007/s11071-017-3676-x

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