بررسی تأثیر توزیع نانولوله‌های کربنی تابعی روی فرکانس‌های ورق قطاعی بر روی بستر الاستیک

1. Rao, S.S. and Sunar, M.“Piezoelectricity and Its Use in Disturbance Sensing and Control of Flexible Structures: A Survey”, App. Mech. Rev. Vol. 47, No. 4, pp. 113-123, 1994.##

2. Zhong, Z. and Shang, E.T. “Three-Dimensional Exact Analysis of a Simply Supported Functionally Gradient Piezoelectric Plate”, Int. J. Sol. Stru.Vol. 40, No. 20, pp. 5335-5352, 2003.##

3. Nie, G.J. and Zhong, Z.“Semi-Analytical Solution for Three-Dimensional Vibration of Functionally Graded Circular Plates”, Com. Meth. App. Mech. Eng. Vol. 196, No's. 49–52, pp. 4901-4910, 2007.##

4. Han, Y. and Elliott, J. “Molecular Dynamics Simulations of The Elastic Properties of Polymer/Carbon Nanotube Composites”, Comput. Mat. Sci. Vol. 39, No. 2, pp. 315-323, 2007.##

5. Liew, K.M., Lei, Z.X., and Zhang, L.W.“Mechanical Analysis of Functionally Graded Carbon Nanotube Reinforced Composites: A Review”, Compos. Stru. Vol. 120, pp. 90-97, 2015.##

6. Ke, L. L., Yang, J. and Kitipornchai, S.“Nonlinear Free Vibration of Functionally Graded Carbon Nanotube-Reinforced Composite Beams”, Compos. Stru. Vol. 92, No. 3, pp. 676-683, 2010.##

7. Nejati, M., Eslampanah, A., and Najafizadeh, M. “Buckling and Vibration Analysis of Functionally Graded Carbon Nanotube-Reinforced Beam Under Axial Load”, Int. J. App. Mech. Vol. 8, No. 1, pp. 165-178, 2016.##

8. Nejati, M., Mohsenimonfared, H., and Asanjarani, A. “Free Vibration Analysis of 2D Functionally Graded Annular Plate Considering the Effect of Material Composition via 2D Differential Quadrature Method”, Mech. Adv. Compos. Stru. Vol. 2, No. 2, pp. 95-111, 2015.##

9. Molla-Alipour, M.“ Dynamic Behavior Analysis of FG Circular and Annular Plates with Stepped Variations of Thickness under Various Load”, Modares Mech. Eng. Vol. 16, No. 7, pp. 251-260, 2016.##

10. Molla-Alipour, M. “Closed-Form Solution of Circular and Annular Plateswith Elastic Boundary Conditions under Non-Uniform Normal and Shear Loads”, Modares Mech. Eng. Vol. 16, No. 6, pp. 29-40, 2016.##

11. ebrahimi, f.,“Free Vibration Analysis Of Thick Functionally Graded Rotating Beam By Differential Transform Method”, Aero. Mech. J. Vol.12, No.4, pp. 49-61, 2017.##

12. Jafari Mehrabadi, s.,“Free Vibration Analysis of FGM Plate Reinforced with Single Wall Carbon Nanotubes Using 3-D Elasticity Theory”, Aero. Mech. J. Vol.11, No.4, pp. 1-14, 2015.##

13. Feli, S., L. Karami and S.S. JAFARI,“Analytical Modeling of Low Velocity Impact on Carbon Nanotube-Reinforced Composite (CNTRC) Plates”, Mech. Adv. Mat. Stru. Vol., pp. 1-13, 2017.##

14. Laura, P.A.A., Gutierrez, R.H. Carnicer, R., and Sanzi, H.C. “Free Vibrations of a Solid Circular Plate of Linearly Varying Thickness and Attached to a Winkler Foundation”, J. Sou. Vib. Vol. 144, No. 1, pp. 149-161, 1991.##

15. Ju, F., Lee, H.P., and Lee, K.H. “Free Vibration of Plates with Stepped Variations in Thickness on Non-Homogeneous Elastic Foundations”, J. of Sou. Vib. Vol. 183, No. 3, pp. 533-545, 1995.##

16. Gupta, U.S., Ansari,  A.H. and Sharma, S. “Buckling and Vibration of Polar Orthotropic Circular Plate Resting on Winkler Foundation”, J.  Sou. Vib. Vol. 297, No's. 3–5, pp. 457-476, 2006.##

17. Lal, R., Gupta, U.S., and Reena, “Quintic Splines In The Study of Transverse Vibrations of Non-Uniform Orthotropic Rectangular Plates”, J. Sou. Vib. Vol. 207, No. 1, pp. 1-13, 1997.##

18. Huang, M., Sakiyama, T., Matsuda, H., and Morita, C. “Free Vibration Analysis of Stepped Rectangular Plates Resting on Non-Homogeneous Elastic Foundations”, Eng. Analys. Bound. Elem. Vol. 50, pp. 180-187, 2015.##

19. Matsunaga, H.,“Vibration and Stability of Thick Plates on Elastic Foundations”, J. Eng. Mech. Vol.126, No.1, pp. 27-34, 2000.##

20. Malekzadeh, P.,“Three-Dimensional Free Vibration Analysis of Thick Functionally Graded Plates on Elastic Foundations”, Compos. Stru. Vol. 89, No. 3, pp. 367-373, 2009.##

21. mousavi, Z. and A.R. Saidi,“Free Vibration Analysis of Thick Functionally Graded Rectangular Plates Based on The Higher-Order Shear and Normal Deformable”, Aero. Mech. J. Vol.12, No.1, pp. 1-12, 2016.##

22. Saidi, A.R. and Z. mousavi,“Free Vibration Analysis of Thick Functionally Graded Piezoelectric Rectangular Plates in Closed Circuit Condition”, Aero. Mech. J. Vol.12, No.1, pp. 67-78, 2016.##

23. Fallah, A., M.M. Aghdam and Kargarnovin, M.H. “Free Vibration Analysis of Moderately Thick Functionally Graded Plates on Elastic Foundation Using the Extended Kantorovich Method”, Arch. App. Mech. Vol. 83, No. 2, pp. 177-191, 2013.##

24. Yas, M.H. and Aragh, B.S.“Free Vibration Analysis of Continuous Grading Fiber Reinforced Plates on Elastic Foundation”, Int. J. Eng. Sci. Vol. 48, No. 12, pp. 1881-1895, 2010.##

25. Malekzadeh, P. and Karami, G. “Vibration of Non-Uniform Thick Plates on Elastic Foundation by Differential Quadrature Method”, Eng. Stru. Vol. 26, No. 10, pp. 1473-1482, 2004.##

26. Xiang, Y.“Vibration of Rectangular Mindlin Plates Resting on Non-Homogenous Elastic Foundations”, Int. J. Mech. Sci. Vol. 45, No's. 6–7, pp. 1229-1244, 2003.##

27. Zhou, D., Cheung, Y.K. Lo, S.H. and Au, F.T.K. “Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation”, Int. J. Num.Meth. Eng. Vol. 59, No. 10, pp. 1313-1334, 2004.##

28. Heshmati, M. and Yas, M.H.“Dynamic Analysis of Functionally Graded Multi-Walled Carbon Nanotube-polystyrene nanocomposite beams subjected to multi-moving loads”, Mat. Des. Vol. 49, pp. 894-904, 2013.##

29. Omidi, M., Rokni D.T, H., Milani, A.S., Seethaler R.J., and Arasteh, R. “Prediction of the Mechanical Characteristics of Multi-Walled Carbon Nanotube/Epoxy Composites Using a New Form of the rule of Mixtures”, Carb. Vol. 48, No. 11, pp. 3218-3228, 2010.##

30. Andrews, R., Jacques, D., Minot, M., and Rantell, T. “Fabrication of Carbon Multiwall Nanotube/Polymer Composites by Shear Mixing”, Mac. Mat. Eng. Vol. 287, No. 6, pp. 395-403, 2002.##

31. Najafizadeh, M.M. and Heydari, H.R. “An Exact Solution For Buckling of Functionally Graded Circular Plates Based on Higher Order Shear Deformation Plate Theory under Uniform Radial Compression”, International J. Mech. Sci. Vol. 50, No. 3, pp. 603-612, 2008.##

32. Razavi, S. and Shooshtari, A. “Nonlinear Free Vibration of Magneto-Electro-Elastic Rectangular Plates”, Compos. Stru. Vol. 119, pp. 377-384, 2015.##

33. Alireza, S., Seyedeh Marzieh, H., Mahmoodi, S.N., and Hamed, K. “Analytical Solution for Nonlinear Free Vibrations of Viscoelastic Microcantilevers Covered with a Piezoelectric Layer”, Sma. Mat. Stru. Vol. 21, No. 7, pp. 075015, 2012.##

34. Jafari, S.S., Rashidi, M.M., and Johnson, S. “Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams”, Lat. Ame. J. Sol. Stru. ABCM J. Vol. 13, No. 7, pp. 1250-1264, 2016.##

35. Ebrahimia, F. and Mokhtaria, M. “Semi-analytical Vibration Characteristics of Rotating Timoshenko Beams Made of Functionally Graded Materials”, Lat. Ame. J. Sol. Stru. Vol. 12, No. 7, pp. 1319-1339, 2015.##

36. Zafarmand, H., Salehi, M. and Asemi, K.“Three Dimensional Free Vibration and Transient Analysis of Two Directional Functionally Graded Thick Cylindrical Panels under Impact Loading”, Lat. Ame. J. Sol. Stru. Vol. 12, No. 2, pp. 205-225, 2015.##

37. Bellman, R. and Casti, J. “Differential Quadrature and Long-Term Integration”, J. of Math. Analy. App. Vol. 34, No. 2, pp. 235-238, 1971.##

38. Bert, C.W. and Malik, M. “Differential Quadrature Method in Computational Mechanics: A Review”, App. Mech. Rev. Vol. 49, No. 1, pp. 1-28, 1996.##

39. Shu, C., “Differential quadrature and its application in engineering” Springer Science & Business Media, 2012.##

40. Jodaei, A., Jalal, M., and Yas, M.H. “Free Vibration Analysis of Functionally Graded Annular Plates by State-Space Based Differential Quadrature Method and Comparative Modeling by ANN”, Compos. Part B: Eng. Vol. 43, No. 2, pp. 340-353, 2012.##