An exact solution for buckling analysis of embedded piezo-electro-magnetically actuated nanoscale beams

- Journal title : Advances in nano research
- Volume 4, Issue 2, 2016, pp.65-84
- Publisher : Techno-Press
- DOI : 10.12989/anr.2016.4.2.065

Title & Authors

An exact solution for buckling analysis of embedded piezo-electro-magnetically actuated nanoscale beams

Ebrahimi, Farzad; Barati, Mohammad Reza;

Ebrahimi, Farzad; Barati, Mohammad Reza;

Abstract

This paper investigates the buckling behavior of shear deformable piezoelectric (FGP) nanoscale beams made of functionally graded (FG) materials embedded in Winkler-Pasternak elastic medium and subjected to an electro-magnetic field. Magneto-electro-elastic (MEE) properties of piezoelectric nanobeam are supposed to be graded continuously in the thickness direction based on power-law model. To consider the small size effects, Eringen`s nonlocal elasticity theory is adopted. Employing Hamilton`s principle, the nonlocal governing equations of the embedded piezoelectric nanobeams are obtained. A Navier-type analytical solution is applied to anticipate the accurate buckling response of the FGP nanobeams subjected to electro-magnetic fields. To demonstrate the influences of various parameters such as, magnetic potential, external electric voltage, power-law index, nonlocal parameter, elastic foundation and slenderness ratio on the critical buckling loads of the size-dependent MEE-FG nanobeams, several numerical results are provided. Due to the shortage of same results in the literature, it is expected that the results of the present study will be instrumental for design of size-dependent MEE-FG nanobeams.

Keywords

piezoelectric nanobeam;magneto-electro-elastic FG nanobeam;buckling;nonlocal elasticity theory;higher order beam theory;

Language

English

Cited by

1.

A new refined nonlocal beam theory accounting for effect of thickness stretching in nanoscale beams,;;;;

2.

Dynamic modeling of embedded curved nanobeams incorporating surface effects,;;

3.

Buckling behavior of smart MEE-FG porous plate with various boundary conditions based on refined theory,;;

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

References

1.

Alizada, A.N. and Sofiyev, A.H. (2011a), "Modified Young's moduli of nano-materials taking into account the scale effects and vacancies", Meccanica., 46(5), 915-920.

2.

Alizada, A.N. and Sofiyev, A.H. (2011b), "On the mechanics of deformation and stability of the beam with a nanocoating", J. Reinf. Plastic. Comp., 0731684411428382.

3.

Alizada, A.N., Sofiyev, A.H. and Kuruoglu, N. (2012), "Stress analysis of a substrate coated by nanomaterials with vacancies subjected to uniform extension load", Acta. Mech., 223(7), 1371-1383.

4.

Annigeri, A.R., Ganesan, N. and Swarnamani, S. (2007), "Free vibration behaviour of multiphase and layered magneto-electro-elastic beam", J. Sound. Vib., 299(1), 44-63.

5.

Ansari, R., Hasrati, E., Gholami, R. and Sadeghi, F. (2015), "Nonlinear analysis of forced vibration of nonlocal third-order shear deformable beam model of magneto-electro-thermo elastic nanobeams", Compos. Part. B. Eng., 83, 226-241.

6.

Barati, M.R., Zenkour, A.M. and Shahverdi, H. (2016), "Thermo-mechanical buckling analysis of embedded nanosize FG plates in thermal environments via an inverse cotangential theory", Compos. Struct., 141(1), 203-212

7.

Chen, W.Q., Lee, K.Y. and Ding, H.J. (2005), "On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates", J. Sound. Vib., 279(1), 237-251.

8.

Daga, A., Ganesan, N. and Shankar, K. (2009), "Transient dynamic response of cantilever magneto-electro-elastic beam using finite elements", Int. J. Comput. Meth. Eng. Sci. Mech., 10(3), 173-185.

9.

Ebrahimi, F. and Salari, E. (2015a), "Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG nanobeams with various boundary conditions", Compos. Part. B. Eng., 78, 272-290.

10.

Ebrahimi, F. and Salari, E. (2015b), "Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments", Compos. Struct., 128, 363-380.

11.

Ebrahimi, F. and Barati, M.R. (2015), "A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams", Arab. J. Sci. Eng., 41(5), 1679-1690.

12.

Eringen, A.C. and Edelen, D. G. B. (1972a), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248.

14.

Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710.

15.

Huang, D.J., Ding, H.J. and Chen, W.Q. (2007), "Analytical solution for functionally graded magneto-electro-elastic plane beams", Int. J. Eng. Sci., 45(2), 467-485.

16.

Kattimani, S.C. and Ray, M.C. (2015), "Control of geometrically nonlinear vibrations of functionally graded magneto-electro-elastic plates", Int. J. Mech. Sci., 99, 154-167.

17.

Ke, L.L. and Wang, Y.S. (2014), "Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory", Phys. E., 63, 52-61.

18.

Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2014), "Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory", Acta. Mech. Sinica., 30(4), 516-525.

19.

Kumaravel, A., Ganesan, N. and Sethuraman, R. (2007), "Buckling and vibration analysis of layered and multiphase magneto-electro-elastic beam under thermal environment", Multidis. Model. Mater. Struct., 3(4), 461-476.

20.

Li, X.Y., Ding, H.J. and Chen, W.Q. (2008), "Three-dimensional analytical solution for functionally graded magneto-electro-elastic circular plates subjected to uniform load", Compos. Struct., 83(4), 381-390.

21.

Li, Y.S., Cai, Z.Y. and Shi, S.Y. (2014), "Buckling and free vibration of magnetoelectroelastic nanoplate based on nonlocal theory", Compos. Struct., 111, 522-529.

22.

Liu, M.F. and Chang, T.P. (2010), "Closed form expression for the vibration problem of a transversely isotropic magneto-electro-elastic plate", J. Appl. Mech., 77(2), 024502.

23.

Mahmoud, S.R., Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi, A. and Bég, O.A. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425.

24.

Milazzo, A.L.B.E.R.T.O., Orlando, C.A.L.O.G.E.R.O. and Alaimo, A.N.D.R.E.A. (2009), "An analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem", Smart. Mater. Struct., 18(8), 085012.

25.

Pan, E. and Han, F. (2005), "Exact solution for functionally graded and layered magneto-electro-elastic plates", Int. J. Eng. Sci., 43(3), 321-339.

26.

Rahmani, O. and Jandaghian, A.A. (2015), "Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory", Appl. Phys. A., 119(3), 1019-1032.

27.

Rahmani, O. and Pedram, O. (2014), "Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory", Int. J. Eng. Sci., 77, 55-70.

28.

Razavi, S. and Shooshtari, A. (2015), "Nonlinear free vibration of magneto-electro-elastic rectangular plates", Compos. Struct., 119, 377-384.

29.

Simsek, M. and Yurtcu, H.H. (2013), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory", Compos. Struct., 97, 378-386.

30.

Sladek, J., Sladek, V., Krahulec, S., Chen, C.S. and Young, D.L. (2015), "Analyses of circular magnetoelectroelastic plates with functionally graded material properties", Mech. Adv. Mater. Struct., 22(6), 479-489.

31.

Van Run, A.M.J.G., Terrell, D.R. and Scholing, J.H. (1974), "An in situ grown eutectic magnetoelectric composite material", J. Mater. Sci., 9(10), 1710-1714.

32.

Wu, B., Zhang, C., Chen, W. and Zhang, C. (2015), "Surface effects on anti-plane shear waves propagating in magneto-electro-elastic nanoplates", Smart. Mater. Struct., 24(9), 095017.

33.

Wu, C.P. and Tsai, Y.H. (2007), "Static behavior of functionally graded magneto-electro-elastic shells under electric displacement and magnetic flux", Int. J. Eng. Sci., 45(9), 744-769.