Journal of Engineering and Applied Sciences

Year: 2016
Volume: 11
Issue: 9
Page No. 2079 - 2084

Non-Linear Dynamics of Flexible Curvilinear Bernoulli-Euler Nano-Beams in a Stationary Temperature Field

Authors : J. Awrejcewicz, I. Kutepov, S.P. Pavlov, I.V. Papkova and A.V. Krysko

References

Aifantis, E.C., 1999. Strain gradient interpretation of size effects. Int. J. Fract., 95: 299-314.
CrossRef  |  Direct Link  |  

Asghari, M., M.H. Kahrobaiyan and M.T. Ahmadian, 2010. A nonlinear Timoshenko beam formulation based on the modified couple stress theory. Int. J. Eng. Sci., 48: 1749-1761.
Direct Link  |  

Asghari, M., M.T. Ahmadian, M.H. Kahrobaiyan and M. Rahaeifard, 2010. On the size-dependent behavior of functionally graded micro-beams. Mater. Des., 31: 2324-2329.
CrossRef  |  

Awrejcewicz, J., A.V. Krysko, I.E. Kutepov, N.A. Zagniboroda and V. Dobriyan et al., 2013. Chaotic dynamics of flexible euler-bernoulli beams. Chaos Interdiscip. J. Nonlinear Sci., 23: 43-130.
Direct Link  |  

Eringen, A.C., 1972. Nonlocal polar elastic continua. Int. J. Eng. Sci., 10: 1-16.
CrossRef  |  Direct Link  |  

Feodosev, V.I., 1963. On a method of solution of the nonlinear problems of stability of deformable systems. J. Appl. Math. Mech., 27: 392-404.

Fleck, N.A. and J.W. Hutchinson, 1997. Strain gradient plasticity. Adv. Appl. Mech., 33: 296-361.

Fleck, N.A., G.M. Muller, M.F. Ashby and J.W. Hutchinson, 1994. Strain gradient plasticity: Theory and experiment. Acta Metall. Mater., 42: 475-487.
CrossRef  |  Direct Link  |  

Fu, Y. and J. Zhang, 2010. Electromechanical dynamic buckling phenomenon in symmetric electric fields actuated microbeams considering material damping. Acta Mech., 215: 29-42.
CrossRef  |  Direct Link  |  

Ghasemi, A.R. and M. Mohandes, 2016. Size-dependent bending of geometrically nonlinear of micro-laminated composite beam based on modified couple stress theory. Mech. Adv. Compos. Struct., ‎3: 53-62.
Direct Link  |  

Gurtin, M.E., J. Weissmuller and F. Larche, 1998. A general theory of curved deformable interfaces in solids at equilibrium. Philos. Mag., 78: 1093-1109.
Direct Link  |  

Jia, X.L. J. Yang and S. Kitipornchai, 2011. Pull-in instability of geometrically nonlinear micro-switches under electrostatic and Casimir forces. Acta Mech., 218: 161-174.
CrossRef  |  Direct Link  |  

Kantor, B.Y., 1971. Nonlinear Problems of the Theory of Inhomogeneous Shallow Shells. Naukova Dumka, Kiev, Ukraine,.

Kiani, K., 2016. Thermo-elasto-dynamic analysis of axially functionally graded non-uniform nanobeams with surface energy. Int. J. Eng. Sci., 106: 57-76.
Direct Link  |  

Krysko, V.A., J. Awrejcewicz and S.A. Komarov, 2005. Nonlinear deformations of spherical panels subjected to transversal load action. Comput. Methods Appl. Mech. Eng., 194: 3108-3126.
Direct Link  |  

Lam, D.C.C., F. Yang, A.C.M. Chong, J. Wang and P. Tong, 2003. Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids, 51: 1477-1508.
CrossRef  |  Direct Link  |  

Lazopoulos, K.A. and A.K. Lazopoulos, 2010. Bending and buckling of thin strain gradient elastic beams. Eur. J. Mech. A. Solids, 29: 837-843.
Direct Link  |  

Ma, H.M., X.L. Gao and J.N. Reddy, 2010. A nonclassical reddy-levinson beam model based on a modified couple stress theory. Int. J. Multiscale Comput. Eng., 8: 167-180.
Direct Link  |  

Ma, H.M., X.L. Gao and J.N. Reddy, 2011. A non-classical mindlin plate model based on a modified couple stress theory. Acta Mech., 220: 217-235.
CrossRef  |  Direct Link  |  

Ma, Q. and D.R. Clarke, 1995. Size dependent hardness of silver single crystals. J. Mater. Res., 10: 853-863.
Direct Link  |  

Mazza, E., S. Abel and J. Dual, 1996. Experimental determination of mechanical properties of Ni and Ni-Fe microbars. Microsyst. Technol., 2: 197-202.
CrossRef  |  Direct Link  |  

Mindlin, R.D. and H.F. Tiersten, 1962. Effects of couple-stresses in linear elasticity. Arch. Rational Mech. Anal., 11: 415-448.
CrossRef  |  

Mojahedi, M., M. Moghimi Zand and M.T. Ahmadian, 2010. Static pull-in analysis of electrostatically actuated microbeams using homotopy perturbation method. Applied Math. Modell., 34: 1032-1041.
CrossRef  |  

Nix, W.D., 1989. Mechanical properties of thin films. Metall. Trans., 20: 2217-2245.
CrossRef  |  Direct Link  |  

Scheible, D.V., A. Erbe, R.H. Blick and G. Corso, 2002. Evidence of a nanomechanical resonator being driven into chaotic response via the Ruelle-Takens route. Appl. Phys. Lett., 81: 1884-1886.
Direct Link  |  

Tikhonov, A.N. and V.Y. Arsenin, 1977. Methods for Solving Ill-Posed Problems. John Wiley and Sons, Hoboken, New Jersey, USA.,.

Toupin, R.A., 1962. Elastic materials with couple-stresses. Arch. Rational Mech. Anal., 11: 385-414.
CrossRef  |  

Yang, F., A.C.M. Chong, D.C.C. Lam and P. Tong, 2002. Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct., 39: 2731-2743.
CrossRef  |  

Design and power by Medwell Web Development Team. © Medwell Publishing 2024 All Rights Reserved