Similar articles

Abstract: The transverse free vibration of nanobeams subjected to an initial axial tension based on nonlocal stress theory is presented. It considers the effects of nonlocal stress field on the natural frequencies and vibration modes. The effects of a small scale parameter at molecular level unavailable in classical macro-beams are investigated for three different types of boundary conditions: simple supports, clamped supports and elastically-constrained supports. Analytical solutions for transverse deformation and vibration modes are derived. Through numerical examples, effects of the dimensionless nanoscale parameter and pre-tension on natural frequencies are presented and discussed.

[1] Benzair, A., Tounsi, A., Besseghier, A., Heireche, H., Moulay, N., Boumia, L., 2008. The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory. Journal of Physics D: Applied Physics, 41(22):225404.

[2] Chen, L.Q., Wu, J., 2005. Bifurcation in transverse vibration of axially accelerating viscoelastic strings. Acta Mechanica Solida Sinica, 26(1):83-86.

[3] Eringen, A.C., 1972. Nonlocal polar elastic continua. International Journal of Engineering Science, 10(1):1-16.

[4] Eringen, A.C., 1983. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics, 54(9):4703-4710.

[5] Eringen, A.C., 2002. Nonlocal Continuum Field Theories. Springer-Verlag, New York, USA, p.285-316.

[6] Eringen, A.C., Edelen, D.G.B., 1972. On nonlocal elasticity. International Journal of Engineering Science, 10(3):233-248.

[7] Fung, Y.C., 1965. Foundations of Solid Mechanics. Prentice-Hall, Englewood Cliffs, NJ, USA, p.305-359.

[8] Kumar, D., Heinrich, C., Wass, A.M., 2008. Buckling analysis of carbon nanotubes modeled using nonlocal continuum theories. Journal of Applied Physics, 103(7):073521.

[9] Lim, C.W., Wang, C.M., 2007. Exact variational nonlocal stress modeling with asymptotic higher-order strain gradients for nanobeams. Journal of Applied Physics, 101(5):054312.

[10] Liu, Y.Q., Zhang, W., 2007. Transverse nonlinear dynamical characteristic of viscoelastic belt. Journal of Beijing University of Technology, 33(11):10-13.

[11] Lu, P., Lee, H.P., Lu, C., Zhang, P.Q., 2006. Dynamic properties of flexural beams using a nonlocal elasticity model. Journal of Applied Physics, 99(7):073510.

[12] Mote, C.D.Jr., 1965. A study of band saw vibrations. Journal of the Franklin Institute, 279(6):430-444.

[13] Mote, C.D.Jr., Naguleswaran, S., 1966. Theoretical and experimental band saw vibrations. ASME Journal of Engineering Industry, 88(2):151-156.

[14] Oz, H.R., Pakdemirli, M., Boyaci, H., 2001. Non-linear vibrations and stability of an axially moving beam with time-dependent velocity. International Journal of Non-Linear Mechanics, 36(1):107-115.

[15] Peddieson, J., Buchanan, G.R., McNitt, R.P., 2003. Application of nonlocal continuum models to nanotechnology. International Journal of Engineering Science, 41(3-5):305-312.

[16] Reddy, J.N., Wang, C.M., 1998. Deflection relationships between classical and third-order plate theories. Acta Mechanica Sinica, 130(3):199-208.

[17] Simpson, A., 1973. Transverse modes and frequencies of beams translating between fixed end supports. Journal of Mechanical Engineering Science, 15(3):159-164.

[18] Tounsi, A., Heireche, H., Berrabah, H.M., Benzair, A., Boumia, L., 2008. Effect of small size on wave propagation in double-walled carbon nanotubes under temperature field. Journal of Applied Physics, 104(10):104301.

[19] Wang, C.M., Duan, W.H., 2008. Free vibration of nanorings/arches based on nonlocal elasticity. Journal of Applied Physics, 104(1):014303.

[20] Wang, C.M., Zhang, Y.Y., Ramesh, S.S., Kitipornchai, S., 2006. Buckling analysis of micro- and nano-rods/tubes based on nonlocal Timoshenko beam theory. Journal of Applied Physics, 39(17):3904-3909.

[21] Wang, C.M., Kitipornchai, S., Lim, C.W., Eisenberger, M., 2008. Beam bending solutions based on nonlocal Timoshenko beam theory. Journal of Engineering Mechanics, ASCE, 134(6):475-481.

[22] Wang, Q., 2005. Wave propagation in carbon nanotubes via nonlocal continuum mechanics. Journal of Applied Physics, 98(12):124301.

[23] Wang, Q., Varadan, V.K., 2006. Vibration of carbon nanotubes studied using nonlocal continuum mechanics. Smart Materials and Structures, 15(2):659-666.

[24] Xie, G.M., 2007. Vibration Mechanics. National Defense Industry Press, Beijing, China, p.198-203 (in Chinese).

[25] Xu, M.T., 2006. Free transverse vibrations of nano-to-micron scale beams. Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences, 462(2074):2977-2995.

[26] Yang, X.D., Chen, L.Q., 2005. Dynamic stability of axially moving viscoelastic beams with pulsating speed. Applied Mathematics and Mechanics, 26(8):905-910.

[27] Yang, X.D., Lim, C.W., 2008. Nonlinear Vibrations of Nano-beams Accounting for Nonlocal Effect. Fourth Jiangsu-Hong Kong Forum on Mechanics and Its Application, Suzhou, China. Jiangsu Society of Mechanics, Nanjing, p.16-17.

[28] Zhang, Y.Q., Liu, G.R., Wang, J.S., 2004. Small-scale effects on buckling of multiwalled carbon nanotubes under axial compression. Physical Review B, 70(20):205430.

[29] Zhang, Y.Q., Liu, G.R., Xie, X.Y., 2005. Free transverse vibrations of double-walled carbon nanotubes using a theory of nonlocal elasticity. Physical Review B, 71(19):195404.