Dynamic Response of Nano Spherical Shell Subjected to Termo-Mechanical Shock Using Nonlocal Elasticity Theory

In this paper, we present an analytical method for
analysis of nano-scale spherical shell subjected to thermo-mechanical
shocks based on nonlocal elasticity theory. Thermo-mechanical
properties of nano shpere is assumed to be temperature dependent.
Governing partial differential equation of motion is solved
analytically by using Laplace transform for time domain and power
series for spacial domain. The results in Laplace domain is
transferred to time domain by employing the fast inverse Laplace
transform (FLIT) method. Accuracy of present approach is assessed
by comparing the the numerical results with the results of published
work in literature. Furtheremore, the effects of non-local parameter
and wall thickness on the dynamic characteristics of the nano-sphere
are studied.

Authors:

• J. Ranjbarn
• A. Alibeigloo

Keywords:

• Nano-scale spherical shell
• nonlocal elasticity theory
• thermomechanical shock.

References:

[1] Y.M. Fu, J.W. Hong, X.Q. Wang, “Analysis of nonlinear vibration for
embedded carbon nanotubes”, J Sound Vib, vol.296, pp. 746–756, 2006.
[2] C. Sun, K. Liu, “Vibration of multi-walled carbon nanotubes with initial
axial loading”, Solid State Commun, vol. 143, pp. 202–207, 2007.
[3] M.Aydogdu, “Vibration of multi-walled carbon nanotubes by
generalized shear deformation theory”, Int J Mech Sci , vol. 50, pp. 837–
844, 2008.
[4] L.L. Ke, Y. Xiang, J. Yang, S. Kitipornchai, “Nonlinear free vibration of
embedded double-walled carbon nanotubes based on nonlocal
Timoshenko beam theory’, Comp Mater Sci, vol. 47, pp. 409–417, 2009.
[5] M.Aydogdu, “Axial vibration of the nanorods with the nonlocal
continuum rod model”, Physica E, vol.4, pp. 861–864, 2009.
[6] J. Yang, L.L. Ke, S. Kitipornchai, “Nonlinear free vibration of singlewalled
carbon nanotubes using nonlocal Timoshenko beam theory”,
Physica E, vol. 42, pp.1727–1735, 2010.
[7] M.Maachou, M.Zidour, H.Baghdadi, N.Ziane, A. Tounsi, “A nonlocal
Levinson beam model for free vibration analysis of zigzag single-walled
carbon nanotubes including thermal effects”, Solid State Commun, vol.
151, pp.1467–1471, 2011.
[8] M.Zidour, K.H.Benrahou, A.Semmah, M.Naceri, H. A.Belhadj, K.
Bakhti, A.Touns, “The thermal effect on vibration of zigzag single
walled carbon nanotubes using nonlocal Timoshenko beam theory”,
Comp Mater Sci,vol.51, pp. 252–260, 2012.
[9] J.W. Yan, K.M. Liew, L.H. He, “Free vibration analysis of single-walled
carbon nanotubes using a higher-order gradient theory”, J Sound Vib,
vol.332, pp.3740–3755, 2013.
[10] M.S. Hoseinzadeh, S.E. Khadem, “A nonlocal shell theory model for
evaluation of thermoelastic damping in the vibration of a double-walled
carbon nanotube”, Physica E, vol.57, pp. 6–11, 2014.
[11] F. Kiani, T. Khosravi, F. Moradi, P. Rahbari, M.J. Aghaei, M. Arabi, H.
Tajik, R Kalantarinejad, “Computational Investigation of Carbon
NanotubesEnhanced Membrane for Water Desalination Based on Flux
and Rejection Characteristics”, J Comput Theor Nanos,vol.11, pp.1237-
1243, 2014.
[12] F. Durbin, “Numerical inversion of Laplace transforms: an efficient
improvement to Dubner and Abate’s method”,Comput J, vol.17, pp.
371–376, 1974
[13] H.M.Wang, H.J.Ding, “Transient responses of a magneto-electro-elastic
hollow sphere for fully coupled spherically symmetric problem”, Eur J
Mech A-Solid, vol.25, pp. 965–980, 2006.