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45. Wang, G.F., Feng, X.Q.: Surface effects on buckling of nanowires under uniaxial compression.
Appl. Phys. Lett. 94, 141913 (2009)
46. Wang, G.F., Feng, X.Q.: Timoshenko beam model for buckling and vibration of nanowires
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Europhy. Lett. 99, 27007 (2012)
48. Zhang, C.L., Chen, W.Q., Zhang, C.: On propagation of anti-plane shear waves in piezoelectric
plates with surface effect. Phys. Lett. A 376, 3281–3286 (2012)
49. Huang, G.Y., Kang, Y.L.: Acoustic vibrations of a circular nanowire by considering the effect
of surface. J. Appl. Phys. 110, 023526 (2011)
50. Assadi, A., Farshi, B.: Size-dependent longitudinal and transverse wave propagation in embedded nanotubes with consideration of surface effects. Acta Mech. 222, 27–39 (2011)
51. Chen, W.Q., Wu, B., Zhang, C.L., Zhang, C.: On wave propagation in anisotropic elastic
cylinders at nanoscale: surface. elasticity and its effect. Acta Mech. 225, 2743–2760 (2014)
52. Wang, G.F., Feng, X.Q.: Effects of surface elasticity and residual surface tension on the natural
frequency of microbeams. Appl. Phys. Lett. 90, 231904 (2007)
53. He, J., Lilley, C.M.: Surface stress effect on bending resonance of nanowires with different
boundary conditions. Appl. Phys. Lett. 93, 263108 (2008)
54. Abbasion, S., Rafsanjani, A., Avazmohammadi, R., Farshidianfar, A.: Free vibration of
microscaled Timoshenko beams. Appl. Phys. Lett. 95, 143122 (2009)
55. Farshi, B., Assadi, A., Alinia-ziazi, A.: Frequency analysis of nanotubes with consideration
of surface effects. Appl. Phys. Lett. 96, 093105 (2010)
59
28. Eringen, A.C.: Microcontinuum Field Theories: II Fluent Media. Springer, Berlin (2001)
29. Kroner, E.: Elasticity theory of materials with long range cohesive forces. Int. J. Sol. Struct.
3, 731–742 (1967)
30. Eringen, A.C.: Linear theory of nonlocal elasticity and dispersion of plane waves. Int. J. Eng.
Sci. 10, 425–435 (1972)
31. Eringen, A.C.: Nonlocal polar elastic continua. Int. J. Eng. Sci. 10, 1–16 (1972)
32. Eringen, A.C., Edelen, D.G.B.: On nonlocal elasticity. Int. J. Eng. Sci. 10, 233–248 (1972)
33. Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703–4710 (1983)
34. Aifantis, E.C.: On the gradient approach Relation to Eringen’s nonlocal theory. Int. J. Eng.
Sci. 49, 1367–1377 (2011)
35. Lim, C., Zhang, G., Reddy, J.: A higher-order nonlocal elasticity and strain gradient theory
and its applications in wave propagation. J. Mech. Phys. Sol. 78, 298–313 (2015)
36. Narendar, S., Gopalakrishnan, S.: Ultrasonic wave characteristics of nanorods via nonlocal
strain gradient models. J. Appl. Phys. 107, 084312–8 (2010)
37. Miller, R.E., Shenoy, V.B.: Size-dependent elastic properties of nanosized structural elements.
Nanotechnology 11, 139–147 (2000)
38. Gavan, K.B., Westra, H.J.R., van der Drift, E.W.J.M., Venstra, W.J., van der Zant, H.S.J.:
Size-dependent effective Young’s modulus of silicon nitride cantilevers. Appl. Phys. Lett. 94,
233108 (2009)
39. Olsson, P.A.T., Park, H.S.: On the importance of surface elastic contributions to the flexural
rigidity of nanowires. J. Mech. Phys. Sol. 60, 2064–2083 (2012)
40. Li, C., Guo, W.L., Kong, Y., Gao, H.J.: Size-dependent piezoelectricity in zinc oxide nanofilms
from first-principles calculations. Appl. Phys. Lett. 90, 033108–033103 (2007)
41. Majdoub, M.S., Sharma, P., Cagin, T.: Enhanced size-dependent piezoelectricity and elasticity
in nanostructures due to the flexoelectric effect. Phys. Rev. B 77, 125424 (2008)
42. He, J., Lilley, C.M.: Surface effect on the elastic behavior of static bending nanowires. Nano
Lett. 8, 1798–1802 (2008)
43. Jiang, L.Y., Yan, Z.: Timoshenko beam model for static bending of nanowires with surface
effects. Phys. E 42, 2274–2279 (2010) 1572
44. Chiu, M.S., Chen, T.Y.: Effects of high-order surface stress on buckling and resonance behavior of nanowires. Acta. Mech. 223, 1473–1484 (2012)
45. Wang, G.F., Feng, X.Q.: Surface effects on buckling of nanowires under uniaxial compression.
Appl. Phys. Lett. 94, 141913 (2009)
46. Wang, G.F., Feng, X.Q.: Timoshenko beam model for buckling and vibration of nanowires
with surface effects. J. Phys. D Appl. Phys. 42, 155411 (2009)
47. Yan, Z., Jiang, L.Y.: Surface effects on the vibration and buckling of piezoelectric nanoplates.
Europhy. Lett. 99, 27007 (2012)
48. Zhang, C.L., Chen, W.Q., Zhang, C.: On propagation of anti-plane shear waves in piezoelectric
plates with surface effect. Phys. Lett. A 376, 3281–3286 (2012)
49. Huang, G.Y., Kang, Y.L.: Acoustic vibrations of a circular nanowire by considering the effect
of surface. J. Appl. Phys. 110, 023526 (2011)
50. Assadi, A., Farshi, B.: Size-dependent longitudinal and transverse wave propagation in embedded nanotubes with consideration of surface effects. Acta Mech. 222, 27–39 (2011)
51. Chen, W.Q., Wu, B., Zhang, C.L., Zhang, C.: On wave propagation in anisotropic elastic
cylinders at nanoscale: surface. elasticity and its effect. Acta Mech. 225, 2743–2760 (2014)
52. Wang, G.F., Feng, X.Q.: Effects of surface elasticity and residual surface tension on the natural
frequency of microbeams. Appl. Phys. Lett. 90, 231904 (2007)
53. He, J., Lilley, C.M.: Surface stress effect on bending resonance of nanowires with different
boundary conditions. Appl. Phys. Lett. 93, 263108 (2008)
54. Abbasion, S., Rafsanjani, A., Avazmohammadi, R., Farshidianfar, A.: Free vibration of
microscaled Timoshenko beams. Appl. Phys. Lett. 95, 143122 (2009)
55. Farshi, B., Assadi, A., Alinia-ziazi, A.: Frequency analysis of nanotubes with consideration
of surface effects. Appl. Phys. Lett. 96, 093105 (2010)