60
2 Size-Dependent Theories of Beams, Plates and Shells
56. Assadi, A.: Size dependent dynamic analysis of nanoplates. J. Appl. Phys. 107, 124310 (2010)
57. Lu, P., Lee, H.P., Lu, C., O’Shea, S.J.: Surface stress effects on the resonance properties of
cantilever sensors. Phys. Rev. B 72, 085405 (2005)
58. He, Q., Lilley, C.M.: Resonant frequency analysis of Timoshenko nanowires with surface
stress for different boundary conditions. J. Appl. Phys. 112, 074322 (2012)
59. Yan, Z., Jiang, Y.: Vibration and buckling analysis of a piezoelectric nanoplate considering
surface effects and in-plane constraints. Proc. R. Soc. A. 468, 3458–3475 (2012)
60. Gao, X.L.: A new Timoshenko beam model incorporating microstructure and surface energy
effects. Acta Mech. 226, 457–474 (2015)
61. Gurtin, M.E., Murdoch, A.I.: A continuum theory of elastic material surfaces. Arch. Ration.
Mech. Anal. 57(4), 291–323 (1975)
62. Koochi, A., Hosseini-Toudeshky, H., Ovesy, H.R., Abadyan, M.: Modeling the influence of
surface effect on instability of nano-cantilever in presence of van der Waals force. Int. J.
Struct. Stab. Dyn. 13(4), 1250072 (2013)
63. Iijima, S.: Helical microtubules of graphitic carbon. Nature 354, 56–58 (1991)
64. Ansari, R., Norouzzadeh, A., Gholami, R., Faghih Shojaei, M., Darabi, M.A.: Geometrically
nonlinear free vibration and instability of fluid-conveying nanoscale pipes including surface
stress effects. Microflu. Nanoflu. 20, 28–42 (2016)
65. Ansari, R., Gholami, R., Norouzzadeh, A., Darabi, M.A.: Wave characteristics of nanotubes
conveying fluid based on the non-classical Timoshenko beam model incorporating surface
energies. Arab. J. Sci. Eng. 41, 4359–4369 (2016)
66. Ansari, R., Gholami, R., Norouzzadeh, A.: Size-dependent thermo-mechanical vibration and
instability of conveying fluid functionally graded nanoshells based on Mindlin’s strain gradient
theory. Thin Wall. Struct. 105, 172–184 (2016)
67. Ansari, R., Gholami, R., Norouzzadeh, A., Sahmani, S.: Size-dependent vibration and instability of fluid-conveying functionally graded microshells based on the modified couple stress
theory. Microflu. Nanoflu. 19, 509–522 (2015)
68. Ansari, R., Gholami, R., Norouzzadeh, A., Darabi, M.: Surface stress effect on the vibration
and instability of nanoscale pipes conveying fluid based on a size-dependent Timoshenko
beam model. Acta Mech. Sin. 31, 708–719 (2015)
69. Ansari, R., Norouzzadeh, A., Gholami, R., Shojaei, M.F., Hosseinzadeh, M.: Size-dependent
nonlinear vibration and instability of embedded fluid-conveying SWBNNTs in thermal environment. Phys E. 61, 148–157 (2014)
70. Wang, L.: Vibration analysis of fluid-conveying nanotubes with consideration of surface
effects. Phys E. 43, 437–439 (2010)
71. Reddy, J.N.: A simple higher-order theory for laminated composite plates. J. Appl. Mech. 51,
745–752 (1984)
72. Thai, H.T., Kim, S.E.: A review of theories for the modeling and analysis of functionally
graded plates and shells. Compos. Struct. 128, 70–86 (2015)
73. Huang, L.Y., Han, Q., Liang, Y.J.: Calibration of nonlocal scale effect parameter for bending
single-layered graphene sheet under molecular dynamics. Nano. 7, 125003–8 (2012)
74. Arash, B., Ansari, R.: Evaluation of nonlocal parameter in the vibrations of single-walled
carbon nanotubes with initial strain. Phys E. 42, 2058–2064 (2010)
75. Duan, W.H., Challamel, N., Wang, C.M., Ding, Z.: Development of analytical vibration solutions for microstructured beam model to calibrate length scale coefficient in nonlocal Timoshenko beams. J. Appl. Phys. 114, 104312–11 (2013)
76. Zhang, Z., Wang, C.M., Challamel, N., Elishakoff, I.: Obtaining Eringen’s length scale coefficient for vibrating nonlocal beams via continualization method. J. Sound Vib. 333, 4977–4990
(2014)
77. Zhang, Z., Wang, C.M., Challamel, N.: Eringen’s length scale coefficient for buckling of
nonlocal rectangular plates from microstructured beam-grid model. Int. J. Sol. Struct. 51,
4307–4315 (2014)
78. Zhang, Z., Wang, C.M., Challamel, N.: Eringen’s length-scale coefficients for vibration and
buckling of nonlocal rectangular plates with simply supported edges. J. Eng. Mech. 141,
04014117–10 (2015)
2 Size-Dependent Theories of Beams, Plates and Shells
56. Assadi, A.: Size dependent dynamic analysis of nanoplates. J. Appl. Phys. 107, 124310 (2010)
57. Lu, P., Lee, H.P., Lu, C., O’Shea, S.J.: Surface stress effects on the resonance properties of
cantilever sensors. Phys. Rev. B 72, 085405 (2005)
58. He, Q., Lilley, C.M.: Resonant frequency analysis of Timoshenko nanowires with surface
stress for different boundary conditions. J. Appl. Phys. 112, 074322 (2012)
59. Yan, Z., Jiang, Y.: Vibration and buckling analysis of a piezoelectric nanoplate considering
surface effects and in-plane constraints. Proc. R. Soc. A. 468, 3458–3475 (2012)
60. Gao, X.L.: A new Timoshenko beam model incorporating microstructure and surface energy
effects. Acta Mech. 226, 457–474 (2015)
61. Gurtin, M.E., Murdoch, A.I.: A continuum theory of elastic material surfaces. Arch. Ration.
Mech. Anal. 57(4), 291–323 (1975)
62. Koochi, A., Hosseini-Toudeshky, H., Ovesy, H.R., Abadyan, M.: Modeling the influence of
surface effect on instability of nano-cantilever in presence of van der Waals force. Int. J.
Struct. Stab. Dyn. 13(4), 1250072 (2013)
63. Iijima, S.: Helical microtubules of graphitic carbon. Nature 354, 56–58 (1991)
64. Ansari, R., Norouzzadeh, A., Gholami, R., Faghih Shojaei, M., Darabi, M.A.: Geometrically
nonlinear free vibration and instability of fluid-conveying nanoscale pipes including surface
stress effects. Microflu. Nanoflu. 20, 28–42 (2016)
65. Ansari, R., Gholami, R., Norouzzadeh, A., Darabi, M.A.: Wave characteristics of nanotubes
conveying fluid based on the non-classical Timoshenko beam model incorporating surface
energies. Arab. J. Sci. Eng. 41, 4359–4369 (2016)
66. Ansari, R., Gholami, R., Norouzzadeh, A.: Size-dependent thermo-mechanical vibration and
instability of conveying fluid functionally graded nanoshells based on Mindlin’s strain gradient
theory. Thin Wall. Struct. 105, 172–184 (2016)
67. Ansari, R., Gholami, R., Norouzzadeh, A., Sahmani, S.: Size-dependent vibration and instability of fluid-conveying functionally graded microshells based on the modified couple stress
theory. Microflu. Nanoflu. 19, 509–522 (2015)
68. Ansari, R., Gholami, R., Norouzzadeh, A., Darabi, M.: Surface stress effect on the vibration
and instability of nanoscale pipes conveying fluid based on a size-dependent Timoshenko
beam model. Acta Mech. Sin. 31, 708–719 (2015)
69. Ansari, R., Norouzzadeh, A., Gholami, R., Shojaei, M.F., Hosseinzadeh, M.: Size-dependent
nonlinear vibration and instability of embedded fluid-conveying SWBNNTs in thermal environment. Phys E. 61, 148–157 (2014)
70. Wang, L.: Vibration analysis of fluid-conveying nanotubes with consideration of surface
effects. Phys E. 43, 437–439 (2010)
71. Reddy, J.N.: A simple higher-order theory for laminated composite plates. J. Appl. Mech. 51,
745–752 (1984)
72. Thai, H.T., Kim, S.E.: A review of theories for the modeling and analysis of functionally
graded plates and shells. Compos. Struct. 128, 70–86 (2015)
73. Huang, L.Y., Han, Q., Liang, Y.J.: Calibration of nonlocal scale effect parameter for bending
single-layered graphene sheet under molecular dynamics. Nano. 7, 125003–8 (2012)
74. Arash, B., Ansari, R.: Evaluation of nonlocal parameter in the vibrations of single-walled
carbon nanotubes with initial strain. Phys E. 42, 2058–2064 (2010)
75. Duan, W.H., Challamel, N., Wang, C.M., Ding, Z.: Development of analytical vibration solutions for microstructured beam model to calibrate length scale coefficient in nonlocal Timoshenko beams. J. Appl. Phys. 114, 104312–11 (2013)
76. Zhang, Z., Wang, C.M., Challamel, N., Elishakoff, I.: Obtaining Eringen’s length scale coefficient for vibrating nonlocal beams via continualization method. J. Sound Vib. 333, 4977–4990
(2014)
77. Zhang, Z., Wang, C.M., Challamel, N.: Eringen’s length scale coefficient for buckling of
nonlocal rectangular plates from microstructured beam-grid model. Int. J. Sol. Struct. 51,
4307–4315 (2014)
78. Zhang, Z., Wang, C.M., Challamel, N.: Eringen’s length-scale coefficients for vibration and
buckling of nonlocal rectangular plates with simply supported edges. J. Eng. Mech. 141,
04014117–10 (2015)