Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Archive of Applied Mechanics
Erschienen in: Archive of Applied Mechanics 9/2019

01.04.2019

A review of mechanical analyses of rectangular nanobeams and single-, double-, and multi-walled carbon nanotubes using Eringen’s nonlocal elasticity theory

verfasst von: Chih-Ping Wu, Jung-Jen Yu

Erschienen in: Archive of Applied Mechanics | Ausgabe 9/2019

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This article is intended to present an overview of various mechanical analyses of rectangular nanobeams and single-, double-, and multi-walled (SW-, DW-, and MW-) carbon nanotubes (CNTs) with combinations of simply supported, free, and clamped edge conditions embedded or non-embedded in an elastic medium, including bending, free vibration, buckling, coupled thermo-elastic and hygro-thermo-elastic, dynamic instability, wave propagation, geometric nonlinear bending, and large amplitude vibration analyses. This review introduces the development of various nonlocal beam and shell theories incorporating Eringen’s nonlocal elasticity theory and the application of strong- and weak-form-based formulations to the current issue. Based on the principle of virtual displacements and Reissner’s mixed variational theorem, the corresponding strong- and weak-form formulations of the local Timoshenko beam theory are reformulated for the free vibration analysis of rectangular nanobeams and SW-, DW-, and MW-CNTs, and presented for illustrative purposes. A comparative study of the results obtained using assorted nonlocal beam and shell theories in combination with the analytical and numerical methods is carried out.
Vorheriger Artikel Dynamic characteristics of a quasi-zero stiffness vibration isolator with nonlinear stiffness and damping
Nächster Artikel Synchronization of two co-rotating rotors coupled with a tensile-spring in a non-resonant system

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
Iijima, S.: Helica microtubes of graphitic carbon. Nature 354, 56–58 (1991)
2.
Li, C., Thostenson, E.T., Chou, T.W.: Sensors and actuators based on carbon nanotubes and their composites: a review. Compos. Sci. Technol. 68, 1227–1249 (2008)
3.
Gao, C., Guo, Z., Liu, J.H., Huang, X.J.: The new age of carbon nanotubes: an updated review of functionalized carbon nanotubes in electrochemical sensors. Nanoscale 4, 1948–1963 (2012)
4.
Wang, Q., Arash, B.: A review on applications of carbon nanotubes and graphenes as nano-resonator sensors. Comput. Mater. Sci. 82, 350–360 (2014)
5.
Chen, W.X., Tu, J.P., Wang, L.Y., Gan, H.Y., Xu, Z.D., Zhang, X.B.: Tribological application of carbon nanotubes in a metal-based composite coating and composites. Carbon 41, 215–222 (2003)
6.
Mittal, G., Dhand, V., Rhee, K.Y., Park, S.J., Lee, W.R.: A review on carbon nanotubes and graphenes as fillers in reinforced polymer nanocomposites. J. Ind. Eng. Chem. 21, 11–25 (2015)
7.
Janas, D., Koziol, K.K.: A review of production methods of carbon nanotube and graphene thin films for electrothermal applications. Nanoscale 6, 3037–3045 (2014)
8.
Ma, L., Dong, X., Chen, M., Zhu, L., Wang, C., Yang, F., Dong, Y.: Fabrication and water treatment applications of carbon nanotubes (CNTs)-based composite membranes: a review. Membranes 7, 16 (2017)
9.
Ren, X., Chen, C., Nagatsu, M., Wang, X.: Carbon nanotubes as adsorbents in environmental pollution management: a review. Chem. Eng. J. 170, 395–410 (2011)
10.
Gohardani, O., Elola, M.C., Elizetxea, C.: Potential and prospective implementation of carbon nanotubes on next generation aircraft and space vehicles: a review of current and expected applications in aerospace sciences. Prog. Aerosp. Sci. 70, 42–68 (2014)
11.
Khare, R., Bose, S.: Carbon nanotube based composites—a review. J. Miner. Mater. Charact. Eng. 4, 31–46 (2005)
12.
Ng, K.W., Lam, W.H., Pichiah, S.: A review on potential applications of carbon nanotubes in marine current turbines. Renew. Sustain. Energy Rev. 28, 331–339 (2013)
13.
Tan, J.M., Arulselvan, P., Fakurazi, S., Ithnin, H., Hussein, M.Z.: A review on characterization and biocompatibility of functionalized carbon nanotubes in drug delivery design. J. Nanomater. 2014, 917024 (2014)
14.
15.
Bianco, A., Kostarelos, K., Prato, M.: Applications of carbon nanotubes in drug delivery. Curr. Opin. Chem. Biol. 9, 674–679 (2005)
16.
Casas, C.D.L., Li, W.: A review of application of carbon nanotubes for lithium ion battery anode material. J. Power Sour. 208, 74–85 (2012)
17.
Datsyuk, V., Kalyva, M., Papagelis, K., Parthenios, J., Tasis, D., Siokou, A., Kallitsis, I., Galiotis, C.: Chemical oxidation of multiwalled carbon nanotubes. Carbon 46, 833–840 (2008)
18.
Jakubus, A., Paszkiewicz, M., Stepnowski, P.: Carbon nanotubes application in the extraction techniques of pesticides: a review. Crit. Rev. Anal. Chem. 47, 76–91 (2017)
19.
Luo, C., Xie, L., Wang, Q., Luo, G., Liu, C.: A review of the application and performance of carbon nanotubes in fuel cells. J. Nanomater. 2015, 560392 (2015)
20.
Ong, Y.T., Ahmad, A.L., Zein, S.H.S., Tan, S.H.: A review on carbon nanotubes in an environmental protection and green engineering perspective. Braz. J. Chem. Eng. 27, 227–242 (2010)
21.
Harris, P.J.F.: Carbon Nanotube Science: Synthesis Properties and Applications. Cambridge University Press, Cambridge (2009)
22.
Thostenson, E.T., Ren, Z., Chou, T.W.: Advances in the science and technology of carbon nanotubes and their composites: a review. Compos. Sci. Technol. 61, 1899–1912 (2001)
23.
De Volder, M.F.L., Tawfick, S.H., Baughman, R.H., Hart, A.J.: Carbon nanotubes: present and future commercial applications. Science 339, 535–539 (2013)
24.
Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703–4710 (1983)
25.
Eringen, A.C.: Nonlocal Continuum Field Theories. Springer-Verlag, New York (2002)MATH
26.
Eringen, A.C., Edelen, D.G.B.: On nonlocal elasticity. Int. J. Eng. Sci. 10, 233–248 (1972)MathSciNetMATH
27.
Reissner, E.: On a certain mixed variational theorem and a proposed application. Int. J. Numer. Methods Eng. 20, 1366–1368 (1984)MATH
28.
Reissner, E.: On a mixed variational theorem and on a shear deformable plate theory. Int. J. Numer. Methods Eng. 23, 193–198 (1986)MATH
29.
Wang, Q., Wang, C.: The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes. Nanotechnology 18, 075702 (2007)
30.
He, A.Q., Kitipornchai, S., Wang, C.M., Liew, K.M.: Modeling of van der Waals force for infinitesimal deformation of multi-walled carbon nanotubes treated as cylindrical shells. Int. J. Solids Struct. 42, 6032–6047 (2005)MATH
31.
He, X.Q., Kitipornchai, S., Liew, K.M.: Buckling analysis of multi-walled carbon nanotubes: a continuum model accounting for van der Waals interaction. J. Mech. Phys. Solids 53, 303–326 (2005)MATH
32.
Ru, C.Q.: Effect of van der Waals forces on axial buckling of a double-walled carbon nanotube. J. Appl. Phys. 87, 7227–7231 (2000)
33.
Ru, C.Q.: Elastic models for carbon nanotubes. Encycl. Nanosci. Nanotech. 2, 731–744 (2004)
34.
Wu, C.P., Hong, Z.L., Wang, Y.M.: Geometrically nonlinear static analysis of an embedded multi-walled carbon nanotube and the van der Waals interaction. J. Nanomech. Micromech. 7, 04017012 (2017)
35.
36.
Wu, C.P., Chen, Y.H., Hong, Z.L., Lin, C.H.: Nonlinear vibration analysis of an embedded multi-walled carbon nanotube. Adv. Nano Res. 6, 163–182 (2018)
37.
Strozzi, M., Pellicano, F.: Linear vibrations of triple-walled carbon nanotubes. Math. Mech. Solids 23, 1456–1481 (2018)MathSciNet
38.
Natsuki, T., Ni, Q.Q., Endo, M.: Analysis of the vibration characteristics of double-walled carbon nanotubes. Carbon 46, 1570–1573 (2008)
39.
Kumar, B.R.: Investigation on mechanical vibration of double-walled carbon nanotubes with inter-tube van der Walls forces. Adv. Nano Res. 6, 135–145 (2018)
40.
Pentaras, D., Elishakoff, I.: Effective approximations for natural frequencies of double-walled carbon nanotubes based on Donnell shell theory. J. Nanotechnol. Eng. Med. 2, 021023 (2011)
41.
Reddy, J.N.: Nonlocal theories for bending, buckling and vibration of beams. Int. J. Eng. Sci. 45, 288–307 (2007)MATH
42.
Reddy, J.N., Pang, S.D.: Nonlocal continuum theories of beams for the analysis of carbon nanotubes. J. Appl. Phys. 103, 023511 (2008)
43.
Thai, H.T.: A nonlocal beam theory for bending, buckling, and vibration of nanobeams. Int. J. Eng. Sci. 52, 56–64 (2012)MathSciNetMATH
44.
Thai, H.T., Vo, T.P.: A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams. Int. J. Eng. Sci. 54, 58–66 (2012)MathSciNetMATH
45.
Aissani, K., Bouiadjra, M.B., Ahouel, M., Tounsi, A.: A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium. Struct. Eng. Mech. 55, 743–763 (2015)
46.
Aydogdu, M.: A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration. Physica E 41, 1651–1655 (2009)
47.
Zhang, Y.Y., Wang, C.M., Challamel, N.: Bending, buckling, and vibration of micro/nanobeams by hybrid nonlocal beam model. J. Eng. Mech. 136, 562–574 (2010)
48.
Ansari, R., Sahmani, S.: Small scale effect on vibrational response of single-walled carbon nanotubes with different boundary conditions based on nonlocal beam models. Commun. Nonlinear Sci. Numer. Simult. 17, 1965–1979 (2012)MathSciNet
49.
Kiani, K., Mehri, B.: Assessment of nanotube structures under a moving nanoparticle using nonlocal beam theories. J. Sound Vib. 329, 2241–2264 (2010)
50.
Mehdipour, I., Soltani, P., Ganji, D.D.: Nonlinear vibration and bending instability of a single-walled carbon nanotube using nonlocal elastic beam theory. Int. J. Nanosci. 10, 447–453 (2011)
51.
Setoodeh, A.R., Khosrownejad, M., Malekzadeh, P.: Exact nonlocal solution for postbuckling of single-walled carbon nanotubes. Physica E 43, 1730–1737 (2011)
52.
Shen, H.S., Zhang, C.L.: Nonlocal beam model for nonlinear analysis of carbon nanotubes on elastomeric substrates. Comput. Mater. Sci. 50, 1022–1029 (2011)
53.
Simsek, M.: Vibration analysis of a single-walled carbon nanotube under action of a moving harmonic load based on nonlocal elasticity theory. Physica E 43, 182–191 (2010)
54.
Ansari, R., Gholami, R., Darabi, M.A.: Thermal buckling analysis of embedded single-walled carbon nanotubes with arbitrary boundary conditions using the nonlocal Timoshenko beam theory. J. Therm. Stress. 4, 1271–1281 (2011)
55.
Benzair, A., Tounsi, A., Besseghier, A., Heireche, H., Moulay, N., Boumia, L.: The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory. J. Phys. D: Appl. Phys. 41, 225404 (2008)
56.
Boumia, L., Zidour, M., Benzair, A., Tounsi, A.: A Timoshenko beam model for vibration analysis of chiral single-walled carbon nanotubes. Physica E 59, 186–191 (2014)
57.
Hosseini-Hashemi, S., Nazemnezhad, R., Bedroud, M.: Surface effects on nonlinear free vibration of functionally graded nanobeams using nonlocal elasticity. Appl. Math. Modell. 38, 3538–3553 (2014)MathSciNetMATH
58.
Lee, H.L., Chang, W.J.: Surface effects on frequency analysis of nanotubes using nonlocal Timoshenko beam theory. J. Appl. Phys. 108, 093503 (2010)
59.
Murmu, T., Pradhan, S.C.: Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM. Physica E 41, 1232–1239 (2009)
60.
Wang, C.M., Zhang, Y.Y., Ramesh, S.S., Kitipornchai, S.: Buckling analysis of micro- and nano-rods/tubes based on nonlocal Timoshenko beam theory. J. Phys. D: Appl. Phys. 39, 3904–3909 (2006)
61.
Wu, C.P., Lai, W.W.: Free vibration of an embedded single-walled carbon nanotube with various boundary conditions using the RMVT-based nonlocal Timoshenko beam theory and DQ method. Physica E 68, 8–21 (2015)
62.
Wu, C.P., Lai, W.W.: Reissner’s mixed variational theorem-based nonlocal Timoshenko beam theory for a single-walled carbon nanotube embedded in an elastic medium and with various boundary conditions. Compos. Struct. 122, 390–404 (2015)
63.
Wu, C.P., Liou, J.Y.: RMVT-based nonlocal Timoshenko beam theory for stability analysis of embedded single-walled carbon nanotubes with various boundary conditions. Int. J. Struct. Stab. Dyn. 16, 1550068 (2016)MathSciNetMATH
64.
Yang, Y., Lim, C.W.: A variational principle approach for buckling of carbon nanotubes based on nonlocal Timoshenko beam models. Nano: Brief Rep. Rev. 6, 363–377 (2011)
65.
Yang, J., Ke, L.L., Kitipornchai, S.: Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory. Physica E 42, 1727–1735 (2010)
66.
Zidour, M., Benrahou, K.H., Semmah, A., Naceri, M., Belhadj, H.A., Bakhti, K., Tounsi, A.: The thermal effect on vibration of zigzag single walled carbon nanotubes using nonlocal Timoshenko beam theory. Comput. Mater. Sci. 51, 252–260 (2012)
67.
Arash, B., Wang, Q.: A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes. Comput. Mater. Sci. 51, 303–313 (2012)
68.
Behera, L., Chakraverty, S.: Recent researches on nonlocal elasticity theory in the vibration of carbon nanotubes using beam models: a review. Arch. Comput. Methods Eng. 24, 481–494 (2017)MathSciNetMATH
69.
Ebrahimi, F., Salari, E.: Thermo-mechanical vibration analysis of a single-walled carbon nanotube embedded in an elastic medium based on higher-order shear deformation beam theory. J. Mech. Sci. Technol. 29, 3797–3803 (2015)
70.
Maachou, M., Zidour, M., Baghdadi, H., Ziane, N., Tounsi, A.: A nonlocal Levinson beam model for free vibration analysis of zigzag single-walled carbon nanotubes including thermal effects. Solid State Commun. 151, 1467–1471 (2011)
71.
Rafiee, R., Moghadam, R.M.: On the modeling of carbon nanotubes: a critical review. Compos. Part B 56, 435–449 (2014)
72.
Adali, S.: Variational principles for transversely vibrating multiwalled carbon nanotubes based on nonlocal Euler–Bernoulli beam model. Nano Lett. 9, 1737–1741 (2009)
73.
Ansari, R., Ramezannezhad, H., Gholami, R.: Nonlocal beam theory for nonlinear vibrations of embedded multiwalled carbon nanotubes in thermal environment. Nonlinear Dyn. 67, 2241–2254 (2012)MathSciNetMATH
74.
Arani, A.G., Rabbani, H., Amir, S., Maraghi, Z.K., Mohammadimehr, M., Haghparast, E.: Analysis of nonlinear vibrations for multi-walled carbon nanotubes embedded in an elastic medium. J. Solid Mech. 3, 258–270 (2011)
75.
Chen, X., Fang, C.Q., Wang, X.: The influence of surface effect on vibration behaviors of carbon nanotubes under initial stress. Physica E 85, 47–55 (2017)
76.
Civalek, O., Demir, C.: Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory. Appl. Math. Modell. 35, 2053–2067 (2011)MathSciNetMATH
77.
Ehteshami, H., Hajabasi, M.A.: Analytical approaches for vibration analysis of multi-walled carbon nanotubes modeled as multiple nonlocal Euler beams. Physica E 44, 270–285 (2011)
78.
Fang, B., Zhen, Y.X., Zhang, C.P., Tang, Y.: Nonlinear vibration analysis of double-walled carbon nanotubes based on nonlocal elasticity theory. Appl. Math. Modell. 37, 1096–1107 (2013)MathSciNetMATH
79.
Khosrozadeh, A., Hajabasi, M.A.: Free vibration of embedded double-walled carbon nanotubes considering nonlinear interlayer van der Waals forces. Appl. Math. Modell. 36, 997–1007 (2012)MathSciNetMATH
80.
Lu, P., Lee, H.P., Lu, C., Zhang, P.Q.: Application of nonlocal beam models for carbon nanotubes. Int. J. Solids Struct. 44, 5289–5300 (2007)MATH
81.
Mohammadimehr, M., Saidi, A.R., Arani, A.G., Arefmanesh, A., Han, Q.: Torsional buckling of a DWCNT embedded on Winkler and Pasternak foundations using nonlocal theory. J. Mech. Sci. Technol. 24, 1289–1299 (2010)
82.
Shakouri, A., Lin, R.M., Ng, T.Y.: Free flexural vibration studies of double-walled carbon nanotubes with different boundary conditions and modeled as nonlocal Euler beams via the Galerkin method. J. Appl. Phys. 106, 094307 (2009)
83.
Wang, B., Deng, Z., Zhang, K., Zhou, J.: Dynamic analysis of embedded curved double-walled carbon nanotubes based on nonlocal Euler–Bernoulli beam theory. Multidisc. Model Mater. Struct. 8, 432–453 (2012)
84.
Yan, Y., Wang, W., Zhang, L.: Applied multiscale method to analysis of nonlinear vibration for double-walled carbon nanotubes. Appl. Math. Modell. 35, 2279–2289 (2011)MathSciNetMATH
85.
Yoon, J., Ru, C.Q., Mioduchowski, A.: Noncoaxial resonance of an isolated multiwall carbon nanotube. Phys. Rev. B 66, 233402 (2002)
86.
Yoon, J., Ru, C.Q., Mioduchowski, A.: Vibration of an embedded multiwalled carbon nanotube. Compos. Sci. Technol. 63, 1533–1542 (2003)
87.
Ansari, R., Gholami, R., Darabi, M.A.: Nonlinear free vibration of embedded double-walled carbon nanotubes with layerwise boundary conditions. Acta Mech. 223, 2523–2536 (2012)MathSciNetMATH
88.
Ansari, R., Gholami, R., Sahmani, S., Norouzzadeh, A., Bazdid-Vahdati, M.: Dynamic stability analysis of embedded multi-walled carbon nanotubes in thermal environment. Acta Mech. Solida Sinica 28, 659–667 (2015)
89.
Ansari, R., Ramezannezhad, H.: Nonlocal Timoshenko beam model for the large-amplitude vibrations of embedded multiwalled carbon nanotubes including thermal effects. Physica E 43, 1171–1178 (2011)
90.
Benguediab, S., Tounsi, A., Zidour, M., Semmah, A.: Chirality and scale effects on mechanical buckling properties of zigzag double-walled carbon nanotubes. Compos. Part B 57, 21–24 (2014)
91.
Ece, M.C., Aydogdu, M.: Nonlocal elasticity effect on vibration of in-plane loaded double-walled carbon nano-tubes. Acta Mech. 190, 185–195 (2007)MATH
92.
Ke, L.L., Xiang, Y., Yang, J., Kitipornchai, S.: Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory. Comput. Mater. Sci. 47, 409–417 (2009)
93.
Kucuk, I., Sadek, I.S., Adali, S.: Variational principles for multiwalled carbon nanotubes undergoing vibrations based on nonlocal Timoshenko beam theory. J. Nanomater. 2010, 461252 (2010)
94.
Soltani, P., Bahar, P., Farshidianfar, A.: An efficient GDQ model for vibration analysis of a multiwall carbon nanotube on Pasternak foundation with general boundary conditions. Proc. IMechE Part C: J. Mech. Eng. Sci. 225, 1730–1741 (2011)
95.
Wang, C.M., Tan, V.B.C., Zhang, Y.Y.: Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes. J. Sound Vib. 294, 1060–1072 (2006)
96.
Aydogdu, M.: Effects of shear deformation on vibration of doublewalled carbon nanotubes embedded in an elastic medium. Arch. Appl. Mech. 78, 711–723 (2008)MATH
97.
Barretta, R., Sciarra, F.M.: Analogies between nonlocal and local Bernoulli–Euler nanobeams. Arch. Appl. Mech. 85, 89–99 (2015)MATH
98.
Barretta, R., Canadija, M., Sciarra, F.M.: A higher-order Eringen model for Bernoulli–Euler nanobeams. Arch. Appl. Mech. 86, 483–495 (2016)MATH
99.
Behera, L., Chakraverty, S.: Application of differential quadrature method in free vibration analysis of nanobeams based on various nonlocal theories. Comput. Math. Appl. 69, 1444–1462 (2015)MathSciNet
100.
Eltaher, M.A., Khairy, A., Sadoun, A.M., Omer, E.I.: Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams. Appl. Math. Comput. 224, 760–774 (2013)MathSciNet
101.
Eltaher, M.A., Khater, M.E., Emam, S.A.: A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams. Appl. Math. Modell. 40, 4109–4128 (2016)MathSciNet
102.
Gheshlaghi, B., Hasheminejad, S.M.: Surface effects on nonlinear free vibration of nanobeams. Compos. Part B 42, 934–937 (2011)
103.
Janghorban, M.: Two different types of differential quadrature methods for static analysis of microbeams based on nonlocal thermal elasticity theory in thermal environment. Arch. Appl. Mech. 82, 669–675 (2012)MATH
104.
Reddy, J.N.: Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates. Int. J. Eng. Sci. 48, 1507–1518 (2010)MathSciNetMATH
105.
Sahmani, S., Ansari, R.: Nonlocal beam models for buckling of nanobeams using state-space method regarding different boundary conditions. J. Mech. Sci. Technol. 25, 2365–2375 (2011)
106.
Togun, N., Bagdatli, S.M.: Nonlinear vibration of a nanobeam on a Pasternak elastic foundation based on non-local Euler–Bernoulli beam theory. Math. Comput. Appl. 21, 3 (2016)MathSciNet
107.
Wang, Y.Z., Li, F.M.: Nonlinear primary resonance of nano beam with axial initial load by nonlocal continuum theory. Int. J. Non-Linear Mech. 61, 74–79 (2014)
108.
Ebrahimi, F., Nasirzadeh, P.: A nonlocal Timoshenko beam theory for vibration analysis of thick nanobeams using differential transform method. J. Theoret. Appl. Mech. 53, 1041–1052 (2015)
109.
Wang, C.M., Kitipornchai, S., Lim, C.W., Eisenberger, M.: Beam bending solutions based on nonlocal Timoshenko beam theory. J. Eng. Mech. 134, 475–481 (2008)
110.
Yang, Q., Lim, C.W., Xiang, Y.: Nonlinear thermal bending for shear deformable nanobeams based on nonlocal elasticity theory. Int. J. Aerosp. Lightweight Struct. 1, 89–107 (2011)
111.
Karlicic, D., Kozic, P., Pavlovic, R.: Nonlocal vibration and stability of a multiple-nanobeam system coupled by the Winkler elastic medium. Appl. Math. Modell. 40, 1599–1614 (2016)MathSciNet
112.
113.
Murmu, T., Adhikari, S.: Axial instability of double-nanobeam-systems. Phys. Lett. A 375, 601–608 (2011)
114.
Murmu, T., Adhikari, S.: Nonlocal elasticity based vibration of initially pre-stressed coupled nanobeam systems. Eur. J. Mech. A/Solids 34, 52–62 (2012)MathSciNetMATH
115.
Zhou, Z., Li, Y., Fan, J., Rong, D., Sui, G., Xu, G.: Exact vibration analysis of a double-nanobeam-systems embedded in an elastic medium by a Hamiltonian-based method. Physica E 99, 220–235 (2018)
116.
Lei, X.W., Natsuki, T., Shi, J.X., Ni, Q.Q.: Surface effects on the vibrational frequency of double-walled carbon nanotubes using the nonlocal Timoshenko beam model. Compos. Part B 43, 64–69 (2012)
117.
Murmu, T., Adhikari, S.: Nonlocal transverse vibration of double-nanobeam-systems. J. Appl. Phys. 108, 083514 (2010)
118.
Ebrahimi, F., Salari, E.: Nonlocal thermos-mechanical vibration analysis of functionally graded nanobeams in thermal environment. Acta Astronaut. 113, 29–50 (2015)
119.
Ebrahimi, F., Barati, M.R.: Small-scale effects on hygro-thermo-mechanical vibration of temperature-dependent nonhomogeneous nanoscale beams. Mech. Adv. Mater. Struct. 24, 924–936 (2017)
120.
Ebrahimi, F., Ghadiri, M., Salari, E., Hosein-Hoseini, S.A., Shaghaghi, G.R.: Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams. J. Mech. Sci. Technol. 29, 1207–1215 (2015)
121.
Ebrahimi, F., Salari, E.: Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments. Compos. Struct. 128, 363–380 (2015)
122.
Ebrahimi, F., Salari, E.: Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method. Compos. Part B 79, 156–169 (2015)
123.
Ebrahimi, F., Salari, E.: Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams. Mech. Adv. Mater. Struct. 23, 1379–1397 (2016)
124.
Ebrahimi, F., Salari, E., Hosseini, S.A.H.: Thermomechanical vibration behavior of FG nanobeams subjected to linear and nonlinear temperature distributions. J. Therm. Stress. 38, 1360–1386 (2015)
125.
El-Borgi, S., Fernandes, R., Reddy, J.N.: Non-local free and forced vibrations of graded nanobeams resting on a non-linear elastic foundation. Int. J. Non-linear Mech. 77, 348–363 (2015)
126.
Eptaimeros, K.G., Koutsoumaris, C.C., Tsamasphyros, G.J.: Nonlocal integral approach to the dynamical response of nanobeams. Int. J. Mech. Sci. 115–116, 68–80 (2016)
127.
Li, L., Hu, Y.: Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material. Int. J. Eng. Sci. 107, 77–97 (2016)MathSciNetMATH
128.
Niknam, H., Aghdam, M.M.: A semi analytical approach for large amplitude free vibration and buckling of nonlocal FG beams resting on elastic foundation. Compos. Struct. 119, 452–462 (2015)
129.
Ebrahimi, F., Barati, M.R.: A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams. Arab. J. Sci. Eng. 41, 1679–1690 (2016)MathSciNetMATH
130.
Ebrahimi, F., Barati, M.R.: Buckling analysis of smart size-dependent higher order magneto-electro-thermo-elastic functionally graded nanosize beams. J. Mech. 33, 23–33 (2017)
131.
Ebrahimi, F., Salari, E.: Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG nanobeams with various boundary conditions. Compos. Part B-Eng. 78, 272–290 (2015)
132.
Ebrahimi, F., Shafiei, N.: Application of Eringen’s nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams. Smart Struct. Syst. 17, 837–857 (2016)
133.
Eltaher, M.A., Khairy, A., Sadoun, A.M., Omer, F.A.: Static and buckling analysis of functionally graded Timoshenko nanobeams. Appl. Math. Comput. 229, 283–295 (2014)MathSciNetMATH
134.
Rahmani, O., Pedram, O.: Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory. Int. J. Eng. Sci. 77, 55–70 (2014)MathSciNetMATH
135.
Li, L., Li, X., Hu, Y.: Free vibration analysis of nonlocal strain gradient beams made of functionally graded material. Int. J. Eng. Sci. 102, 77–92 (2016)MATH
136.
Ebrahimi, F., Barati, M.R.: Vibration analysis of embedded size dependent FG nanobeams based on third-order shear deformation beam theory. Struct. Eng. Mech. 61, 721–736 (2017)
137.
Eltaher, M.A., Emam, S.A., Mahmoud, F.F.: Static and stability analysis of nonlocal functionally graded nanobeams. Compos. Struct. 96, 82–88 (2013)
138.
Eltaher, M.A., Alshorbagy, A.E., Mahmoud, F.F.: Vibration analysis of Euler–Bernoulli nanobeams by using finite element method. Appl. Math. Modell. 37, 4787–4797 (2013)MathSciNetMATH
139.
Nguyen, N.T., Kim, N.I., Lee, J.: Mixed finite element analysis of nonlocal Euler–Bernoulli nanobeams. Finites Elem. Anal. Des. 106, 65–72 (2015)
140.
Pradhan, S.C.: Nonlocal finite element analysis and small scale effects of CNTs with Timoshenko beam theory. Finites Elem. Anal. Des. 50, 8–20 (2012)
141.
Pradhan, S.C., Mandal, U.: Finite element analysis of CNT’s based on nonlocal elasticity and Timoshenko beam theory including thermal effect. Physica E 53, 223–232 (2013)
142.
143.
Polit, O., Merzouki, T., Ganapathi, M.: Elastic stability of curved nanobeam based on higher-order shear deformation theory and nonlocal analysis by finite element approach. Finites Elem. Anal. Des. 146, 1–15 (2018)MathSciNet
144.
Reddy, J.N., El-Borgi, S.: Eringen’s nonlocal theories of beams accounting for moderate rotations. Int. J. Eng. Sci. 82, 159–177 (2014)MathSciNetMATH
145.
Reddy, J.N., El-Borgi, S., Romanoff, J.: Nonlinear analysis of functionally graded microbeams using Eringen’s nonlocal differential model. Int. J. Nonlinear Mech. 67, 308–318 (2014)
146.
Kuo, Y.L.: Nonlinear finite element analysis of nonlocal elastic nanobeams with large-amplitude vibrations. J. Comput. Theor. Nanosci. 10, 488–495 (2013)
147.
Nguyen, N.T., Kim, N.I., Lee, J.: Static behavior of nonlocal Euler–Bernoulli beam model embedded in an elastic medium using mixed finite element formulation. Struct. Eng. Mech. 63, 137–146 (2017)
148.
Ribeiro, P., Thomas, O.: Nonlinear modes of vibration and internal resonances in nonlocal beams. J. Comput. Nonlinear Dyn. 12, 031017 (2017)
149.
Ansari, R., Rajabiehfard, R., Arash, B.: Thermal buckling of multiwalled carbon nanotubes using a semi-analytical finite element approach. J. Therm. Stress. 34, 817–834 (2011)
150.
Alshorbagy, A.E., Eltaher, M.A., Mahmoud, F.F.: Static analysis of nanobeams using nonlocal FEM. J. Mech. Sci. Technol. 27, 2035–2041 (2013)
151.
Demir, C., Civalek, O.: A new nonlocal FEM via Hermitian cubic shape functions for thermal vibration of nano beams surrounded by an elastic matrix. Compos. Struct. 168, 872–884 (2017)
152.
Eltaher, M.A., Hamed, M.A., Sadoun, A.M., Mansour, A.: Mechanical analysis of higher order gradient nanobeams. Appl. Math. Comput. 229, 260–272 (2014)MathSciNetMATH
153.
154.
Mahmoud, F.F., Eltaher, M.A., Alshorbagy, A.E., Meletis, E.I.: Static analysis of nanobeams including surface effects by nonlocal finite element. J. Mech. Sci. Technol. 26, 3555–3563 (2012)
155.
Phadikar, J.K., Pradhan, S.C.: Variational formulation and finite element analysis for nonlocal elastic nanobeams and nanoplates. Comput. Mater. Sci. 49, 492–499 (2010)
156.
Sciarra, F.M.: Finite element modelling of nonlocal beams. Physica E 59, 144–149 (2014)
157.
Alotta, G., Failla, G., Zingales, M.: Finite element method for a nonlocal Timoshenko beam model. Fin. Elem. Anal. Des. 89, 77–92 (2014)
158.
Preethi, K., Rajagopal, A., Reddy, J.N.: Surface and nonlocal effects for nonlinear analysis of Timoshenko beams. Int. J. Nonlinear Mech. 76, 100–111 (2015)
159.
Gholami, R., Ansari, R.: Nonlinear resonance responses of geometrically imperfect shear deformable including surface stress effects. Int. J. Nonlinear Mech. 97, 115–125 (2017)
160.
Eltaher, M.A., Emam, S.A., Mahmoud, F.F.: Free vibration analysis of functionally graded size-dependent nanobeams. Appl. Math. Comput. 218, 7406–7420 (2012)MathSciNetMATH
161.
Hamed, M.A., Eltaher, M.A., Sadoun, A.M., Almitani, K.H.: Free vibration of symmetric and sigmoid functionally graded nanobeams. Appl. Phys. A 122, 829–839 (2016)
162.
Eltaher, M.A., Mahmoud, F.F., Assie, A.E., Meletis, F.A.: Static and buckling analysis of functionally graded Timoshenko nanobeams. Appl. Math. Comput. 229, 283–295 (2014)MathSciNet
163.
Carrera, E.: An assessment of mixed and classical theories on global and local response of multilayered orthotropic plates. Compos. Struct. 50, 183–198 (2000)
164.
Carrera, E.: An assessment of mixed and classical theories for the thermal stress analysis of orthotropic multilayered plates. J. Therm. Stress. 23, 797–831 (2000)
165.
Carrera, E.: Historical review of zig-zag theories for multilayered plates and shells. Appl. Mech. Rev. 56, 287–308 (2003)
166.
Carrera, E.: Assessment of theories for free vibration analysis of homogeneous and multilayered plates. Shock Vib. 11, 261–270 (2004)
167.
Wu, C.P., Li, H.Y.: The RMVT- and PVD-based finite layer methods for the three-dimensional analysis of multilayered composite and FGM plates. Compos. Struct. 92, 2476–2496 (2010)
168.
Wu, C.P., Li, H.Y.: RMVT- and PVD-based finite layer methods for the quasi-3D free vibration analysis of multilayered composite and FGM plates. CMC Comput. Mater. Contin. 19, 155–198 (2010)
169.
Wu, C.P., Chiu, K.H., Wang, Y.M.: A review on the three-dimensional analytical approaches of multilayered and functionally graded piezoelectric plates and shells. CMC Comput. Mater. Contin. 8, 93–132 (2008)
170.
Brischetto, S., Carrera, E.: Refined 2D models for the analysis of functionally graded piezoelectricity plates. J. Intell. Mater. Syst. Struct. 20, 1783–1797 (2009)
171.
Brischetto, S., Carrera, E.: Advanced mixed theories for bending analysis of functionally graded plates. Comput. Struct. 88, 1474–1483 (2010)
172.
Brischetto, S., Carrera, E.: Coupled thermos-electro-mechanical analysis of smart plates embedding composite and piezoelectric layers. J. Therm. Stress. 35, 766–804 (2012)
173.
Wu, C.P., Li, H.Y.: RMVT-based finite cylindrical prism methods for multilayered functionally graded circular hollow cylinders with various boundary conditions. Compos. Struct. 100, 592–608 (2013)
174.
Wu, C.P., Liu, Y.C.: A review of semi-analytical numerical methods for laminated composite and multilayered functionally graded elastic/piezoelectric plates and shells. Compos. Struct. 147, 1–15 (2016)
175.
Wu, C.P., Peng, S.T., Chen, Y.C.: RMVT- and PVD-based finite cylindrical layer methods for the three-dimensional buckling analysis of multilayered FGM cylinders under axial compression. Appl. Math. Modell. 38, 233–252 (2014)MathSciNetMATH
176.
Wang, Y.M., Chen, S.M., Wu, C.P.: A meshless collocation method based on the differential reproducing kernel interpolation. Comput. Mech. 45, 585–606 (2010)MathSciNetMATH
177.
Bert, C.W., Malik, M.: Differential quadrature method in computational mechanics: a review. Appl. Mech. Rev. 49, 1–27 (1996)
178.
Du, H., Lim, M.K., Lin, R.M.: Application of generalized differential quadrature method to structural problems. Int. J. Numer. Methods Eng. 37, 1881–1896 (1994)MathSciNetMATH
179.
Wu, C.P., Lee, C.Y.: Differential quadrature solution for the free vibration analysis of laminated conical shells with variable stiffness. Int. J. Mech. Sci. 43, 1853–1869 (2001)MATH
180.
Cowper, G.R.: The shear coefficient in Timoshenko’s beam theory. J. Appl. Mech. 33, 335–340 (1966)MATH
181.
Chen, S.M., Wu, C.P., Wang, Y.M.: Hermite DRK interpolation-based collocation method for the analysis of Bernoulli–Euler beams and Kirchhoff–Love plates. Comput. Mech. 47, 425–453 (2011)MathSciNetMATH
182.
Reddy, J.N.: An Introduction to the Finite Element Method. McGraw-Hill, New York (1984)MATH
183.
Strozzi, M., Smirnov, V.V., Manevitch, L.I., Pellicano, F.: Nonlinear vibrations and energy exchange of single-walled carbon nanotubes. Radial breathing modes. Compos. Struct. 184, 613–632 (2018)MATH
184.
Strozzi, M., Smirnov, V.V., Manevitch, L.I., Milani, M., Pellicano, F.: Nonlinear vibrations and energy exchange of single-walled carbon nanotubes. Circumferential flexural modes. J. Sound Vib. 381, 156–178 (2016)MATH
185.
Strozzi, M., Manevitch, L.I., Pellicano, F., Smirnov, V.V., Shepelev, D.S.: Low-frequency linear vibrations of single-walled carbon nanotubes: analytical and numerical models. J. Sound Vib. 333, 2936–2957 (2014)
186.
Hu, Y.G., Liew, K.M., Wang, Q., He, X.Q., Yakobson, B.I.: Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes. J. Mech. Phys. Solids 56, 3475–3485 (2008)MATH
187.
Shen, H.S., Zhang, C.L.: Torsional buckling and postbuckling of double-walled carbon nanotubes by nonlocal shear deformable shell model. Compos. Struct. 92, 1073–1084 (2010)
188.
Shen, H.S., Zhang, C.L., Xiang, Y.: Nonlocal shear deformable shell model for thermal postbuckling of axially compressed double-walled carbon nanotubes. Philos. Mag. 90, 3189–3214 (2010)
189.
Shen, H.S., Zhang, C.L.: Nonlocal shear deformable shell model for post-buckling of axially compressed double-walled carbon nanotubes embedded in an elastic matrix. J. Appl. Mech. 77, 041006 (2010)
190.
Ansari, R., Rouhi, H., Sahmani, S.: Free vibration analysis of single- and double-walled carbon nanotubes based on nonlocal elastic shell models. J. Vib. Control 20, 670–678 (2014)MathSciNetMATH
191.
Ansari, R., Rouhi, H.: Analytical treatment of the free vibration of single-walled carbon nanotubes based on the nonlocal Flugge shell theory. J. Eng. Mater. Technol. 134, 011008 (2012)
192.
Arani, A.G., Barzoki, A.A.M., Kolahchi, R., Loghman, A.: Pasternak foundation effect on the axial and torsional waves propagation in embedded DWCNTs using nonlocal elasticity cylindrical shell theory. J. Mech. Sci. Tech. 25, 2385–2391 (2011)
193.
Ansari, R., Sahmani, A., Rouhi, H.: Axial buckling analysis of single-walled carbon nanotubes in thermal environments via the Rayleigh–Ritz technique. Comput. Mater. Sci. 50, 3050–3055 (2011)
194.
Ansari, R., Shahabodini, A., Rouhi, H.: A thickness-independent nonlocal shell model for describing the stability behavior of carbon nanotubes under compression. Compos. Struct. 100, 323–331 (2013)
195.
Fazelzadeh, S.A., Ghavanloo, E.: Nonlocal anisotropic elastic shell model for vibrations of single-walled carbon nanotubes with arbitrary chirality. Compos. Struct. 94, 1016–1022 (2012)
196.
Ghavanloo, E., Fazelzadeh, S.A.: Vibration characteristics of single-walled carbon nanotubes based on an anisotropic elastic shell model including chirality effect. Appl. Math. Modell. 36, 4988–5000 (2012)
197.
Ghorbanpour Arani, A., Mohammadimehr, M., Arefmanesh, A., Ghasemi, A.: Transverse vibration of short carbon nanotubes using cylindrical shell and beam models. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 224, 745–756 (2010)
198.
Hosseini-Ara, R., Mirdamadi, H.R., Khademyzadeh, H., Salimi, H.: Thermal effect on dynamic stability of single-walled carbon nanotubes in low and high temperatures based on nonlocal shell theory. Adv. Mater. Res. 622, 959–964 (2013)
199.
Rahmanian, M., Torkaman-Asadi, M.A., Firouz-Abadi, R.D., Kouchakzadeh, M.A.: Free vibration analysis of carbon nanotubes resting on Winkler foundations based on nonlocal models. Physica B: Condens. Matter. 484, 83–94 (2016)
200.
Rouhi, H.: Free vibration analysis of single- and double-walled carbon nanotubes based on nonlocal elastic shell models. J. Vib. Control 20, 670–678 (2014)MathSciNetMATH
201.
Soltani, P., Saberian, J., Bahramian, R.: Nonlinear vibration analysis of single-walled carbon nanotube with shell model based on the nonlocal elasticity theory. J. Comput. Nonlinear Dyn. 11, 011002 (2016)
202.
Wang, Q., Varadan, V.K.: Application of nonlocal elastic shell theory in wave propagation analysis of carbon nanotubes. Smart Mater. Struct. 16, 178–190 (2007)
203.
Zhang, Y.Y., Wang, C.M., Duan, W.H., Zong, Z.: Assessment of continuum mechanica models in predicting buckling strains of single-walled carbon nanotubes. Nanotechnology 20, 395707 (2009)
204.
Ansari, R., Torabi, J., Faghih Shojaei, M.: An efficient numerical method for analyzing the thermal effects on the vibration embedded single-walled carbon nanotubes based on the nonlocal shell model. Mech. Adv. Mater. Struct. 25, 500–511 (2018)
205.
Brischetto, S.: A continuum elastic three-dimensional model for natural frequencies of single-walled carbon nanotubes. Compos. Part B 61, 222–228 (2014)
206.
Gafour, Y., Zidour, M., Tounsi, A., Heireche, H., Semmah, A.: Sound wave propagation in zigzag double-walled carbon nanotubes embedded in an elastic medium using nonlocal elasticity theory. Physica E 48, 118–123 (2013)
207.
Rouhi, H., Ansari, R.: Nonlocal analytical Fugge shell model for axial buckling of double-walled carbon nanotubes with different end conditions. Nano 7, 1250018 (2012)
208.
Ru, C.Q.: Axially compressed buckling of a doublewalled carbon nanotube embedded in an elastic medium. J. Mech. Phys. Solids 49, 1265–1279 (2001)MATH
209.
Ansari, R., Rouhi, H., Sahmani, S.: Thermal effect on axial buckling behavior of multi-walled carbon nanotubes based on nonlocal shell model. Physica E 44, 373–378 (2011)
210.
Ansari, R., Shahabodini, A., Rouhi, H., Alipour, A.: Thermal buckling analysis of multi-walled carbon nanotubes through a nonlocal shell theory incorporating interatomic potentials. J. Therm. Stress. 36, 56–70 (2013)
211.
He, X.Q., Eisenberger, M., Liew, K.M.: The effect of van der Waals interaction modeling on the vibration characteristics of multiwalled carbon nanotubes. J. Appl. Phys. 100, 124317 (2006)
212.
He, X.Q., Kitipornchai, S., Wang, C.M., Xiang, Y., Zhou, Q.: A nonlinear van der Waals force model for multiwalled carbon nanotubes modeled by a nested system of cylindrical shells. J. Appl. Mech. 77, 061006 (2010)
213.
Ru, C.Q.: Column buckling of multiwalled carbon nanotubes with interlayer radial displacements. Phys. Rev. B 62, 16962 (2000)
214.
Wang, C.Y., Ru, C.Q., Mioduchowski, A.: Free vibration of multiwall carbon nanotubes. J. Appl. Phys. 97, 114323 (2005)
215.
Yan, Y., Wang, W.Q., Zhang, L.X.: Nonlocal effect on axially compressed buckling of triple-walled carbon nanotubes under temperature field. Appl. Math. Modell. 34, 3422–3429 (2010)MathSciNetMATH
216.
Zhang, Y.Y., Wang, C.M., Duan, W.H., Xiang, Y., Zong, Z.: Assessment of continuum mechanics models in predicting buckling strains of single-walled carbon nanotubes. Nanotechnology 20, 395707 (2009)
217.
Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity. Dover, New York (1944)MATH
218.
Flügge, W.: Stresses in Shells. Springer-Verlag, New York (1973)MATH
219.
Donnell, L.H.: Beams, Plates, and Shells. McGraw-Hill, New York (1976)MATH
220.
Sanders, J.L.: An Improved First Approximation Theory for Thin Shells. NASA-TR-R24 (1959)
221.
Soedel, W.: Vibrations of Shells and Plates. Marcel Dekker Inc, New York (1993)MATH
222.
Leissa, A.W.: Vibration of Shells. NASA Report No. SP-288 (1973)
223.
Soldatos, K.P.: A comparison of some shell theories used for the dynamic analysis of cross-ply laminated circular cylindrical panels. J. Sound Vib. 97, 305–319 (1984)
224.
Chandrashekhara, K., Kumar, D.V.T.G.P.: Assessment of shell theories for the static analysis of cross-ply laminated circular cylindrical shells. Thin-Walled Struct. 22, 291–318 (1995)
225.
Silvestre, N.: On the accuracy of shell models for torsional buckling of carbon nanotubes. Eur. J. Mech. A Solids 32, 103–108 (2012)MATH
226.
Silvestre, N., Wang, C.M., Zhang, Y.Y., Xiang, Y.: Sanders shell model for buckling of single-walled carbon nanotubes with small aspect ratio. Compos. Struct. 93, 1683–1692 (2011)
227.
Wang, C.M., Tay, Z.Y., Chowdhuary, A.N.R., Duan, W.H., Zhang, Y.Y., Silvestre, N.: Examination of cylindrical shell theories for buckling of carbon nanotubes. Int. J. Struct. Stab. Dyn. 11, 1025–1058 (2011)
228.
Duan, W.H., Wang, C.M., Zhang, Y.Y.: Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics. J. Appl. Phys. 101, 024305 (2007)
Metadaten
Titel
A review of mechanical analyses of rectangular nanobeams and single-, double-, and multi-walled carbon nanotubes using Eringen’s nonlocal elasticity theory
verfasst von
Chih-Ping Wu
Jung-Jen Yu
Publikationsdatum
01.04.2019
Verlag
Springer Berlin Heidelberg
Erschienen in
Archive of Applied Mechanics / Ausgabe 9/2019
Print ISSN: 0939-1533
Elektronische ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-019-01542-z

Weitere Artikel der Ausgabe 9/2019

Archive of Applied Mechanics 9/2019 Zur Ausgabe

Original

An investigation of the dynamic performance of lateral inerter-based vibration isolator with geometrical nonlinearity

Original

Synchronization of two co-rotating rotors coupled with a tensile-spring in a non-resonant system

Original

Effective out-of-plane rigidities of 2D lattices with different unit cell topologies

Original

Revisiting the fundamental structural dynamic systems: the effect of low gravity

Original

Steady-state dynamic response of a gradient elastic half-plane to a load moving on its surface with constant speed

Original

A constitutive level-set model for shape memory polymers and shape memory polymeric composites

Premium Partner

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen. 

    Zur Marktübersicht
    Bildnachweise