Have a personal or library account? Click to login
Vibrations of the Euler–Bernoulli Beam Under a Moving Force based on Various Versions of Gradient Nonlocal Elasticity Theory: Application in Nanomechanics Cover

Vibrations of the Euler–Bernoulli Beam Under a Moving Force based on Various Versions of Gradient Nonlocal Elasticity Theory: Application in Nanomechanics

Open Access
|Jun 2020

References

  1. A. C. Eringen, Nonlocal polar elastic continua, International Journal of Engineering Science 1972; 10: 1–16.
  2. A. C. Eringen, Linear theory of nonlocal elasticity and dispersion of plane waves, International Journal of Engineering Science 1972; 5: 425–435.
  3. A. C. Eringen, D. G. B. Edelen, On nonlocal elasticity, International Journal of Engineering Science 1972; 3: 233–248.
  4. A. C. Eringen, On differential-equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 1983; 9: 4703–4710.
  5. M. Aydogdu, Axial vibration of the nanorods with the nonlocal continuum rod model, Physica E Low-dimensional Systems Nanostructures 2009; 41(5): 861–864.
  6. M. Danesh, A. Farajpour, M. Mohammadi, Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications 2012; 39 (1): 23–27.
  7. Z. X. Huang, Nonlocal effects of longitudinal vibration in nanorod with internal long range interactions, International Journal of Solid and Structures 2012; 49: 2150–2154.
  8. M. Aydogdu, M. Arda, Force vibration of nanorods using nonlocal elasticity, Advances in Nano Research 2016; 4: (4): 265–279.
  9. J. Peddieson, G. R. Buchanan, R. P. McNitt, Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science 2003; 41: 305–312.
  10. J. N. Reddy, Nonlocal theories for bending, buckling and vibration of beam, International Journal of Engineering Science 2007; 45: 288–307.
  11. R. Ansari, R. Gholami, H. Rouchi, Vibration analysis of single-walled carbon nanotubes using gradient elasticity theories, Composites: Part B 2012; 43: 2985–2989.
  12. M. Aydogdu, A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration, Physica E 2009; 41: 1651–1655.
  13. D. Karličić, T. Murmu, S. Adhikari, M. McCarthy, Non-local Structural Mechanics 2016; WILEY.
  14. H. Askes, E. C. Aifantis, Gradient elasticity and flexural wave dispersion in carbon nanotubes, Physical Review B: Condensed Matter and Materials Physics 2009; 80: 1955412.
  15. D. Karličić, P. Kozić, R. Pavlović, Flexural vibration and buckling analysis of single-walled carbon nanotubes using different gradient elasticity theories based on Reddy and Huu-Tai formulations, Journal of Theoretical and Applied Mechanics, 2015; 53 (1): 217–233.
  16. R. Rafie, R. M. Moghadam, On the modeling of carbon nanotubes: A critical review, Composites: Part B 2014; 56: 435–449.
  17. S. I. Yengejeh, S. A. Kazami, A. Öchsner, Advances in mechanical analysis of structurally and atomically modified carbon nanotubes and degenerated nanostructures: A review, Composites Part B 2016; 86: 95–107.
  18. S. Gopalakrishnan, S. Narendar, Wave Propagation in Nanostructures 2013; Springer.
  19. Elishakoff I., Carbon Nanotubes and Nanosensors: Vibration, Buckling and Balistic Impact, ISTE, London and John Wiley & Sons, New York, 2012.
  20. K. Kiani, B. Mehri, Assessment of nanotube structures under a moving nanoparticle using nonlocal beam theories, Journal of Sound and Vibration 2010;329 (11): 2241–2264.
  21. K. Kiani, Application of nonlocal beam models to double walled carbon nanotubes under a moving nanoparticle. Part I: theoretical formulations, Acta Mechanica 2011; 216: 165–195.
  22. K. Kiani, Application of nonlocal beam models to double-walled carbon nanotubes under a moving nanoparticle. Part II: parametric study, Acta Mechanica 2011; 216: 197–206.
  23. K. Kiani, Longitudinal and transverse vibration of a single-walled carbon nanotube subjected to a moving nanoparticle accounting for both nonlocal and inertial effects, Physica E: Low-dimensional Systems and Nanostructures 2010; 42 (9): 2391–2401.
  24. K. Kiani, A. Nikkhoo, B. Mehri, Prediction capabilities of classical and shear deformable beam theories excited by a moving mass, Journal of Sound and Vibration 2009; 320: 632–648.
  25. K. Kiani, Small-scale effect on the vibration of thin nanoplates subjected to a moving nanoparticle via nonlocal continuum theory, Journal of Sound and Vibration 2011; 330; 4896–4914.
  26. M. Şimşek, Vibration analysis of a single-walled carbon nanotube under action of a moving harmonic load based on nonlocal elasticity theory, Physica E 2010; 43: 182–191.
  27. S.A.H. Hosseini, O. Rahmani, Exact solution for axial and transverse dynamic response of functionally graded nanobeam under moving constant load based on nonlocal elasticity theory, Meccanica 2017, 52: 1441–1457.
  28. M. Pourseifi, O. Rahmami, S.A.H. Hoseini, Active vibration control of nanotube structures under a moving nanoparticle based on the nonlocal continuum theories, Meccanica 2015; 50 (5):1351–1369.
  29. B. Mehri, A. Davar, O. Rahmani, Dynamic Green function solution of beams under a moving load with different boundary conditions, Scientia Iranica 2009; 16 (3): 273–279.
  30. G. Szefer, D. Jasińska, Continuum molecular modelling of nanostructured materials, 2010, 189–201, in Alberts (eds.) Continuous Media with Microstructure, Springer, Berlin, Heidelberg.
  31. G. Szefer, Molecular modeling of stresses and deformations in nanostructured materials, International Journal of Applied Mathematics and Computer Science, 2004; 14 (4): 541–548.
  32. Y. Shirai, J.F. Morin, T. Sasaki, J.M. Guerrero, J.M. Recent progress on nanovehicles, Chemical Society Reviews 2006; 35 (11): 1043–1055.
  33. R. Lipowsky, S. Klumpp, “Life is motion”: multiscale motility of molecular motors, Physica A- Statistical Mechanics and its Applications 2005; 352 (1): 53–112.
  34. L. Fryba, Vibration of Solids and Structures under Moving Loads, Telford, London, 1999.
  35. G. Romano, R. Barretta, Stress-driven versus strain-driven nonlocal integral model for elastic nano-beams, Composite Part B: Engineering 2017; 114: 184–188.
  36. E.C. Aifantis, On the role of gradients in the localization of deformation and fracture, International Journal of Engineering Science, 1992, 30, 1279–1299.
  37. E.C. Aifantis, Gradient deformation models at nano, micro, and macro scales, Journal of Engineering Materials and Technology, ASCE, 1999, 121, April, 189–202.
  38. E.C. Aifantis, On the gradient approach- Relation to Eringen’s nonlocal theory, International Journal of Engineering Science 2011; 49: 1367–1377.
  39. C.W. Lim, G. Zhang, J.N. Reddy, A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, Journal of the Mechanics and Physics of Solids, 2015, 78, 298–313.
  40. J. Fernandez-Saez, R. Zaera, J.A. Loya, J.N. Reddy, Bending of Euler-Bernoulli beams using Eringen’s integral formulation: A paradox resolved, International Journal of Engineering Science 2016; 99: 107–116.
  41. P. Śniady, Dynamic response of a Timoshenko beam to a moving force, Journal of Applied Mechanics, ASME 2008; 75: 024503–1-024503-4.
  42. J. Rusin, P. Śniady, P. Śniady, Vibrations of double-string complex system under moving force. Closed solutions, Journal of Sound and Vibration 2011; 330: 404–415.
  43. K. Misiurek, P. Śniady, Vibrations of sandwich beam due to a moving force, Composite Structures 2013; 104: 85–93.
  44. P. Śniady, M. Podwórna, R. Idzikowski, Stochastic vibrations of the Euler-Bernoulli beam based on various versions of the gradient nonlocal elasticity theory, Probabilistic Engineering Mechanics 2019; 56: 27–34.
DOI: https://doi.org/10.2478/sgem-2019-0049 | Journal eISSN: 2083-831X | Journal ISSN: 0137-6365
Language: English
Page range: 306 - 318
Submitted on: Jan 14, 2020
Accepted on: Apr 16, 2020
Published on: Jun 29, 2020
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Publication frequency: 4 times per year

© 2020 Śniady Paweł, Katarzyna Misiurek, Olga Szyłko-Bigus, Idzikowski Rafał, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.