Have a personal or library account? Click to login
Effect of Kerr Foundation and in-Plane Forces on Free Vibration of FGM Nanobeams with Diverse Distribution of Porosity Cover

Effect of Kerr Foundation and in-Plane Forces on Free Vibration of FGM Nanobeams with Diverse Distribution of Porosity

By: Piotr Jankowski  
Open Access
|Nov 2020

References

  1. 1. Ashoori A.R, Salari E., Sadough Vanini S.A., (2017), A Thermo-Electro-Mechanical Vibration Analysis of Size-Dependent Functionally Graded Piezoelectric Nanobeams, Advances in High Temperature Ceramic Matrix Composites and Materials for Sustainable Development; Ceramic Transactions, Vol. 263, 547–558.10.1002/9781119407270.ch49
  2. 2. Aydogdu M., (2009), A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration, Physica E: Low-dimensional Systems and Nanostructures, Vol. 41(9), 1651–1655.10.1016/j.physe.2009.05.014
  3. 3. Bhushan B. (Ed), (2004), Springer Handbook of Nanotechnology, Springer Verlag, Berlin.10.1007/978-3-662-40019-7
  4. 4. El-Borgi S., Fernandes R., Reddy J.N., (2015), Non-local free and forced vibrations of graded nanobeams resting on a non-linear elastic foundation, International Journal of Non-Linear Mechanics, Vol. 77, 348–363.10.1016/j.ijnonlinmec.2015.09.013
  5. 5. Eltaher M.A., Emam S.A., Mahmoud F.F., (2012), Free vibration analysis of functionally graded size-dependent nanobeams. Applied Mathematics and Computation, Vol. 218(14), 7406–7420.10.1016/j.amc.2011.12.090
  6. 6. Eltaher M.A., Emam S.A., Mahmoud F.F., (2013), Static and stability analysis of nonlocal functionally graded nanobeams, Composite Structures, Vol. 96, 82–88.10.1016/j.compstruct.2012.09.030
  7. 7. Eltaher M.A., Fouda N., El-midany, T., Sadoun, A.M., (2018), Modified porosity model in analysis of functionally graded porous nanobeams. Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 40, 141.10.1007/s40430-018-1065-0
  8. 8. Eringen A.C., (1972), Nonlocal polar elastic continua. International Journal of Engineering Science, Vol. 10(1), 1–16.10.1016/0020-7225(72)90070-5
  9. 9. Eringen A.C., Edelen D.G.B., (1972), On nonlocal elasticity. International Journal of Engineering Science, Vol. 10(3), 233–248.10.1016/0020-7225(72)90039-0
  10. 10. Ghadiri M., Rajabpour A., Akbarshahi A., (2017), Non-linear forced vibration analysis of nanobeams subjected to moving concentrated load resting on a viscoelastic foundation considering thermal and surface effects, Applied Mathematical Modelling, Vol. 50, 676–694.10.1016/j.apm.2017.06.019
  11. 11. Karami B., Janghorban M., (2019), A new size-dependent shear deformation theory for free vibration analysis of functionally graded/anisotropic nanobeams, Thin-Walled Structures, Vol. 143, 106227.10.1016/j.tws.2019.106227
  12. 12. Kerr A.D., (1965), A study of a new foundation model. Acta Mechanica, Vol. 1(2), 135–147.10.1007/BF01174308
  13. 13. Kim J., Żur K.K., Reddy, J.N., (2019), Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates, Composite Structures, Vol. 209, 879–888.10.1016/j.compstruct.2018.11.023
  14. 14. Lam D.C.C., Yang F., Chong A.C.M., Wang J., Tong P., (2003), Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids, Vol. 51(8), 1477–1508.10.1016/S0022-5096(03)00053-X
  15. 15. Leondes C.T. (Ed), (2006), MEMS/NEMS Handbook Techniques and Applications, Springer, New York.10.1007/b136111
  16. 16. Li L., Hu Y., (2015), Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory, International Journal of Engineering Science, Vol. 97, 84–94.10.1016/j.ijengsci.2015.08.013
  17. 17. Lim C.W., Li C., Yu J.-L., (2010), Free vibration of pre-tensioned nanobeams based on nonlocal stress theory, Journal of Zhejiang University-SCIENCE A, Vol. 11, 34–42.10.1631/jzus.A0900048
  18. 18. Lim C.W., Zhang G., Reddy J.N., (2015), A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. Journal of the Mechanics and Physics of Solids, Vol. 78, 298–313.10.1016/j.jmps.2015.02.001
  19. 19. Lu L., Guo X., Zhao J., (2017), Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory, International Journal of Engineering Science, Vol. 116, 12–24.10.1016/j.ijengsci.2017.03.006
  20. 20. Lv Z., Qiu Z., Zhu J., Zhu B., Yang W., (2018), Nonlinear free vibration analysis of defective FG nanobeams embedded in elastic medium, Composite Structures, Vol. 202, 675–685.10.1016/j.compstruct.2018.03.068
  21. 21. Lyshevski S.E., (2002), MEMS and NEMS: System, Devices and Structures, CRC Press, New York.
  22. 22. Mindlin R.D., (1964), Micro-structure in linear elasticity. Archive for Rational Mechanics and Analysis, Vol. 16, 51–78.10.1007/BF00248490
  23. 23. Mindlin R.D., (1965), Second gradient of strain and surface-tension in linear elasticity. International Journal of Solids and Structures Vol. 1(4), 417–438.10.1016/0020-7683(65)90006-5
  24. 24. Nazemnezhad R., Hosseini-Hashemi S., (2014), Nonlocal nonlinear free vibration of functionally graded nanobeams, Composite Structures, Vol. 110, 192–199.10.1016/j.compstruct.2013.12.006
  25. 25. Pasternak P.L., (1954), On a New method of Analysis of an Elastic Foundation by Means of Two Foundation Constants, Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu I Arkhitekture, Moscow.
  26. 26. Rahmani O., Jandaghian A.A., (2015), Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory. Applied Physics A, Vol. 119, 1019–1032.10.1007/s00339-015-9061-z
  27. 27. Reddy J.N., (2017), Energy principles and variational methods in applied mechanics, John Wiley & Sons, New York.
  28. 28. Reza Barati M., (2017), Investigating dynamic response of porous inhomogeneous nanobeams on hybrid Kerr foundation under hygro-thermal loading, Applied Physics A, Vol. 123, 332.10.1007/s00339-017-0908-3
  29. 29. Saffari S., Hashemian M., Toghraie D., (2017), Dynamic stability of functionally graded nanobeam based on nonlocal Timoshenko theory considering surface effects, Physica B: Condensed Matter, Vol. 520, 97–105.10.1016/j.physb.2017.06.029
  30. 30. Sahmani S., Ansari R., (2011), Nonlocal beam models for buckling of nanobeams using state-space method regarding different boundary conditions, Journal of Mechanical Science and Technology, Vol. 25, 2365.10.1007/s12206-011-0711-6
  31. 31. Shafiei N., Mirjavadi S.S., Afshari B.M., Rabby S., Kazemi, M., (2017), Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams, Computer Methods in Applied Mechanics and Engineering, Vol. 322, 615–632.10.1016/j.cma.2017.05.007
  32. 32. Şimşek M., (2014), Large amplitude free vibration of nanobeams with various boundary conditions based on the nonlocal elasticity theory, Composites Part B: Engineering, Vol. 56, 621–628.10.1016/j.compositesb.2013.08.082
  33. 33. Şimşek M., (2016), Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach, International Journal of Engineering Science, Vol. 105, 12–27.10.1016/j.ijengsci.2016.04.013
  34. 34. Thai H.T., (2012), A nonlocal beam theory for bending, buckling, and vibration of nanobeams, International Journal of Engineering Science, Vol. 52, 56–64.10.1016/j.ijengsci.2011.11.011
  35. 35. Thai H.T., Vo T.P., (2012a), A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams. International Journal of Engineering Science, Vol. 54, 58–66.10.1016/j.ijengsci.2012.01.009
  36. 36. Thai H.T., Vo, T.P., (2012b), Bending and free vibration of functionally graded beams using various higher order shear deformation beam theories. International Journal of Mechanical Sciences, Vol. 62(1), 57–66.10.1016/j.ijmecsci.2012.05.014
  37. 37. Timoshenko S., Woinowsky-Krieger S., (1959), Theory of plates and shells, McGraw-Hill Book Company, New York.
  38. 38. Toupin R,A., (1962), Elastic materials with couple-stresses. Archive for Rational Mechanics and Analysis, Vol. 11, 385–414.10.1007/BF00253945
  39. 39. Yang F., Chong A.C.M., Lam D.C.C., Tong P., (2002), Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, Vol. 39(10), 2731–2743.10.1016/S0020-7683(02)00152-X
  40. 40. Zhang K, Ge M.-H., Zhao C., Deng Z-C., Lu, X-J., (2019), Free vibration of nonlocal Timoshenko beams made of functionally graded materials by Symplectic method, Composites Part B: Engineering, 156, 174–184.10.1016/j.compositesb.2018.08.051
DOI: https://doi.org/10.2478/ama-2020-0020 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088
Language: English
Page range: 135 - 143
Submitted on: Jun 19, 2020
Accepted on: Oct 23, 2020
Published on: Nov 20, 2020
Published by: Bialystok University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2020 Piotr Jankowski, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.