A semi analytical approach for large amplitude free vibration and buckling of nonlocal FG beams resting on elastic foundation
Source abstract
Abstract
Abstract In this paper, an attempt is made to obtain a closed form solution for both natural frequency and buckling load of nonlocal FG beams resting on nonlinear elastic foundation. Implementing Eringen’s nonlocal elasticity theory, the effect of nonlocality is introduced into the Euler–Bernoulli beam theory to obtain the nonlinear governing partial differential equation. Application of the Galerkin technique to the governing equation leads to a nonlinear ODE in the time-domain. Finally, natural frequency of the FG nano beam is obtained using He’s variational method. It is shown that considering the nonlocal effects decreases the buckling load as well as natural frequency. Results also reveal that effects of nonlocal parameters on fully clamped beams are more than other types of boundary conditions. Moreover, it is shown that the effect of nonlocality decreases by increasing length of the beam.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Nonlocal and gradient elasticity in micro/nano structures · Composite Structure Analysis and Optimization · Numerical methods in engineering
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (37)
Show source-provided references
1. Establishing foundations of the mechanics of nanocomposites (Review)10.1007/s10778-011-0440-7 ↗
2. Analytical nanoscience and nanotechnology today and tomorrow10.1007/s00216-008-2130-9 ↗
3. Couple stress based strain gradient theory for elasticity10.1016/S0020-7683(02)00152-X ↗
4. Strain gradient interpretation of size effects10.1023/A:1018625006804 ↗
5. Eringen · 2010
6. A general theory of curved deformable interfaces in solids at equilibrium10.1080/01418619808239977 ↗
7. Application of nonlocal continuum models to nanotechnology10.1016/S0020-7225(02)00210-0 ↗
8. Application of nonlocal continuum mechanics to static analysis of micro- and nano-structures10.1016/j.physleta.2006.10.093 ↗
9. Nonlocal theories for bending, buckling and vibration of beams10.1016/j.ijengsci.2007.04.004 ↗
10. Buckling analysis of single walled carbon nanotube on Winkler foundation using nonlocal elasticity theory and DTM10.1016/j.commatsci.2010.11.001 ↗
11. Small-scale effects on buckling of multiwalled carbon nanotubes under axial compression10.1103/PhysRevB.70.205430 ↗
12. Effect of small length scale on elastic buckling of multi-walled carbon nanotubes under radial pressure10.1016/j.physleta.2005.09.036 ↗
13. Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM10.1016/j.physe.2009.02.004 ↗
14. Variational formulation and finite element analysis for nonlocal elastic nanobeams and nanoplates10.1016/j.commatsci.2010.05.040 ↗
15. Nonlocal transverse vibration of double-nanobeam-systems10.1063/1.3496627 ↗
16. A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams10.1016/j.ijengsci.2012.01.009 ↗
17. Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials
18. Pull-in instabilities in functionally graded microthermoelectromechanical systems10.1080/01495730802250714 ↗
19. Pull-in analysis of electrically actuated viscoelastic microbeams based on a modified couple stress theory10.1007/s11012-012-9545-2 ↗
20. Effect of nonlinear elastic foundation on large amplitude free and forced vibration of functionally graded beam10.1016/j.compstruct.2014.04.003 ↗
21. Nonlinear free vibration and post-buckling analysis of functionally graded beams on nonlinear elastic foundation10.1016/j.euromechsol.2011.01.005 ↗
22. Nanoscale compositionally graded thin-film electrolyte membranes for low-temperature solid oxide fuel cells10.1002/aenm.201100751 ↗
23. Fabrication and characterization of functionally graded nano-micro porous titanium surface by anodizing10.1002/jbm.b.31124 ↗
24. Fabrication of functionally graded nano-TiO2-reinforced epoxy matrix composites10.1002/pc.22695 ↗
25. Fabrication and characterization of functionally graded synthetic graphite/phenolic nanocomposites10.1016/j.msea.2012.02.097 ↗
26. Free vibration analysis of functionally graded size-dependent nanobeams10.1016/j.amc.2011.12.090 ↗
27. Static and stability analysis of nonlocal functionally graded nanobeams10.1016/j.compstruct.2012.09.030 ↗
28. Nonlocal effects in the free longitudinal vibration of axially functionally graded tapered nanorods10.1016/j.commatsci.2012.04.001 ↗
29. Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory10.1016/j.compstruct.2012.10.038 ↗
30. Longitudinal and transverse instabilities of moving nanoscale beam-like structures made of functionally graded materials10.1016/j.compstruct.2013.07.035 ↗
31. Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory10.1016/j.ijengsci.2013.12.003 ↗
32. Nonlocal nonlinear free vibration of functionally graded nanobeams10.1016/j.compstruct.2013.12.006 ↗
33. Small-scale effect on the free in-plane vibration of nanoplates by nonlocal continuum model10.1016/j.physe.2009.05.013 ↗
34. The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes10.1088/0957-4484/18/7/075702 ↗
35. Postbuckling and free vibrations of composite beams10.1016/j.compstruct.2008.06.006 ↗
36. Approximate analytical methods
37. Variational approach for nonlinear oscillators10.1016/j.chaos.2006.10.026 ↗