Finite Element Model of Functionally Graded Nanobeam for Free Vibration Analysis

Yıl 2019, Cilt: 11 Sayı: 2, 387 - 400, 25.07.2019

Büşra Uzun Mustafa Özgür Yaylı

https://doi.org/10.24107/ijeas.569798

Cited By: 4

Öz

In the present study, free vibration of functionally graded (FG)
nanobeam is investigated. The variation of material properties is assumed in
the thickness direction according to the power law. FG nanobeam is modeled as
Euler-Bernoulli beam with different boundary conditions and investigated based
on Eringen’s nonlocal elasticity theory. Governing equations are derived via Hamilton
principle. Frequency values are found by using finite element method. FG
nanobeam is composed of silicon carbide (SiC) and stainless steel (SUS304). The
effects of dimensionless small-scale parameters (e₀a/L), power law
exponent (k) and boundary conditions on frequencies are examined for FG
nanobeam.

Anahtar Kelimeler

Functionally graded nanobeam, nonlocal elasticity theory, free vibration, finite element method

Kaynakça

• Akgöz, B. and Civalek, Ö., Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory. Composite Structures, 98, 314-322, 2013.
• Ebrahimi, F., Ghadiri, M., Salari, E., Hoseini, S.A.H. and Shaghaghi, G.R., Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams. Journal of Mechanical Science and Technology, 29(3), 1207-1215, 2015.
• Eringen, A.C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of applied physics, 54(9), 4703-4710, 1983.
• Yayli, M.Ö., Effects of rotational restraints on the thermal buckling of carbon nanotube. Micro & Nano Letters, 14(2), 158-162, 2019.
• Mercan, K., Numanoglu, H.M., Akgöz, B., Demir, C. and Civalek, Ö., Higher-order continuum theories for buckling response of silicon carbide nanowires (SiCNWs) on elastic matrix. Archive of Applied Mechanics, 87(11), 1797-1814, 2017.
• Wang, C.M., Zhang, Y. Y., Ramesh, S.S. and Kitipornchai, S., Buckling analysis of micro-and nano-rods/tubes based on nonlocal Timoshenko beam theory. Journal of Physics D: Applied Physics, 39(17), 3904, 2006.
• Naghinejad, M. and Ovesy, H.R., Free vibration characteristics of nanoscaled beams based on nonlocal integral elasticity theory. Journal of Vibration and Control, 24(17), 3974-3988, 2018.
• Yaylı, M.Ö., Buckling Analysis of a Rotationally Restrained Single Walled Carbon Nanotube Embedded In An Elastic Medium Using Nonlocal Elasticity. International Journal Of Engineering & Applied Sciences, 8(2), 40-50, 2016.
• Eltaher, M.A., Emam, S.A. and Mahmoud, F.F., Static and stability analysis of nonlocal functionally graded nanobeams. Composite Structures, 96, 82-88, 2013.
• Thai, H.T., A nonlocal beam theory for bending, buckling, and vibration of nanobeams. International Journal of Engineering Science, 52, 56-64, 2012.
• Tounsi, A., Benguediab, S., Adda, B., Semmah, A. and Zidour, M., Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes. Advances in nano research, 1(1), 1-11, 2013.
• Thai, S., Thai, H.T., Vo, T.P. and Patel, V.I., A simple shear deformation theory for nonlocal beams. Composite Structures, 183, 262-270, 2018.
• Ebrahimi, F. and Salari, E., Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG nanobeams with various boundary conditions. Composites Part B: Engineering, 78, 272-290, 2015.
• Yayli, M.Ö., Buckling analysis of a cantilever single-walled carbon nanotube embedded in an elastic medium with an attached spring. Micro & Nano Letters, 12(4), 255-259, 2017.
• Yayli, M.Ö., On the axial vibration of carbon nanotubes with different boundary conditions. Micro & Nano Letters, 9(11), 807-811, 2014.
• Civalek, Ö. and Demir, Ç., Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory. Applied Mathematical Modelling, 35(5), 2053-2067, 2011.
• Kadıoğlu, H.G. and Yaylı, M.Ö., Buckling Analysis of Non-Local Timoshenko Beams by Using Fourier Series. International Journal Of Engineering & Applied Sciences, 9(4), 89-99, 2017.
• Zargaripoor, A., Daneshmehr, A., Isaac Hosseini, I., and Rajabpoor, A., Free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory using finite element method. Journal of Computational Applied Mechanics, 49(1), 86-101, 2018.
• Reddy, J.N., Energy Principles and Variational Methods in Applied Mechanics, John Wiley & Sons; 2nd edition, 2002.
• Talha, M. and Singh, B.N., Static response and free vibration analysis of FGM plates using higher order shear deformation theory. Applied Mathematical Modelling, 34(12), 3991-4011, 2010.