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Bending and Vibration Analysis of Curved FG Nanobeams via Nonlocal Timoshenko Model

Seyyed Amirhosein Hosseini, Omid Rahmani

Article ID: 401
Vol 2, Issue 2, 2018, Article identifier:

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The bending and vibration behavior of a curved FG nanobeam using the nonlocal Timoshenko beam theory is analyzed in this paper. It is assumed that the material properties vary through the radius direction.  The governing equations were obtained using Hamilton principle based on the nonlocal Timoshenko model of curved beam. An analytical approach for a simply supported boundary condition is conducted to analyze the vibration and bending of curved FG nanobeam. In the both mentioned analysis, the effect of significant parameter such as opening angle, the power law index of FGM, nonlocal parameter, aspect ratio and mode number are studied. The accuracy of the solution is examined by comparing the results obtained with the analytical and numerical results published in the literatures.


Curved nanobeam; Vibration and bending; Nonlocal elasticity theory; Analytical solution; Functionally graded curved beam;

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Kiani, K., 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(20): p. 4896-4914.

Niknam, H. and M. Aghdam, A semi analytical approach for large amplitude free vibration and buckling of nonlocal FG beams resting on elastic foundation. Composite Structures, 2015. 119: p. 452-462.

Eringen, A.C. and D. Edelen, On nonlocal elasticity. International Journal of Engineering Science, 1972. 10(3): p. 233-248.

Zhang, Y., G. Liu, and X. Xie, Free transverse vibrations of double-walled carbon nanotubes using a theory of nonlocal elasticity. Physical Review B, 2005. 71(19): p. 195404.

Wang, Q. and V. Varadan, Vibration of carbon nanotubes studied using nonlocal continuum mechanics. Smart Materials and Structures, 2006. 15(2): p. 659.

Hu, Y.-G., et al., Nonlocal shell model for elastic wave propagation in single-and double-walled carbon nanotubes. Journal of the Mechanics and Physics of Solids, 2008. 56(12): p. 3475-3485.

Reddy, J. and S. Pang, Nonlocal continuum theories of beams for the analysis of carbon nanotubes. Journal of Applied Physics, 2008. 103(2): p. 023511.

Aydogdu, M., A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration. Physica E: Low-dimensional Systems and Nanostructures, 2009. 41(9): p. 1651-1655.

Reddy, J., Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates. International Journal of Engineering Science, 2010. 48(11): p. 1507-1518.

Hosseini-Hashemi, S., et al., Surface effects on free vibration of piezoelectric functionally graded nanobeams using nonlocal elasticity. Acta Mechanica, 2014. 225(6): p. 1555-1564.

Pirmohammadi, A.A., et al., Modeling and active vibration suppression of a single-walled carbon nanotube subjected to a moving harmonic load based on a nonlocal elasticity theory. Applied Physics A, 2014. 117(3): p. 1547-1555.

Shi, J.-X., et al., Nonlocal vibration analysis of nanomechanical systems resonators using circular double-layer graphene sheets. Applied Physics A, 2014. 115(1): p. 213-219.

Ansari, R., R. Gholami, and S. Sahmani, Prediction of compressive post-buckling behavior of single-walled carbon nanotubes in thermal environments. Applied Physics A, 2013. 113(1): p. 145-153.

Reddy, J., Nonlocal theories for bending, buckling and vibration of beams. International Journal of Engineering Science, 2007. 45(2): p. 288-307.

Rahmani, O. and A.A. Jandaghian, Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory. Applied Physics A, 2015. 119(3): p. 1019-1032.

Natsuki, T., N. Matsuyama, and Q.-Q. Ni, Vibration analysis of carbon nanotube-based resonator using nonlocal elasticity theory. Applied Physics A, 2015. 120(4): p. 1309-1313.

Rahmani, O., et al., Torsional Vibration of Cracked Nanobeam Based on Nonlocal Stress Theory with Various Boundary Conditions: An Analytical Study. International Journal of Applied Mechanics, 2015. 07(03): p. 1550036.

Hosseini, S. and 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(6): p. 1441-1457.

Hosseini, S.A.H. and O. Rahmani, Free vibration of shallow and deep curved FG nanobeam via nonlocal Timoshenko curved beam model. Applied Physics A, 2016. 122(3): p. 1-11.

Misagh, Z. and H. Seyed Amirhosein, A semi analytical method for electro-thermo-mechanical nonlinear vibration analysis of nanobeam resting on the Winkler-Pasternak foundations with general elastic boundary conditions. Smart Materials and Structures, 2016. 25(8): p. 085005.

Sourki, R. and S.A. Hosseini, Coupling effects of nonlocal and modified couple stress theories incorporating surface energy on analytical transverse vibration of a weakened nanobeam. The European Physical Journal Plus, 2017. 132(4): p. 184.

Lee, H.-L. and W.-J. Chang, Surface effects on frequency analysis of nanotubes using nonlocal Timoshenko beam theory. Journal of Applied Physics, 2010. 108(9): p. 093503.

Wang, C., Y. Zhang, and X. He, Vibration of nonlocal Timoshenko beams. Nanotechnology, 2007. 18(10): p. 105401.

Rahmani, O. and O. Pedram, Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory. International Journal of Engineering Science, 2014. 77: p. 55-70.

Ebrahimi, F. and E. Salari, Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment. Acta Astronautica, 2015. 113: p. 29-50.

Komijani, M., et al., Vibration of thermo-electrically post-buckled rectangular functionally graded piezoelectric beams. Composite Structures, 2013. 98: p. 143-152.

Eltaher, M., S.A. Emam, and F. Mahmoud, Static and stability analysis of nonlocal functionally graded nanobeams. Composite Structures, 2013. 96: p. 82-88.

Eltaher, M., et al., Static and buckling analysis of functionally graded Timoshenko nanobeams. Applied Mathematics and Computation, 2014. 229: p. 283-295.

Şimşek, M. and H. Yurtcu, Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory. Composite Structures, 2013. 97: p. 378-386.

KANANIPOUR, H., I. KERMANI, and H. CHAVOSHI, Nonlocal beam model for dynamic analysis of curved nanobeams and rings.

Farshi, B., A. Assadi, and A. Alinia-Ziazi, Frequency analysis of nanotubes with consideration of surface effects. Applied Physics Letters, 2010. 96: p. 093105.

Wang, C.M. and W. Duan, Free vibration of nanorings/arches based on nonlocal elasticity. Journal of Applied Physics, 2008. 104: p. 014303.

Medina, L., R. Gilat, and S. Krylov, Symmetry breaking in an initially curved micro beam loaded by a distributed electrostatic force. International Journal of Solids and Structures, 2012. 49: p. 1864-1876.

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