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http://dx.doi.org/10.12989/scs.2016.20.5.1119

A hybrid inverse method for small scale parameter estimation of FG nanobeams  

Darabi, A. (Department of Civil and Environmental Engineering, School of Engineering Shiraz University)
Vosoughi, Ali R. (Department of Civil and Environmental Engineering, School of Engineering Shiraz University)
Publication Information
Steel and Composite Structures / v.20, no.5, 2016 , pp. 1119-1131 More about this Journal
Abstract
As a first attempt, an inverse hybrid numerical method for small scale parameter estimation of functionally graded (FG) nanobeams using measured frequencies is presented. The governing equations are obtained with the Eringen's nonlocal elasticity assumptions and the first-order shear deformation theory (FSDT). The equations are discretized by using the differential quadrature method (DQM). The discretized equations are transferred from temporal domain to frequency domain and frequencies of the nanobeam are obtained. By applying random error to these frequencies, measured frequencies are generated. The measured frequencies are considered as input data and inversely, the small scale parameter of the beam is obtained by minimizing a defined functional. The functional is defined as root mean square error between the measured frequencies and calculated frequencies by the DQM. Then, the conjugate gradient (CG) optimization method is employed to minimize the functional and the small scale parameter is obtained. Efficiency, convergence and accuracy of the presented hybrid method for small scale parameter estimation of the beams for different applied random error, boundary conditions, length-to-thickness ratio and volume fraction coefficients are demonstrated.
Keywords
small scale parameter estimation; nanobeams; hybrid numerical method;
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1 Ansari, R., Mohammadi, V., Faghih Shojaei, M., Gholami, R. and Rouhi, H. (2014), "Nonlinear vibration analysis of Timoshenko nanobeams based on surface stress elasticity theory", Eur. J. Mech. A-Solid., 45, 143-152.   DOI
2 Chan, K.T. and Zhao, Y. (2011), "The dispersion characteristics of the waves propagating in a spinning single-walled carbon nanotube", Sci. China-Phys. Mech. Astron., 54(10), 1854-1865.   DOI
3 Duan, W.H., Wang, C.M. and Zhang, Y.Y. (2007), "Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics", J. Appl. Phys., 101(2), 024305.   DOI
4 Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710.   DOI
5 Hosseini-Hashemi, S., Nazemnezhad, R. and Rokni, H. (2015), "Nonlocal nonlinear free vibration of nanobeams with surface effect", Eur. J. Mech. A-Solid., 52, 44-53.   DOI
6 Huang, L.Y., Han, Q. and Liang, Y.J. (2012), "Calibration of nonlocal scale effect parameter for bending single-layered grapheme sheet under molecular dynamics", Nano., 7(5), 1250033.   DOI
7 Khademolhosseini, F., Phani, A.S., Nojeh, A. and Rajapakse, N. (2012), "Nonlocal continuum modeling and molecular dynamics simulation of torsional vibration of carbon nanotubes", IEEE Trans. Nanotech., 11(1), 34-43.   DOI
8 Malekzadeh, P. and Shojaee, M. (2013), "Surface and nonlocal effects on the nonlinear free vibration of non-uniform nanobeams", Compos. B. Eng., 52, 84-92.   DOI
9 Nazemnezhad, R. and Hosseini-Hashemi, S. (2014), "Nonlocal nonlinear free vibration of functionally graded nanobeams", Compos. Struct., 110, 192-199.   DOI
10 Ogata, S., Li, J. and Yip, S. (2002), "Ideal pure shear strength of aluminum and copper", Sci., 298(5594), 807-811.   DOI
11 Shen, H.S. and Zhang, C.L. (2010), "Torsional buckling and postbuckling of double-walled carbon nanotubes by nonlocal shear deformable shell model", Compos. Struct., 92(5), 1073-1084.   DOI
12 Vosoughi, A.R. (2014), "Thermal postbuckling analysis of functionally graded beams", J. Therm. Stress., 37(4), 532-544.   DOI
13 Vosoughi, A.R. (2016), "Nonlinear free vibration of functionally graded nanobeams on nonlinear elastic foundation", Iran. J. Sci. Tech. Trans. Civil Eng., 45(1), 581-586.
14 Wang, L.F. and Hu, H.Y. (2005), "Flexural wave propagation in single-walled carbon nanotubes", Phys. Rev. B., 71(19), 195412.   DOI
15 Vosoughi, A.R., Malekzadeh, P. and Razi, H. (2013), "Response of moderately thick laminated composite plates on elastic foundation subjected to moving load", Compos. Struct., 97, 286-295.   DOI
16 Vosoughi, A.R. and Nikoo, M.R. (2015), "Maximum fundamental frequency and thermal buckling temperature of laminated composite plates by a new hybrid multi-objective optimization technique", Thin-Wall. Struct., 95, 408-415.   DOI
17 Wang, Q. (2005), "Wave propagation in carbon nanotubes via nonlocal continuum mechanics", J. Appl. Phys., 98(12), 124301.   DOI
18 Wang, Q., Han, Q.K. and Wen, B.C. (2008), "Estimate of material properties of carbon nanotubes via nonlocal elasticity", Adv. Theor. Appl. Mech., 1(1), 1-10.
19 Zenkour, A.M. and Abouelregal, A.E. (2014), "The effect of two temperatures on a FG nanobeam induced by a sinusoidal pulse heating", Struct. Eng. Mech., Int. J., 51(2), 199-214.   DOI
20 Zenkour, A.M. and Abouelregal, A.E. (2015), "Thermoelastic interaction in functionally graded nanobeams subjected to time-dependent heat flux", Steel Compos. Struct., 18(4), 909-924.   DOI
21 Zhang, X., Jiao, K., Sharma, P. and Takobson, B.I. (2006), "An atomistic and non-classical continuum field theoretic perspective of elastic interactions between defects (force dipoles) of various symmetries and application to grapheme", J. Mech. Phys. Solid., 54(11), 2304-2329.   DOI
22 Zhang, Y.Q., Liu, G.R. and Xie, X.Y. (2005), "Free transverse vibrations of double-walled carbon nanotubes using a theory of nonlocal elasticity", Phys. Rev. B., 71(19), 195404.   DOI
23 Zhu, R., Pan, E., Chung, P.W., Cai, X., Liew, K.M., Buldum, A. (2006), "Atomistic calculation of elastic moduli in strained silicon", Semiconduct. Sci. Tech., 21: 906-911.   DOI