Browse > Article
http://dx.doi.org/10.12989/scs.2020.36.2.179

On resonance behavior of porous FG curved nanobeams  

She, Gui-Lin (College of Mechanical Engineering, Guizhou University)
Liu, Hai-Bo (College of Mechanical and Electric Engineering, Hunan University of Science and Technology)
Karami, Behrouz (Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University)
Publication Information
Steel and Composite Structures / v.36, no.2, 2020 , pp. 179-186 More about this Journal
Abstract
In this paper, the forced resonance vibration of porous functionally graded (FG) curved nanobeam is examined. In order to capture the hardening and softening mechanisms of nanostructure, the nonlocal strain gradient theory is employed to build the size-dependent model. Using the Timoshenko beam theory together with the Hamilton principle, the equations of motion for the curved nanobeam are derived. Then, Navier series are used in order to obtain the dynamical deflections of the porous FG curved nanobeam with simply-supported ends. It is found that the resonance position of the nanobeam is very sensitive to the nonlocal and strain gradient parameters, material variation, porosity coefficient, as well as geometrical conditions. The results indicate that the resonance position is postponed by increasing the strain gradient parameter, while the nonlocal parameter has the opposite effect on the results. Furthermore, increasing the opening angle or length-to-thickness ratio will result in resonance position moves to lower-load frequency.
Keywords
resonance phenomena; porous materials; curved nano-beams; nonlocal strain gradient theory;
Citations & Related Records
Times Cited By KSCI : 14  (Citation Analysis)
연도 인용수 순위
1 Ahmadi, H. (2019), "Nonlinear primary resonance of imperfect spiral stiffened functionally graded cylindrical shells surrounded by damping and nonlinear elastic foundation", Eng. Comput., 35, 1491-1505. http://doi.org/10.1007/s00366-018-0679-2.   DOI
2 Akgoz, B. and Civalek, O. (2014), "Longitudinal vibration analysis for microbars based on strain gradient elasticity theory", J. Sound Vib., 20(4), 606-614. https://doi.org/10.1177/1077546312463752.
3 Akgoz, B. and Civalek, O. (2015), "A microstructure-dependent sinusoidal plate model based on the strain gradient elasticity theory", Acta Mech., 226, 2277-2294. https://doi.org/10.1007/s00707-015-1308-4.   DOI
4 Akgoz, B. and Civalek, O. (2016), "Bending analysis of embedded carbon nanotubes resting on an elastic foundation using strain gradient theory", Acta Astronaut., 119, 1-12. https://doi.org/10.1016/j.actaastro.2015.10.021.   DOI
5 Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2019b), "On the resonance of functionally graded nanoplates using bi-Helmholtz nonlocal strain gradient theory", Int. J. Eng. Sci., 144, 103143. https://doi.org/1016/j.ijengsci.2019.103143.   DOI
6 Karami, B., Shahsavari, D. and Janghorban, M. (2019c), "On the dynamics of porous doubly-curved nanoshells", Int. J. Eng. Sci., 143, 39-55. https://doi.org/10.1016/j.ijengsci.2019.06.014.   DOI
7 Zenkour, A.M. (2018), "A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities", Compos. Struct., 201, 38-48. https://doi.org/10.1016/j.compstruct.2018.05.147.   DOI
8 Zenkour, A.M. and Radwan, A.F. (2019), "Bending response of FG plates resting on elastic foundations in hygrothermal environment with porosities", Compos. Struct., 213, 133-143. https://doi.org/10.1016/j.compstruct.2019.01.065.   DOI
9 Akgoz, B. and Civalek, O. (2017), "Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams", Compos. Part B: Eng., 129, 77-87. https://doi.org/10.1016/j.compositesb.2017.07.024.   DOI
10 Demir, C. and Civalek, O. (2013), "Torsional and longitudinal frequency and wave response of microtubules based on the nonlocal continuum and nonlocal discrete models", Appl. Math. Model., 37(22), 9355-9367. http://doi.org/10.1016/j.apm.2013.04.050.   DOI
11 Khaniki, H.B. (2018), "On vibrations of nanobeam systems", Int. J. Eng. Sci., 124, 85-103. https://doi.org/10.1016/j.ijengsci.2017.12.010.   DOI
12 Lei, Y.-L., Gao, K., Wang, X. and Yang, J. (2020), "Dynamic behaviors of single- and multi-span functionally graded porous beams with flexible boundary constraints", Appl. Math. Model.,83, 754-776. https://doi.org/10.1016/j.apm.2020.03.017.   DOI
13 Lim, C.W., Zhang, G. and Reddy, J.N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solids, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001.   DOI
14 Lu, L., Guo, X. and Zhao, J. (2019), "A unified size-dependent plate model based on nonlocal strain gradient theory including surface effects", Appl. Math. Model., 68, 583-602. https://doi.org/10.1016/j.apm.2018.11.023.   DOI
15 Machado, S.P. and Piovan, M.T. (2013), "Nonlinear dynamics of rotating box fgm beams using nonlinear normal modes", Thin Wall. Struct., 62, 158-168. https://doi.org/10.1016/j.tws.2012.09.005.   DOI
16 Malikan, M., Krasheninnikov, M. and Eremeyev, V.A. (2020), "Torsional stability capacity of a nano-composite shell based on a nonlocal strain gradient shell model under a three-dimensional magnetic field", Int. J. Eng. Sci., 148, UNSP 103234. https://doi.org/10.1016/j.ijengsci.2019.103210.
17 Apuzzo, A., Barretta, R., Fabbrocino, F., Faghidian, S.A., Luciano, R. and de Sciarra, F.M. (2019), "Axial and torsional free vibrations of elastic nano-beams by stress-driven two-phase elasticity", J. Appl. Comput. Mech., 5(2), 402-413. https://doi.org/10.22055/jacm.2018.26552.1338.
18 Amar, L.H.H., Kaci, A., Yeghnem, R. and Tounsi, A. (2018), "A new four-unknown refined theory based on modified couple stress theory for size-dependent bending and vibration analysis of functionally graded micro-plate", Steel Compos. Struct., 26(1), 89-102. http://dx.doi.org/10.12989/scs.2018.26.1.089.   DOI
19 Anirudh, B., Ben Zineb, T., Polit, O., Ganapathi, M. and Prateek, G. (2020), "Nonlinear bending of porous curved beams reinforced by functionally graded nanocomposite graphene platelets applying an efficient shear flexible finite element approach", Int. J. Nonlin. Mech., 119, 103346. https://doi.org/10.1016/j.ijnonlinmec.2019.103346.   DOI
20 Ansari, R. and Gholami, R. (2016), "Nonlinear primary resonanc of third-order shear deformable functionally graded nanocomposite rectangular plates reinforced by carbon nanotubes", Compos. Struct., 154, 707-723. http://doi.org/10.1016/j.compstruct.2016.07.023.   DOI
21 Arefi, M. and Zenkour, A.M. (2018a), "Thermal stress and deformation analysis of a size-dependent curved nanobeam based on sinusoidal shear deformation theory", Alex. Eng. J., 57(3), 2177-2185. http://doi.org/10.1016/j.aej.2017.07.003.   DOI
22 Arefi, M. and Zenkour, A.M. (2018b), "Size-dependent vibration and electro-magneto-elastic bending responses of sandwich piezomagnetic curved nanobeams", Steel Compos. Struct., 29(5), 579-590. http://doi.org/10.12989/scs.2018.29.5.579.   DOI
23 Ebrahimi, F. and Barati, M.R. (2017), "Size-dependent dynamic modeling of inhomogeneous curved nanobeams embedded in elastic medium based on nonlocal strain gradient theory", Appl. Phys. A-Mater., 231(23), 4457-4469. https://doi.org/10.1177/0954406216668912.
24 Du, C. and Li, Y. (2014), "Nonlinear internal resonance of functionally graded cylindrical shells using the hamiltonian dynamics", Acta Mech. Solida Sin., 27(6), 635-647. http://doi.org/10.1016/S0894-9166(15)60008-8   DOI
25 Du, C. and Li, Y. (2013), "Nonlinear resonance behavior of functionally graded cylindrical shells in thermal environments", Compos. Struct., 102, 164-174. http://doi.org/10.1016/j.compstruct.2013.02.028.   DOI
26 Ebrahimi, F. and Barati, M. (2017), "A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams", Compos. Struct., 159(1), 174-182. http://doi.org/10.1016/j.compstruct.2016.09.058.   DOI
27 Eltaher, M.A., Fouda, N., El-Midany, T. and Sadoun, A.M. (2018), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Brazil. Soc. Mech. Sci. Eng., 40(3), 141. https://doi.org/10.1007/s40430-018-1065-0.   DOI
28 Faghidian, S.A. (2016), "Unified formulation of the stress field of saint-Venant's flexure problem for symmetric cross-sections", Int. J. Mech. Sci., 111-112, 65-72. https://doi.org/10.1016/j.ijmecsci.2016.04.003.   DOI
29 Faghidian, S.A. (2017), "Unified formulations of the shear coefficients in timoshenko beam theory", J. Eng. Mech., 143(9), 06017013. http://doi.org/10.1061/(ASCE)EM.1943-7889.0001297.   DOI
30 Marami, G., Nazari, S.A., Faghidian, S.A., Vakili-Tahami, F. and Etemadi, S. (2016), "Improving the mechanical behavior of the adhesively bonded joints using RGO additive", Int. J. Adhes. Adhes., 70, 277-286. https://doi.org/10.1016/j.ijadhadh.2016.07.014.   DOI
31 Barretta, R. Ali Faghidian, S. and Marotti de Sciarra, F., Penna, R., and Pinnola F.P. (2020), "On torsion of nonlocal Lam strain gradient FG elastic beams", Compos. Struct., 233, 111550. https://doi.org/10.1016/j.compstruct.2019.111550.   DOI
32 Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007.   DOI
33 Barretta, R. and de Sciarra, F.M. (2018), "Constitutive boundary conditions for nonlocal strain gradient elastic nano-beams", Int. J. Eng. Sci., 130, 187-198. https://doi.org/10.1016/j.ijengsci.2018.05.009.   DOI
34 Barretta, R. and de Sciarra, F.M. (2019), "Variational nonlocal gradient elasticity for nano-beams", Int. J. Eng. Sci., 143, 73-91. https://doi.org/10.1016/j.ijengsci.2019.06.016.   DOI
35 Barretta, R., Sciarra, F.M.d. and Vaccaro, M.S. (2019), "On nonlocal mechanics of curved elastic beams", Int. J. Eng. Sci., 144, 103140. http://doi.org/10.1016/j.ijengsci.2019.103140.   DOI
36 Barretta, R. Ali Faghidian, S. and Marotti de Sciarra, F. (2019), "Stress-driven nonlocal integral elasticity for axisymmetric nano-plates", Int. J. Eng. Sci., 136, 38-52. https://doi.org/10.1016/j.ijengsci.2019.01.003.   DOI
37 Civalek, O. and Demir, C. (2016), "A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method", Appl. Math. Comput., 289, 335-352. http://doi.org/10.1016/j.amc.2016.05.034.   DOI
38 Civalek, O. and Demir, C. (2011), "Bending analysis of microtubules using nonlocal Euler-Bernoulli beam theory", Appl. Math. Model., 35(5): 2053-2067. http://doi.org/10.1016/j.apm.2010.11.004.   DOI
39 Civalek, O., Uzun, B., Yayli, M.O. and Akgoz, B. (2020), "Size-dependent transverse and longitudinal vibrations of embedded carbon and silica carbide nanotubes by nonlocal finite element method", Eur. Phys. J. Plus, 135, 381. https://doi.org/10.1140/epjp/s13360-020-00385-w.   DOI
40 Farokhi, H. and Ghayesh, M.H. (2015), "Nonlinear resonant response of imperfect extensible timoshenko microbeams", Int. J. Mech. Mater. Des., 13(1), 43-55. http://doi.org/10.1007/s10999-015-9316-z.   DOI
41 Farokhi, H., Ghayesh, M. H., Kosasih, B. and Akaber, P. (2015), "On the nonlinear resonant dynamics of timoshenko microbeams: effects of axial load and geometric imperfection", Meccanica, 51(1), 155-169. http://doi.org/10.1007/s11012-015-0196-y.   DOI
42 Fattahi, A.M., Safaei, B. and Moaddab, E. (2019), "The application of nonlocal elasticity to determine vibrational behavior of FG nanoplates", Steel Compos. Struct., 32(2), 281-292. http://doi.org/10.12989/scs.2019.32.2.281.   DOI
43 Fourn, H., Atmane, H.A., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., 27(1), 109-122. http://dx.doi.org/10.12989/scs.2018.27.1.109.   DOI
44 Ganapathi, M. and Polit, O. (2017), "A nonlocal higher-order model including thickness stretching effect for bending and buckling of curved nanobeams", Appl. Math. Model., 57, 121-141. http://doi.org/10.1016/j.apm.2017.12.025   DOI
45 Ganapathi, M., Merzouki, M. and Polit, O. (2018), "Vibration study of curved nanobeams based on nonlocal higher-order shear deformation theory using finite element approach", Compos. Struct., 184(15), 821-838. http://doi.org/10.1016/j.compstruct.2017.10.066   DOI
46 Ghayesh, M.H. and Farajpour, A. (2018), "Nonlinear mechanics of nanoscale tubes via nonlocal strain gradient theory", Int. J. Eng. Sci., 129, 84-95. https://doi.org/10.1016/j.ijengsci.2018.04.003.   DOI
47 Attia, M.A. and Rahman, A.A.A. (2018), "On vibrations of functionally graded viscoelastic nanobeams with surface effects", Int. J. Eng. Sci., 127, 1-32. https://doi.org/10.1016/j.ijengsci.2018.02.005.   DOI
48 Medina, L., Gilat, R., Ilic, B. and Krylov, S. (2014), "Experimental investigation of the snap-through buckling of electrostatically actuated initially curved pre-stressed micro beams", Sensor. Actuat. A-Phys., 220, 323-332. https://doi.org/10.1016/j.sna.2014.10.016.   DOI
49 Moradi-Dastjerdi, R. and Behdinan, K. (2019), "Thermoelastic static and vibrational behaviors of nanocomposite thick cylinders reinforced with graphene", Steel Compos. Struct., 31(5), 529-539. https://doi.org/10.12989/scs.2019.31.5.529.   DOI
50 Nami, M.R. and Janghorban, M. (2014), "Resonance behavior of FG rectangular micro/nano plate based on nonlocal elasticity theory and strain gradient theory with one gradient constant", Compos. Struct., 111, 349-353. https://doi.org/10.1016/j.compstruct.2014.01.012.   DOI
51 Romano, G., Barretta, A. and Barretta, R. (2012), "On torsion and shear of saint-venant beams", Eur. J. Mech. A-Solid., 35, 47-60. https://doi.org/10.1016/j.euromechsol.2012.01.007.
52 Numanoglu, H.M., Akgoz, B. and Civalek, O. (2018), "On dynamic analysis of nanorods", Int. J. Eng. Sci., 130, 33-50. https://doi.org/10.1016/j.ijengsci.2018.05.001.   DOI
53 Polit, O., Merzouki, T. and Ganapathi, M. (2018), "Elastic stability of curved nanobeam based on higher-order shear deformation theory and nonlocal analysis by finite element approach", Finite Elem. Anal. Des., 146, 1-15. https://doi.org/10.1016/j.finel.2018.04.002.   DOI
54 Qi, L., Huang, S., Fu, G., Zhou, S. and Jiang, X. (2018), "On the mechanics of curved flexoelectric microbeams", Int. J. Eng. Sci., 124, 1-15. https://doi.org/10.1016/j.ijengsci.2017.11.022.   DOI
55 She, G.L., Jiang, X.Y. and Karami, B. (2019), "On thermal snap - buckling of FG curved nanobeams", Mater. Res., Express, 6, 115008. https://doi.org/10.1088/2053-1591/ab44f1.   DOI
56 Hosseini, S. and Rahmani, O. (2016), "Free vibration of shallow and deep curved FG nanobeam via nonlocal Timoshenko curved beam model", Appl. Phys. A, 122(3), 1-11. https://doi.org/10.1007/s00339-016-9696-4.
57 Ghayesh M.H., Farokhi, H., Gholipour, A., Hussain, S. and Arjomandi M. (2017), "Resonance responses of geometrically imperfect functionally graded extensible microbeams", J. Comput. Nonlin. Dyn., 12, 051002. https://doi.org/10.1115/1.4035214.   DOI
58 Gurses, M., Akgoz, B. and Civalek, O. (2012), "Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation", Appl. Math. Comput., 219(6), 3226-3240. https://doi.org/10.1016/j.amc.2012.09.062.   DOI
59 Heydari, A. (2018), "Exact vibration and buckling analyses of arbitrary gradation of nano-higher order rectangular beam", Steel Compos. Struct., 28(5),589-606. http://dx.doi.org/10.12989/scs.2018.28.5.589.   DOI
60 Jalaei, M.H. and Civalek, O. (2019), "On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam", Int. J. Eng. Sci., 143, 14-32. https://doi.org/10.1016/j.ijengsci.2019.06.013.   DOI
61 Jandaghian, A.A. and Rahmani, O. (2017), "Vibration analysis of FG nanobeams based on third order shear deformation theory under various boundary conditions", Steel Compos. Struct., 25(1), 67-78. https://doi.org/10.12989/scs.2017.25.1.067.   DOI
62 Karami, B., Shahsavari, D., Janghorban, M. and Tounsi, A. (2019a), "Resonance behavior of functionally graded polymer composite nanoplates reinforced with graphene nanoplatelets", Int. J. Mech. Sci., 156, 94-105. https://doi.org/10.1016/j.ijmecsci.2019.03.036.   DOI
63 Tang, Y.G., Liu, Y. and Zhao, D. (2018), "Effects of neutral surface deviation on nonlinear resonance of embedded temperature-dependent functionally graded nanobeams", Compos. Struct., 184, 969-879. https://doi.org/10.1016/j.compstruct.2017.10.058.   DOI