Nonlinear large-amplitude oscillations of PFG composite rectangular microplates based upon the modified strain gradient elasticity theory. (English) Zbl 1536.74121
Summary: In this research work, the nonlinear large-amplitude free vibration characteristics of composite microplates made of a porous functionally graded (PFG) material are addressed numerically in the presence of different size-dependent strain gradient tensors as microscale. Accordingly, for the first time, the effect of each microstructural tensor is analyzed separately on the nonlinear free oscillations of PFG microplates with and without a central cutout. In order to fulfill this goal, the isogeometric computation approach is engaged to integrate the finite element approach into the nonuniform B-spline-based computer aided design tool. Accordingly, the geometry of the microplate with a central cutout is modeled smoothly to verify \(C^{-1}\) continuity based upon a refined higher-order plate formulations. In this regard, the microstructural-dependent frequency responses associated with the nonlinear free oscillations of microplates are traced. In both the cases of simply supported and clamped boundary conditions, it was revealed that the fundamental frequency is enhanced about 1.20% by considering only the symmetric rotation gradient tensor, about 3.27% by taking only the dilatation gradient tensor, and 9.43% by considering only the deviatoric stretch gradient tensor. On the other hand, the anisotropic character of PFG composite microplates results in an unsymmetrical frequency response curve, as the nonlinear frequencies associated with negative oscillation amplitudes are a bit higher than those of positive ones.
Keywords:
micromechanics; size dependency; isogeometric approach; nonlinear dynamics; geometric approximationReferences:
| [1] | Sahmani, S.et al., Mechanical and biological performance of axially loaded novel bio-nanocomposite sandwich plate-type implant coated by biological polymer thin film, J. Mech. Behav. Biomed. Mater.88 (2018) 238-250. |
| [2] | Sahmani, S., Khandan, A., Saber-Samandari, S. and Aghdam, M. M., Vibrations of beam-type implants made of 3D printed bredigite-magnetite bio-nanocomposite scaffolds under axial compression: Application, communication and simulation, Ceram. Int.44 (2018) 11282-11291. |
| [3] | Sahmani, S., Shahali, M., Ghadiri Nejad, M., Khandan, A., Aghdam, M. M. and Saber-Samandari, S., Effect of copper oxide nanoparticles on electrical conductivity and cell viability of calcium phosphate scaffolds with improved mechanical strength for bone tissue engineering, Eur. Phys. J. Plus134 (2019) 7. |
| [4] | Sahmani, S., Khandan, A., Esmaeili, S. and Saber-Samandari, S., Calcium phosphate-PLA scaffolds fabricated by fused deposition modeling technique for bone tissue applications: Fabrication, characterization and simulation, Ceram. Int.46 (2020) 2447-2456. |
| [5] | Zuo, X., Yan, Z., Hou, K., Yang, H. and Xi, Y., Highly stable hierarchical porous nanosheet composite phase change materials for thermal energy storage, Appl. Therm. Eng.163 (2019) 114417. |
| [6] | Jeong, J. H., Kim, Y. A. and Kim, B.-H., Electrospun polyacrylonitrile/cyclodextrin-derived hierarchical porous carbon nanofiber/MnO_2 composites for supercapacitor applications, Carbon164 (2020) 296-304. |
| [7] | Ansari, R., Hassani, H., Gholami, R. and Rouhi, H., Thermal postbuckling analysis of FG-CNTRC plates with various shapes and temperature-dependent properties using the VDQ-FEM technique, Aerosp. Sci. Technol.106 (2020) 106078. |
| [8] | Ansari, R., Hassani, R., Gholami, R. and Rouhi, H., Nonlinear bending analysis of arbitrary-shaped porous nanocomposite plates using a novel numerical approach, Int. J. NonLinear Mech.126 (2020) 103556. |
| [9] | Chen, S.et al., A novel porous composite membrane of PHA/PVA via coupling of electrospinning and spin coating for antibacterial applications, Mater. Lett.301 (2021) 130279. |
| [10] | Sun, Y.et al., Fabrication of porous polyaniline/MWCNTs coated Co_9S_8 composite for electrochemical hydrogen storage application, J. Phys. Chem. Solids157 (2021) 110235. |
| [11] | Gholami, R. and Ansari, R., Thermal postbuckling of temperature-dependent functionally graded nanocomposite annular sector plates reinforced by carbon nanotubes, Int. J. Struct. Stab. Dyn.21 (2021) 2150026. · Zbl 1535.74489 |
| [12] | Hwang, J., Kim, Y., Yang, H. and Oh, J. H., Fabrication of hierarchically porous structured PDMS composites and their application as a flexible capacitive pressure sensor, Compos. B: Eng.211 (2021) 108607. |
| [13] | Prakash, C., Singh, S., Ramakrishna, S., Krolczyk, G. and Le, C. H., Microwave sintering of porous Ti-Nb-HA composite with high strength and enhanced bioactivity for implant applications, J. Alloys Compd.824 (2021) 153774. |
| [14] | Ansari, R., Hassani, R., Gholami, R. and Rouhi, H., Buckling and postbuckling of plates made of FG-GPL-reinforced porous nanocomposite with various shapes and boundary conditions, Int. J. Struct. Stab. Dyn.21 (2021) 2150063. · Zbl 1535.74095 |
| [15] | Sahmani, S. and Ansari, R., Nonlocal beam models for buckling of nanobeams using state-space method regarding different boundary conditions, J. Mech. Sci. Technol.25 (2011) 2365. |
| [16] | Farahmand, H., Ahmadi, A. and Arabnejad, S., A novel application of higher continuity finite element in vibration analysis of micro-plates, Int. J. Struct. Stab. Dyn.13 (2013) 1250080. · Zbl 1359.74133 |
| [17] | Ahmadi, A. R., Farahmand, H. and Arabnejad, S., Static deflection analysis of flexural simply supported sectorial micro-plate using P-version finite-element method, Int. J. Multiscale Comput. Eng.9 (2011) 193-200. |
| [18] | Sahmani, S., Bahrami, M., Aghdam, M. M. and Ansari, R., Surface effects on the nonlinear forced vibration response of third-order shear deformable nanobeams, Compos. Struct.118 (2014) 149-158. |
| [19] | Sahmani, S., Bahrami, M. and Ansari, R., Surface energy effects on the free vibration characteristics of postbuckled third-order shear deformable nanobeams, Compos. Struct.116 (2014) 552-561. |
| [20] | Sedighi, H. M., Keivani, M. and Abadyan, M., Modified continuum model for stability analysis of asymmetric FGM double-sided NEMS: Corrections due to finite conductivity, surface energy and nonlocal effect, Compos. B: Eng.83 (2015) 117-133. |
| [21] | Li, L., Li, X. and Hu, Y., Free vibration analysis of nonlocal strain gradient beams made of functionally graded material, Int. J. Eng. Sci.102 (2016) 77-92. · Zbl 1423.74399 |
| [22] | Farahmand, H., Naseralavi, S. S., Iranmanesh, A. and Mohammadi, M., Navier solution for buckling analysis of size-dependent functionally graded micro-plates, Lat. Am. J. Solids Struct.13 (2016) 3161-3173. |
| [23] | Simsek, M., Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach, Int. J. Eng. Sci.105 (2016) 12-27. · Zbl 1423.74412 |
| [24] | Sahmani, S. and Aghdam, M. M., Nonlinear vibrations of pre-and post-buckled lipid supramolecular micro/nano-tubules via nonlocal strain gradient elasticity theory, J. Biomech.65 (2017) 49-60. |
| [25] | Sahmani, S. and Aghdam, M. M., Size-dependent axial instability of microtubules surrounded by cytoplasm of a living cell based on nonlocal strain gradient elasticity theory, J. Theor. Biol.422 (2017) 59-71. · Zbl 1370.92024 |
| [26] | Sahmani, S. and Aghdam, M. M., Size-dependent nonlinear bending of micro/nano-beams made of nanoporous biomaterials including a refined truncated cube cell, Phys. Lett. A381 (2017) 3818-3830. |
| [27] | Khakalo, S., Balobanov, V. and Niiranen, J., Modelling size-dependent bending, buckling and vibrations of 2D triangular lattices by strain gradient elasticity models: Applications to sandwich beams and auxetics, Int. J. Eng. Sci.127 (2018) 33-52. · Zbl 1423.74343 |
| [28] | Sahmani, S. and Fattahi, A. M., Small scale effects on buckling and postbuckling behaviors of axially loaded FGM nanoshells based on nonlocal strain gradient elasticity theory, Appl. Math. Mech.39 (2018) 561-580. · Zbl 1390.74152 |
| [29] | Thanh, C.-L., Tran, L. V., Vu-Huu, T., Nguyen-Xuan, H. and Abdel-Wahab, M., The size-dependent thermal bending and buckling analyses of composite laminate microplate based on new modified couple stress theory and isogeometric analysis, Comput. Methods Appl. Mech. Eng.350 (2019) 337-361. · Zbl 1441.74082 |
| [30] | Thanh, C.-L., Tran, L. V., Bui, T. T. Q., Nguyen, H. X. and Abdel-Wahab, M., Isogeometric analysis for size-dependent nonlinear thermal stability of porous FG microplates, Compos. Struct.221 (2019) 110838. |
| [31] | Sahmani, S., Fattahi, A. M. and Ahmed, N. A., Analytical mathematical solution for vibrational response of postbuckled laminated FG-GPLRC nonlocal strain gradient micro/nanobeams, Eng. Comput.35 (2019) 1173-1189. |
| [32] | Gholami, R., Ansari, R. and Rouhi, H., Nonlinear pull-in instability of strain gradient microplates made of functionally graded materials, Int. J. Struct. Stab. Dyn.19 (2019) 1950007. · Zbl 1535.74394 |
| [33] | Mercan, K., Emsen, E. and Civalek, O., Effect of silicon dioxide substrate on buckling behavior of zinc oxide nanotubes via size-dependent continuum theories, Compos. Struct.218 (2019) 130-141. |
| [34] | Sarafraz, A., Sahmani, S. and Aghdam, M. M., Nonlinear secondary resonance of nanobeams under subharmonic and superharmonic excitations including surface free energy effects, Appl. Math. Model.66 (2019) 195-226. · Zbl 1481.74465 |
| [35] | Tang, H., Li, L. and Hu, Y., Coupling effect of thickness and shear deformation on size-dependent bending of micro/nano-scale porous beams, Appl. Math. Model.66 (2019) 527-547. · Zbl 1481.74467 |
| [36] | Gholami, Y., Ansari, R., Gholami, R. and Rouhi, H., Nonlinear bending analysis of nanoplates made of FGMs based on the most general strain gradient model and 3D elasticity theory, Eur. Phys. J. Plus134 (2019) 167. |
| [37] | Sahmani, S. and Safaei, B., Nonlinear free vibrations of bi-directional functionally graded micro/nano-beams including nonlocal stress and microstructural strain gradient size effects, Thin-Walled Struct.140 (2019) 342-356. |
| [38] | Sahmani, S. and Safaei, B., Nonlocal strain gradient nonlinear resonance of bi-directional functionally graded composite micro/nano-beams under periodic soft excitation, Thin-Walled Struct.143 (2019) 106226. |
| [39] | Sahmani, S. and Safaei, B., Influence of homogenization models on size-dependent nonlinear bending and postbuckling of bi-directional functionally graded micro/nano-beams, Appl. Math. Model.82 (2020) 336-358. · Zbl 1481.74640 |
| [40] | Fang, J., Zheng, S., Xiao, J. and Zhang, X., Vibration and thermal buckling analysis of rotating nonlocal functionally graded nanobeams in thermal environment, Aerosp. Sci. Technol.106 (2020) 106146. |
| [41] | Farahmand, H., Analytical solutions of bending and free vibration of moderately thick micro-plate via two-variable strain gradient theory, J. Braz. Soc. Mech. Sci. Eng.42 (2020) 251. |
| [42] | Farahmand, H. and Yasaie, P., Instability analysis of moderately thick porous micro-plate via two-variable strain gradient theory, Arc. Appl. Mech.91 (2021) 4459-4473. |
| [43] | Li, Q., Wu, D., Gao, W. and Tin-Loi, F., Size-dependent instability of organic solar cell resting on Winkler-Pasternak elastic foundation based on the modified strain gradient theory, Int. J. Mech. Sci.177 (2020) 105306. |
| [44] | Yuan, Y., Zhao, X., Zhao, Y., Sahmani, S. and Safaei, B., Dynamic stability of nonlocal strain gradient FGM truncated conical microshells integrated with magnetostrictive facesheets resting on a nonlinear viscoelastic foundation, Thin-Walled Struct.159 (2021) 107249. |
| [45] | Yuan, Y., Zhao, K., Han, Y., Sahmani, S. and Safaei, B., Nonlinear oscillations of composite conical microshells with in-plane heterogeneity based upon a couple stress-based shell model, Thin-Walled Struct.154 (2020) 106857. |
| [46] | Yuan, Y., Zhao, K., Zhao, Y., Sahmani, S. and Safaei, B., Couple stress-based nonlinear buckling analysis of hydrostatic pressurized functionally graded composite conical microshells, Mech. Mater.148 (2020) 103507. |
| [47] | Fan, L., Sahmani, S. and Safaei, B., Couple stress-based dynamic stability analysis of functionally graded composite truncated conical microshells with magnetostrictive facesheets embedded within nonlinear viscoelastic foundations, Eng. Comput.37 (2021) 1635-1655. |
| [48] | Karamanli, A. and Vo, T. P., Size-dependent behaviour of functionally graded sandwich microbeams based on the modified strain gradient theory, Compos. Struct.246 (2020) 112401. |
| [49] | Lin, F., Tong, L. H., Shen, H.-S., Lim, C. W. and Xiang, Y., Assessment of first and third order shear deformation beam theories for the buckling and vibration analysis of nanobeams incorporating surface stress effects, Int. J. Mech. Sci.186 (2020) 105873. |
| [50] | Fan, F., Xu, Y., Sahmani, S. and Safaei, B., Modified couple stress-based geometrically nonlinear oscillations of porous functionally graded microplates using NURBS-based isogeometric approach, Comput. Methods Appl. Mech. Eng.372 (2020) 113400. · Zbl 1506.74181 |
| [51] | Fan, F., Sahmani, S. and Safaei, B., Isogeometric nonlinear oscillations of nonlocal strain gradient PFGM micro/nano-plates via NURBS-based formulation, Compos. Struct.255 (2021) 112969. |
| [52] | Fan, F., Safaei, B. and Sahmani, S., Buckling and postbuckling response of nonlocal strain gradient porous functionally graded micro/nano-plates via NURBS-based isogeometric analysis, Thin-Walled Struct.159 (2021) 107231. |
| [53] | Fan, F., Cai, X., Sahmani, S. and Safaei, B., Isogeometric thermal postbuckling analysis of porous FGM quasi-3D nanoplates having cutouts with different shapes based upon surface stress elasticity, Compos. Struct.262 (2021) 113604. |
| [54] | Tang, Y. and Qing, H., Elastic buckling and free vibration analysis of functionally graded Timoshenko beam with nonlocal strain gradient integral model, Appl. Math. Model.96 (2021) 657-677. · Zbl 1481.74311 |
| [55] | Belarbi, M.-O.et al., Nonlocal finite element model for the bending and buckling analysis of functionally graded nanobeams using a novel shear deformation theory, Compos. Struct.264 (2021) 113712. |
| [56] | Song, R., Sahmani, S. and Safaei, B., Isogeometric nonlocal strain gradient quasi-three-dimensional plate model for thermal postbuckling of porous functionally graded microplates with central cutout with different shapes, Appl. Math. Mech.42 (2021) 771-786. · Zbl 1476.83019 |
| [57] | Chen, S. X., Sahmani, S. and Safaei, B., Size-dependent nonlinear bending behavior of porous FGM quasi-3D microplates with a central cutout based on nonlocal strain gradient isogeometric finite element modelling, Eng. Comput.37 (2021) 1657-1678. |
| [58] | Rao, R., Sahmani, S. and Safaei, B., Isogeometric nonlinear bending analysis of porous FG composite microplates with a central cutout modeled by the couple stress continuum quasi-3D plate theory, Arch. Civ. Mech. Eng.21 (2021) 98. |
| [59] | Yin, S., Xiao, Z., Deng, Y., Zhang, G., Liu, J. and Gu, S., Isogeometric analysis of size-dependent Bernoulli-Euler beam based on a reformulated strain gradient elasticity theory, Comput. Struct.253 (2021) 106577. |
| [60] | Wang, B. B., Lu, C., Fan, C. Y. and Zhao, M. H., A meshfree method with gradient smoothing for free vibration and buckling analysis of a strain gradient thin plate, Eng. Anal. Bound. Elem.132 (2021) 159-167. · Zbl 1521.74106 |
| [61] | Bacciocchi, M. and Tarantino, A. M., Analytical solutions for vibrations and buckling analysis of laminated composite nanoplates based on third-order theory and strain gradient approach, Compos. Struct.272 (2021) 114083. |
| [62] | Hou, R., Sahmani, S. and Safaei, B., Nonlinear oscillations of elliptical and sector prefabricated nanoplate-type structures made of functionally graded building material, Phys. Scr.96 (2021) 115704. |
| [63] | Wang, P., Yuan, P., Sahmani, S. and Safaei, B., Surface stress size dependency in nonlinear free oscillations of FGM quasi-3D nanoplates having arbitrary shapes with variable thickness using IGA, Thin-Walled Struct.166 (2021) 108101. |
| [64] | Yang, Z., Lu, H., Sahmani, S. and Safaei, B., Isogeometric couple stress continuum-based linear and nonlinear flexural responses of functionally graded composite microplates with variable thickness, Arch. Civ. Mech. Eng.21 (2021) 114. |
| [65] | Tang, P., Sun, Y., Sahmani, S. and Madyira, M. D., Isogeometric small-scale-dependent nonlinear oscillations of quasi-3D FG inhomogeneous arbitrary-shaped microplates with variable thickness, J. Brazil. Soc. Mech. Sci. Eng.43 (2021) 343. |
| [66] | Li, Y. S. and Xiao, T., Free vibration of the one-dimensional piezoelectric quasicrystal microbeams based on modified couple stress theory, Appl. Math. Model.96 (2021) 733-750. · Zbl 1481.74282 |
| [67] | Tao, C. and Dai, T., Isogeometric analysis for size-dependent nonlinear free vibration of graphene platelet reinforced laminated annular sector microplates, Eur. J. Mech. A Solids86 (2021) 104171. · Zbl 1479.74057 |
| [68] | Sahmani, S. and Safaei, B., Microstructural-dependent nonlinear stability analysis of random checkerboard reinforced composite micropanels via moving Kriging meshfree approach, Eur. Phys. J. Plus136 (2021) 806. |
| [69] | Sun, J. H., Zhou, Z. D., Sahmani, S. and Safaei, B., Microstructural size dependency in nonlinear lateral stability of random reinforced microshells via meshfree-based applied mathematical modeling, Int. J. Struct. Stab. Dyn.21 (2021) 2150164. · Zbl 1535.74522 |
| [70] | Zhang, Y., Sahmani, S. and Safaei, B., Meshfree-based applied mathematical modeling for nonlinear stability analysis of couple stress-based lateral pressurized randomly reinforced microshells, Eng. Comput. (2021), https://doi.org/10.1007/s00366-021-01472-x. |
| [71] | Phung-Van, P., Thai, C. H., Nguyen-Xuan, H. and Abdel-Wahab, M., An isogeometric approach of static and free vibration analyses for porous FG nanoplates, Eur. J. Mech. A Solids78 (2019) 103851. · Zbl 1472.74206 |
| [72] | Senthilnathan, N. R., Lim, S. P., Lee, K. H. and Chow, S. T., Buckling of shear-deformable plates, AIAA J.25 (1987) 1268-1271. |
| [73] | Yang, F.et al., Couple stress based strain gradient theory for elasticity, Int. J. Solids Struct.39 (2002) 2731-2743. · Zbl 1037.74006 |
| [74] | Crisfield, M. A., Nonlinear Finite Element Analysis of Solids and Structures (John Wiley & Sons, Chichester, UK, 1991). · Zbl 0809.73005 |
| [75] | Ke, L. L., Wang, Y. S., Yang, J. and Kitipornchai, S., Nonlinear free vibration of size-dependent functionally graded microbeams, Int. J. Eng. Sci.50 (2012) 256-267. · Zbl 1423.74395 |
| [76] | Wang, Y.-G., Lin, W.-H. and Liu, N., Large amplitude free vibration of size-dependent circular microplates based on the modified couple stress theory, Int. J. Mech. Sci.71 (2013) 51-57. |
| [77] | Gholami, R. and Ansari, R., A most general strain gradient plate formulation for size-dependent geometrically nonlinear free vibration analysis of functionally graded shear deformable rectangular microplates, Nonlinear Dyn.84 (2016) 2403-2422. |
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