Abstract
An iterative algorithm is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the nth approximation is derived from the previous ones. As a first endeavor, the nonlinear dynamic instability performance of the electrical plate on the nonlinear elastic substrate using an iterative algorithm is scrutinized in this research. A nonlinear elastic foundation is assumed to be in contact with the electrical plate during deformation. The nonlinear coupled dynamic equations governing the transverse and longitudinal motions of the electrical plate are derived using Hamilton’s principle method, the von Kármán geometric nonlinearity, and improved higher-order shear deformation theory. The iterative algorithm based generalized differential quadrature method (IAB-GDQM) is applied for solving the nonlinear equations with the aid of nonlinear boundary domains. Parametric studies are implemented to explore the impacts of the applied voltage, geometry of the plate, and nonlinear factor on large amplitude motion, and nonlinear dynamics of the presented system for various boundary domains. Results show that the nonlinear dynamic depends on nonlinear elastic foundation effects and the applied voltage, which can be used to design the electrically structures in different environmental conditions accurately.
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References
Ebrahimi F, Habibi M, Safarpour H (2019) On modeling of wave propagation in a thermally affected GNP-reinforced imperfect nanocomposite shell. Eng Comput 35(4):1375–1389
Al-Furjan M, Safarpour H, Habibi M, Safarpour M, Tounsi A (2020) A comprehensive computational approach for nonlinear thermal instability of the electrically FG-GPLRC disk based on GDQ method. Eng Comput. https://doi.org/10.1007/s00366-020-01088-7
Safarpour M, Ebrahimi F, Habibi M, Safarpour H (2020) On the nonlinear dynamics of a multi-scale hybrid nanocomposite disk. Eng Comput. https://doi.org/10.1007/s00366-020-00949-5
Moayedi H, Ebrahimi F, Habibi M, Safarpour H, Foong LK (2020) Application of nonlocal strain–stress gradient theory and GDQEM for thermo-vibration responses of a laminated composite nanoshell. Eng Comput. https://doi.org/10.1007/s00366-020-01002-1
Shariati A, Habibi M, Tounsi A, Safarpour H, Safa M (2020) Application of exact continuum size-dependent theory for stability and frequency analysis of a curved cantilevered microtubule by considering viscoelastic properties. Eng Comput. https://doi.org/10.1007/s00366-020-01024-9
Al-Furjan M, Habibi M, Chen G, Safarpour H, Safarpour M, Tounsi A (2020) Chaotic simulation of the multi-phase reinforced thermo-elastic disk using GDQM. Eng Comput. https://doi.org/10.1007/s00366-020-01144-2
Al-Furjan M, Oyarhossein MA, Habibi M, Safarpour H, Jung DW (2020) Wave propagation simulation in an electrically open shell reinforced with multi-phase nanocomposites. Eng Comput. https://doi.org/10.1007/s00366-020-01167-9
Wang Y, Yuan Y, Wang Q, Liu C, Zhi Q, Cao J (2020) Changes in air quality related to the control of coronavirus in China: implications for traffic and industrial emissions. Sci Total Environ 731:139133
Hu J, Zhang H, Liu L, Zhu X, Zhao C, Pan Q (2020) Convergent multiagent formation control with collision avoidance. IEEE Trans Rob 36(6):1805–1818
Hu J, Wang M, Zhao C, Pan Q, Du C (2020) Formation control and collision avoidance for multi-UAV systems based on Voronoi partition. Sci China Technol Sci 63(1):65–72
Yu D, Mao Y, Gu B, Nojavan S, Jermsittiparsert K, Nasseri M (2020) A new LQG optimal control strategy applied on a hybrid wind turbine/solid oxide fuel cell/in the presence of the interval uncertainties. Sustain Energy Grids Netw 21:100296. https://doi.org/10.1016/j.segan.2019.100296
Zhao X, Ye Y, Ma J, Shi P, Chen H (2020) Construction of electric vehicle driving cycle for studying electric vehicle energy consumption and equivalent emissions. Environ Sci Pollut Res. https://doi.org/10.1007/s11356-020-09094-4
Ma L, Liu X, Moradi Z (2021) On the chaotic behavior of graphene-reinforced annular systems under harmonic excitation. Eng Comput. https://doi.org/10.1007/s00366-020-01210-9
Wu T, Cao J, Xiong L, Zhang H (2019) New stabilization results for semi-markov chaotic systems with fuzzy sampled-data control. Complexity. https://doi.org/10.1155/2019/7875305
Shi K, Tang Y, Zhong S, Yin C, Huang X, Wang W (2018) Nonfragile asynchronous control for uncertain chaotic Lurie network systems with Bernoulli stochastic process. Int J Robust Nonlinear Control 28(5):1693–1714
Shi K, Tang Y, Liu X, Zhong S (2017) Non-fragile sampled-data robust synchronization of uncertain delayed chaotic Lurie systems with randomly occurring controller gain fluctuation. ISA Trans 66:185–199
Dong Q, Cui L (2021) Reliability analysis of a system with two-stage degradation using Wiener processes with piecewise linear drift. IMA J Manag Math 32(1):3–29. https://doi.org/10.1093/imaman/dpaa009
Niu Z, Zhang B, Wang J, Liu K, Chen Z, Yang K, Zhou Z, Fan Y, Zhang Y, Ji D (2020) The research on 220 GHz multicarrier high-speed communication system. China Commun 17(3):131–139
Huo S-Y, Huang H-B, Wang L-J, Chen J-J (2020) Deterministic interface modes in two-dimensional acoustic systems. Int J Modern Phys B. https://doi.org/10.1142/S0217979221500107
Hu J, Zhang H, Li Z, Zhao C, Xu Z, Pan Q (2020) Object traversing by monocular UAV in outdoor environment. Asian J Control. https://doi.org/10.1002/asjc.2415
Xu S, Wang J, Shou W, Ngo T, Sadick A-M, Wang X (2020) Computer vision techniques in construction: a critical review. Arch Comput Methods Eng. https://doi.org/10.1007/s11831-020-09504-3
Yue H, Wang H, Chen H, Cai K, Jin Y (2020) Automatic detection of feather defects using Lie group and fuzzy Fisher criterion for shuttlecock production. Mech Syst Signal Process 141:106690
Ye X, Wang S, Zhang S, Xiao X, Xu F (2020) The compaction effect on the performance of a compaction-grouted soil nail in sand. Acta Geotechnica. https://doi.org/10.1007/s11440-020-01017-4
Zhu J, Shi Q, Wu P, Sheng Z, Wang X (2018) Complexity analysis of prefabrication contractors’ dynamic price competition in mega projects with different competition strategies. Complexity. https://doi.org/10.1155/2018/5928235
Lv X, Li N, Xu X, Yang Y (2020) Understanding the emergence and development of online travel agencies: a dynamic evaluation and simulation approach. Internet Res 30(6):1783–1810
Ran W, Liu S, Zhang Z (2020) A polling-based dynamic order-picking system considering priority orders. Complexity. https://doi.org/10.1155/2020/4595316
Wang L, Huang Y, Xie Y, Du Y (2020) A new regularization method for dynamic load identification. Sci Prog 103(3):0036850420931283
Zuo C, Chen Q, Gu G, Feng S, Feng F, Li R, Shen G (2013) High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection. Opt Lasers Eng 51(8):953–960
Zhu G, Wang S, Sun L, Ge W, Zhang X (2020) Output feedback adaptive dynamic surface sliding-mode control for quadrotor UAVs with tracking error constraints. Complexity. https://doi.org/10.1155/2020/8537198
Zhang Z, Liu M, Zhou M, Chen J (2020) Dynamic reliability analysis of nonlinear structures using a Duffing-system-based equivalent nonlinear system method. Int J Approx Reason 126:84–97
Chen H, Qiao H, Xu L, Feng Q, Cai K (2019) A fuzzy optimization strategy for the implementation of RBF LSSVR model in vis–NIR analysis of pomelo maturity. IEEE Trans Industr Inf 15(11):5971–5979
Al-Furjan M, Habibi M, won Jung D, Sadeghi S, Safarpour H, Tounsi A, Chen G (2020) A computational framework for propagated waves in a sandwich doubly curved nanocomposite panel. Eng Comput. https://doi.org/10.1007/s00366-020-01130-8
Li J, Tang F, Habibi M (2020) Bi-directional thermal buckling and resonance frequency characteristics of a GNP-reinforced composite nanostructure. Eng Comput. https://doi.org/10.1007/s00366-020-01110-y
Al-Furjan M, Mohammadgholiha M, Alarifi IM, Habibi M, Safarpour H (2020) On the phase velocity simulation of the multi curved viscoelastic system via an exact solution framework. Eng Comput. https://doi.org/10.1007/s00366-020-01152-2
Li Y, Li S, Guo K, Fang X, Habibi M (2020) On the modeling of bending responses of graphene-reinforced higher order annular plate via two-dimensional continuum mechanics approach. Eng Comput. https://doi.org/10.1007/s00366-020-01166-w
Bai Y, Alzahrani B, Baharom S, Habibi M (2020) Semi-numerical simulation for vibrational responses of the viscoelastic imperfect annular system with honeycomb core under residual pressure. Eng Comput. https://doi.org/10.1007/s00366-020-01191-9
Al-Furjan M, Fereidouni M, Habibi M, Abd Ali R, Ni J, Safarpour M (2020) Influence of in-plane loading on the vibrations of the fully symmetric mechanical systems via dynamic simulation and generalized differential quadrature framework. Eng Comput. https://doi.org/10.1007/s00366-020-01177-7
Al-Furjan M, Habibi M, Ni J, won Jung D, Tounsi A (2020) Frequency simulation of viscoelastic multi-phase reinforced fully symmetric systems. Eng Comput. https://doi.org/10.1007/s00366-020-01200-x
Li B-H, Liu Y, Zhang A-M, Wang W-H, Wan S (2020) A survey on blocking technology of entity resolution. J Comput Sci Technol 35(4):769–793
Zhu J, Wang X, Wang P, Wu Z, Kim MJ (2019) Integration of BIM and GIS: geometry from IFC to shapefile using open-source technology. Autom Construct 102:105–119
Liu Y, Zhang B, Feng Y, Lv X, Ji D, Niu Z, Yang Y, Zhao X, Fan Y (2020) Development of 340-GHz transceiver front end based on GaAs monolithic integration technology for THz active imaging array. Appl Sci 10(21):7924
Huang Z, Zheng H, Guo L, Mo D (2020) Influence of the position of artificial boundary on computation accuracy of conjugated infinite element for a finite length cylindrical shell. Acoust Aust 48(2):287–294
Al-Furjan M, Habibi M, Safarpour H (2020) Vibration control of a smart shell reinforced by graphene nanoplatelets. Int J Appl Mech 12(06):2050066
Al-Furjan MSH, Moghadam SA, Dehini R, Shan L, Habibi M, Safarpour H (2020) Vibration control of a smart shell reinforced by graphene nanoplatelets under external load: semi-numerical and finite element modeling. Thin-Walled Struct. https://doi.org/10.1016/j.tws.2020.107242
Shi X, Li J, Habibi M (2020) On the statics and dynamics of an electro-thermo-mechanically porous GPLRC nanoshell conveying fluid flow. Mech Based Design Struct Mach. https://doi.org/10.1080/15397734.2020.1772088
Habibi M, Safarpour M, Safarpour H (2020) Vibrational characteristics of a FG-GPLRC viscoelastic thick annular plate using fourth-order Runge-Kutta and GDQ methods. Mech Based Design Struct Mach. https://doi.org/10.1080/15397734.2020.1779086
Ghabussi A, Habibi M, NoormohammadiArani O, Shavalipour A, Moayedi H, Safarpour H (2020) Frequency characteristics of a viscoelastic graphene nanoplatelet–reinforced composite circular microplate. J Vibr Control. https://doi.org/10.1177/1077546320923930
Safarpour M, Ghabussi A, Ebrahimi F, Habibi M, Safarpour H (2020) Frequency characteristics of FG-GPLRC viscoelastic thick annular plate with the aid of GDQM. Thin-Walled Struct 150:106683
Jermsittiparsert K, Ghabussi A, Forooghi A, Shavalipour A, Habibi M, won Jung D, Safa M (2020) Critical voltage, thermal buckling and frequency characteristics of a thermally affected GPL reinforced composite microdisk covered with piezoelectric actuator. Mech Based Design Struct Mach. https://doi.org/10.1080/15397734.2020.1748052
Lori ES, Ebrahimi F, Supeni EEB, Habibi M, Safarpour H (2020) The critical voltage of a GPL-reinforced composite microdisk covered with piezoelectric layer. Eng Comput. https://doi.org/10.1007/s00366-020-01004-z
Al-Furjan M, Dehini R, Khorami M, Habibi M, won Jung D (2020) On the dynamics of the ultra-fast rotating cantilever orthotropic piezoelectric nanodisk based on nonlocal strain gradient theory. Composite Struct. https://doi.org/10.1016/j.compstruct.2020.112990
Wang F, Onsorynezhad S Backward mechanical-electric coupling effect of a frequency-up-conversion piezoelectric energy harvester. In: International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2019. American Society of Mechanical Engineers, p V008T010A036
Shariati A, Ghabussi A, Habibi M, Safarpour H, Safarpour M, Tounsi A, Safa M (2020) Extremely large oscillation and nonlinear frequency of a multi-scale hybrid disk resting on nonlinear elastic foundation. Thin-Walled Struct 154:106840. https://doi.org/10.1016/j.tws.2020.106840
Habibi M, Taghdir A, Safarpour H (2019) Stability analysis of an electrically cylindrical nanoshell reinforced with graphene nanoplatelets. Compos B Eng 175:107125
Onsorynezhad S, Abedini A, Wang F Analytical study of a piezoelectric frequency up-conversion harvester under sawtooth wave excitation. In: Dynamic Systems and Control Conference, 2018. American Society of Mechanical Engineers, p V002T018A004
Saeidi Rashk Olia A, Perić D (2021) Thermo-mechanical soil structure interaction in single energy piles exhibiting reversible interface behavior. Int J Geomech. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002014
Olia ASR, Perić D Cross validation of analytical solutions against the computational model predictions of the response of semi floating energy pile. In: E3S Web of Conferences, 2020. EDP Sciences, p 05020. https://doi.org/10.1051/e3sconf/202020505020
Olia ASR, Perić D Cross validation of analytical solutions against the computational model predictions of the response of end bearing energy pile. In: E3S Web of Conferences, 2020. EDP Sciences, p 05019. https://doi.org/10.1051/e3sconf/202020505019
Gao N, Guo X, Deng J, Cheng B, Hou H (2021) Elastic wave modulation of double-leaf ABH beam embedded mass oscillator. Appl Acoust 173:107694
Gao N, Tang L, Deng J, Lu K, Hou H, Chen K (2021) Design, fabrication and sound absorption test of composite porous metamaterial with embedding I-plates into porous polyurethane sponge. Appl Acoust 175:107845
Gao N, Wu J, Lu K, Zhong H (2021) Hybrid composite meta-porous structure for improving and broadening sound absorption. Mech Syst Signal Process 154:107504
Sun L, Yang Z, Jin Q, Yan W (2020) Effect of axial compression ratio on seismic behavior of GFRP reinforced concrete columns. Int J Struct Stabil Dyn 20(6):2040004
Sun H, Gao C, Zhang Z, Liao X, Wang X, Yang J (2019) High-resolution anisotropic prestack Kirchhoff dynamic focused beam migration. IEEE Sens J 20(20):11753–11760
Abedini M, Mutalib AA, Zhang C, Mehrmashhadi J, Raman SN, Alipour R, Momeni T, Mussa MH (2020) Large deflection behavior effect in reinforced concrete columns exposed to extreme dynamic loads. Front Struct Civ Eng 14(2):532–553
Gholipour G, Zhang C, Mousavi AA (2020) Numerical analysis of axially loaded RC columns subjected to the combination of impact and blast loads. Eng Struct 219:110924
Zhu L, Zhang C, Guan X, Uy B, Sun L, Wang B (2018) The multi-axial strength performance of composited structural BCW members subjected to shear forces. Steel Composite Struct 27(1):75–87
Zhang C, Gholipour G, Mousavi AA (2019) Nonlinear dynamic behavior of simply-supported RC beams subjected to combined impact-blast loading. Eng Struct 181:124–142
Alam Z, Zhang C, Samali B (2020) The role of viscoelastic damping on retrofitting seismic performance of asymmetric reinforced concrete structures. Earthq Eng Eng Vib 19(1):223–237
Sheng D, Zhang S, Yu Z, Zhang J (2013) Assessing frost susceptibility of soils using PCHeave. Cold Reg Sci Technol 95:27–38. https://doi.org/10.1016/j.coldregions.2013.08.003
Zhang S, Leng W, Zhang F, Xiong Y (2012) A simple thermo-elastoplastic model for geomaterials. Int J Plast 34:93–113. https://doi.org/10.1016/j.ijplas.2012.01.011
Zhang S, Teng J, He Z, Liu Y, Liang S, Yao Y, Sheng D (2016) Canopy effect caused by vapour transfer in covered freezing soils. Géotechnique 66(11):927–940. https://doi.org/10.1680/jgeot.16.P.016
Ghabussi A, Asgari Marnani J, Rohanimanesh MS (2021) Seismic performance assessment of a novel ductile steel braced frame equipped with steel curved damper. Structures 31:87–97. https://doi.org/10.1016/j.istruc.2021.01.073
Aalipour F, Das T (2020) Shaping the transient response of nonlinear systems to satisfy a class of integral constraints. arXiv preprint arXiv:2012.12493
Reddy J, Phan N (1985) Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory. J Sound Vib 98(2):157–170
Mahmoudi A, Benyoucef S, Tounsi A, Benachour A, Adda Bedia EA, Mahmoud S (2019) A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations. J Sandwich Struct Mater 21(6):1906–1929
Zhao Y, Moradi Z, Davoudi M et al (2021) Bending and stress responses of the hybrid axisymmetric system via state-space method and 3D-elasticity theory. Eng Comput. https://doi.org/10.1007/s00366-020-01242-1
Wang Q (2002) On buckling of column structures with a pair of piezoelectric layers. Eng Struct 24(2):199–205. https://doi.org/10.1016/S0141-0296(01)00088-8
Ebrahimi F, Barati MR, Civalek Ö (2019) Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures. Eng Comput. https://doi.org/10.1007/s00366-019-00742-z
Shariati A, Mohammad-Sedighi H, Żur KK, Habibi M, Safa M (2020) Stability and dynamics of viscoelastic moving Rayleigh beams with an asymmetrical distribution of material parameters. Symmetry 12(4):586
Matouk H, Bousahla AA, Heireche H, Bourada F, Bedia E, Tounsi A, Mahmoud S, Tounsi A, Benrahou K (2020) Investigation on hygro-thermal vibration of P-FG and symmetric S-FG nanobeam using integral Timoshenko beam theory. Adv Nano Res 8(4):293–305. https://doi.org/10.12989/anr.2020.8.4.293
Bendenia N, Zidour M, Bousahla AA, Bourada F, Tounsi A, Benrahou KH, Bedia E, Mahmoud S, Tounsi A (2020) Deflections, stresses and free vibration studies of FG-CNT reinforced sandwich plates resting on Pasternak elastic foundation. Comput Concrete 26(3):213–226
Karami B, Janghorban M, Tounsi A (2019) Galerkin’s approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions. Eng Comput 35(4):1297–1316. https://doi.org/10.1007/s00366-018-0664-9
Shi K, Tang Y, Liu X, Zhong S (2017) Secondary delay-partition approach on robust performance analysis for uncertain time-varying Lurie nonlinear control system. Optim Control Appl Methods 38(6):1208–1226
Zhang X, Wang Y, Chen X, Su C-Y, Li Z, Wang C, Peng Y (2018) Decentralized adaptive neural approximated inverse control for a class of large-scale nonlinear hysteretic systems with time delays. IEEE Trans Syst Man Cybernet 49(12):2424–2437
Long Q, Wu C, Wang X (2015) A system of nonsmooth equations solver based upon subgradient method. Appl Math Comput 251:284–299
Ren J, Zhang C, Hao Q (2020) A theoretical method to evaluate honeynet potency. Future Gener Comput Syst 116:76–85
Zhang J, Liu B (2019) A review on the recent developments of sequence-based protein feature extraction methods. Curr Bioinform 14(3):190–199
Zenggang X, Zhiwen T, Xiaowen C, Xue-min Z, Kaibin Z, Conghuan Y (2019) Research on image retrieval algorithm based on combination of color and shape features. J Signal Process Syst. https://doi.org/10.1007/s11265-019-01508-y
Liu J, Wu C, Wu G, Wang X (2015) A novel differential search algorithm and applications for structure design. Appl Math Comput 268:246–269
Rahimi R, Tavakol-Davani H, Graves C, Gomez A, Valipour MF (2020) Compound inundation impacts of coastal climate change: sea-level rise, groundwater rise, and coastal precipitation. Water 12(10):2776
Tavakol-Davani H, Rahimi R, Burian S, Pomeroy C, McPherson B, Apul D (2019) Combining hydrologic analysis and life cycle assessment approaches to evaluate sustainability of water infrastructure: uncertainty analysis. Water 11(12):2592
Ahmadi A, Kerachian R, Rahimi R, Skardi MJE (2019) Comparing and combining Social Network Analysis and Stakeholder Analysis for natural resource governance. Environ Dev 32:100451
Liu E, Guo B, Lv L, Qiao W, Azimi M (2020) Numerical simulation and simplified calculation method for heat exchange performance of dry air cooler in natural gas pipeline compressor station. Energy Sci Eng 8(6):2256–2270
Liu E, Wang X, Zhao W, Su Z, Chen Q (2021) Analysis and research on pipeline vibration of a natural gas compressor station and vibration reduction measures. Energy Fules 35(1):479–492
Peng S, Chen Q, Zheng C, Liu E (2020) Analysis of particle deposition in a new-type rectifying plate system during shale gas extraction. Energy Sci Eng 8(3):702–717
Peng S, Zhang Z, Liu E, Liu W, Qiao W (2021) A new hybrid algorithm model for prediction of internal corrosion rate of multiphase pipeline. J Nat Gas Sci Eng 85:103716
Liew K, Yang J, Kitipornchai S (2003) Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading. Int J Solids Struct 40(15):3869–3892
Khdeir A (1988) Free vibration and buckling of symmetric cross-ply laminated plates by an exact method. J Sound Vib 126(3):447–461. https://doi.org/10.1016/0022-460X(88)90223-4
Thinh TI, Nguyen MC, Ninh DG (2014) Dynamic stiffness formulation for vibration analysis of thick composite plates resting on non-homogenous foundations. Compos Struct 108:684–695. https://doi.org/10.1016/j.compstruct.2013.10.022
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This work was supported by the Research team project of Nanning University (2018KYTD03), the Science and Technology Planning Project of Yongning Zone of Nanning (20180205A).
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Huang, X., Zhu, Y., Vafaei, P. et al. An iterative simulation algorithm for large oscillation of the applicable 2D-electrical system on a complex nonlinear substrate. Engineering with Computers 38, 3137–3149 (2022). https://doi.org/10.1007/s00366-021-01320-y
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DOI: https://doi.org/10.1007/s00366-021-01320-y