Abstract
This is the first research on the nonlinear frequency analysis of a multi-scale hybrid nanocomposite (MHC) disk (MHCD) resting on an elastic foundation subjected to nonlinear temperature gradient and mechanical loading is investigated. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macroscale, respectively. We present a modified Halpin–Tsai model to predict the effective properties of the MHCD. The displacement–strain of nonlinear vibration of multi-scale laminated disk via third-order shear deformation theory (TSDT) and using Von Karman nonlinear shell theory is obtained. Hamilton’s principle is employed to establish the governing equations of motion, which is finally solved by generalized differential quadrature method (GDQM) and perturbation method (PM). Finally, the results show that FG patterns, different orientation angle of the fiber, the VF and WCNT parameters, axial load, nonlinear temperature gradient, and applied temperature of the top surface play an essential impact on the linear and nonlinear dynamic responses of the MHCD. The more significant outcome of this research is that the effects of the VF, WCNT, \(\theta\), and β parameters on the nonlinear frequency of the MHCD can be considered at the higher value of the large deflection parameter and the effect of negative axial load on the dynamic responses of the structure is more intensive. As an applicable result show that the best functionally graded (FG) pattern for serving the highest nonlinear dynamic response of an MHC reinforced annular plate is FG-A.
Similar content being viewed by others
References
Alipour M, Torabi MA, Sareban M, Lashini H, Sadeghi E, Fazaeli A et al (2019) Finite element and experimental method for analyzing the effects of martensite morphologies on the formability of DP steels. Mech Based Des Struct Mach. https://doi.org/10.1080/15397734.2019.1633343
Hosseini S, Habibi M, Assempour A (2018) Experimental and numerical determination of forming limit diagram of steel-copper two-layer sheet considering the interface between the layers. Modares Mech Eng 18:174–181
Habibi M, Hashemi R, Ghazanfari A, Naghdabadi R, Assempour A (2018) Forming limit diagrams by including the M–K model in finite element simulation considering the effect of bending. Proc Inst Mech Eng Part L 232:625–636
Moayedi H, Darabi R, Ghabussi A, Habibi M, Foong LK (2020) Weld orientation effects on the formability of tailor welded thin steel sheets. Thin Walled Struct 149:106669. https://doi.org/10.1016/j.tws.2020.106669
Habibi M, Hashemi R, Tafti MF, Assempour A (2018) Experimental investigation of mechanical properties, formability and forming limit diagrams for tailor-welded blanks produced by friction stir welding. J Manuf Process 31:310–323
Habibi M, Ghazanfari A, Assempour A, Naghdabadi R, Hashemi R (2017) Determination of forming limit diagram using two modified finite element models. Mech Eng 48(4):141–144
Ghazanfari A, Assempuor A, Habibi M, Hashemi R (2016) Investigation on the effective range of the through thickness shear stress on forming limit diagram using a modified Marciniak-Kuczynski model. Modares Mech Eng 16:137–143
Habibi M, Hashemi R, Sadeghi E, Fazaeli A, Ghazanfari A, Lashini H (2016) Enhancing the mechanical properties and formability of low carbon steel with dual-phase microstructures. J Mater Eng Perform 25:382–389
Fazaeli A, Habibi M, Ekrami A (2016) Experimental and finite element comparison of mechanical properties and formability of dual phase steel and ferrite-pearlite steel with the same chemical composition. Metallurgical Eng 19(2):84–93 ed, 2016
Ghazanfari A, Soleimani SS, Keshavarzzadeh M, Habibi M, Assempuor A, Hashemi R (2019) Prediction of FLD for sheet metal by considering through-thickness shear stresses. Mech Based Des Struct Mach. https://doi.org/10.1080/15397734.2019.1662310
Ghabussi A, Ashrafi N, Shavalipour A, Hosseinpour A, Habibi M, Moayedi H et al (2019) Free vibration analysis of an electro-elastic GPLRC cylindrical shell surrounded by viscoelastic foundation using modified length-couple stress parameter. Mech Based Des Struct Mach. https://doi.org/10.1080/15397734.2019.1705166
Habibi M, Mohammadi A, Safarpour H, Ghadiri M (2019) Effect of porosity on buckling and vibrational characteristics of the imperfect GPLRC composite nanoshell. Mech Based Des Struct Mach. https://doi.org/10.1080/15397734.2019.1701490
Habibi M, Mohammadi A, Safarpour H, Shavalipour A, Ghadiri M (2019) Wave propagation analysis of the laminated cylindrical nanoshell coupled with a piezoelectric actuator. Mech Based Des Struct Mach. https://doi.org/10.1080/15397734.2019.1697932
Ebrahimi F, Mohammadi K, Barouti MM, Habibi M (2019) Wave propagation analysis of a spinning porous graphene nanoplatelet-reinforced nanoshell. Waves Random Complex Media. https://doi.org/10.1080/17455030.2019.1694729
Shokrgozar A, Safarpour H, Habibi M (2019) Influence of system parameters on buckling and frequency analysis of a spinning cantilever cylindrical 3D shell coupled with piezoelectric actuator. Proc the Inst Mech Eng Part C. https://doi.org/10.1177/0954406219883312
Habibi M, Hashemabadi D, Safarpour H (2019) Vibration analysis of a high-speed rotating GPLRC nanostructure coupled with a piezoelectric actuator. Euro Phys J Plus 134:307
Mohammadgholiha M, Shokrgozar A, Habibi M, Safarpour H (2019) Buckling and frequency analysis of the nonlocal strain–stress gradient shell reinforced with graphene nanoplatelets. J Vib Control 25:2627–2640
Ebrahimi F, Habibi M, Safarpour H (2019) On modeling of wave propagation in a thermally affected GNP-reinforced imperfect nanocomposite shell. Eng Comput 35:1375–1389
Safarpour H, Hajilak ZE, Habibi M (2019) A size-dependent exact theory for thermal buckling, free and forced vibration analysis of temperature dependent FG multilayer GPLRC composite nanostructures restring on elastic foundation. Int J Mech Mater Des 15:569–583
Hashemi HR, Alizadeh AA, Oyarhossein MA, Shavalipour A, Makkiabadi M, Habibi M (2019) Influence of imperfection on amplitude and resonance frequency of a reinforcement compositionally graded nanostructure. Waves Random Complex Media. https://doi.org/10.1080/17455030.2019.1662968
Ebrahimi F, Hashemabadi D, Habibi M, Safarpour H (2019) Thermal buckling and forced vibration characteristics of a porous GNP reinforced nanocomposite cylindrical shell. Microsyst Technol. https://doi.org/10.1007/s00542-019-04542-9
Mohammadi A, Lashini H, Habibi M, Safarpour H (2019) Influence of viscoelastic foundation on dynamic behaviour of the double walled cylindrical inhomogeneous micro shell using MCST and with the aid of GDQM. J Solid Mech 11:440–453
Pourjabari A, Hajilak ZE, Mohammadi A, Habibi M, Safarpour H (2019) Effect of porosity on free and forced vibration characteristics of the GPL reinforcement composite nanostructures. Comput Math Appl 77:2608–2626
Habibi M, Mohammadgholiha M, Safarpour H (2019) Wave propagation characteristics of the electrically GNP-reinforced nanocomposite cylindrical shell. J Braz Soc Mech Sci Eng 41:221
Safarpour H, Pourghader J, Habibi M (2019) Influence of spring-mass systems on frequency behavior and critical voltage of a high-speed rotating cantilever cylindrical three-dimensional shell coupled with piezoelectric actuator. J Vib Control 25:1543–1557
Ebrahimi F, Hajilak ZE, Habibi M, Safarpour H (2019) Buckling and vibration characteristics of a carbon nanotube-reinforced spinning cantilever cylindrical 3D shell conveying viscous fluid flow and carrying spring-mass systems under various temperature distributions. Proc Inst Mech Eng Part C. https://doi.org/10.1177/0954406219832323
Esmailpoor Hajilak Z, Pourghader J, Hashemabadi D, Sharifi Bagh F, Habibi M, Safarpour H (2019) Multilayer GPLRC composite cylindrical nanoshell using modified strain gradient theory. Mech Based Des Struct Mach. https://doi.org/10.1080/15397734.2019.1566743
Safarpour H, Ghanizadeh SA, Habibi M (2018) Wave propagation characteristics of a cylindrical laminated composite nanoshell in thermal environment based on the nonlocal strain gradient theory. Euro Phys J Plus 133:532
Sun J, Zhao J (2018) Multi-layer graphene reinforced nano-laminated WC-Co composites. Mater Sci Eng A 723:1–7
Gao W, Dimitrov D, Abdo H (2018) Tight independent set neighborhood union condition for fractional critical deleted graphs and ID deleted graphs. Discrete Cont Dyn Syst-S 12:711–721
Gao W, Guirao JLG, Basavanagoud B, Wu J (2018) Partial multi-dividing ontology learning algorithm. Inf Sci 467:35–58
Gao W, Wang W, Dimitrov D, Wang Y (2018) Nano properties analysis via fourth multiplicative ABC indicator calculating. Arab J Chem 11:793–801
Gao W, Wu H, Siddiqui MK, Baig AQ (2018) Study of biological networks using graph theory. Saudi J Biol Sci 25:1212–1219
Gao W, Guirao JLG, Abdel-Aty M, Xi W (2019) An independent set degree condition for fractional critical deleted graphs. Discrete Cont Dyn Syst-S 12:877–886
Qiao W, Yang Z, Kang Z, Pan Z (2020) Short-term natural gas consumption prediction based on Volterra adaptive filter and improved whale optimization algorithm. Eng Appl Artif Intell 87:103323
Qiao W, Yang Z (2019) Forecast the electricity price of US using a wavelet transform-based hybrid model. Energy. https://doi.org/10.1016/j.energy.2019.116704
Qiao W, Yang Z (2019) Solving large-scale function optimization problem by using a new metaheuristic algorithm based on quantum dolphin swarm algorithm. IEEE Access 7:138972–138989
Qiao W, Tian W, Tian Y, Yang Q, Wang Y, Zhang J (2019) The forecasting of PM2. 5 using a hybrid model based on wavelet transform and an improved deep learning algorithm. IEEE Access 7:142814–142825
Qiao W, Yang Z (2019) Modified dolphin swarm algorithm based on chaotic maps for solving high-dimensional function optimization problems. IEEE Access 7:110472–110486
Qiao W, Huang K, Azimi M, Han S (2019) A novel hybrid prediction model for hourly gas consumption in supply side based on improved machine learning algorithms. IEEE Access. https://doi.org/10.1109/ACCESS.2019.2918156
Ebrahimi-Mamaghani A, Mirtalebi SH, Ahmadian M-T (2019) Magneto-mechanical stability of axially functionally graded supported nanotubes. Materials Res Express. https://doi.org/10.1088/2053-1591/ab4d77
Esfahani S, Khadem SE, Mamaghani AE (2019) Nonlinear vibration analysis of an electrostatic functionally graded nano-resonator with surface effects based on nonlocal strain gradient theory. Int J Mech Sci 151:508–522
Habibi M, Mohammadgholiha M, Safarpour H (2019) Correction to: Wave propagation characteristics of the electrically GNP-reinforced nanocomposite cylindrical shell. J Braz Soc Mech Sci Eng 41:250
Shokrgozar A, Ghabussi A, Ebrahimi F, Habibi M, Safarpour H (2020) Viscoelastic dynamics and static responses of a graphene nanoplatelets-reinforced composite cylindrical microshell. Mech Based Des Struct Mach 4:1–28. https://doi.org/10.1080/15397734.2020.1719509
Pourjabari A, Hajilak ZE, Mohammadi A, Habibi M, Safarpour H (2019) Effect of porosity on free and forced vibration characteristics of the GPL reinforcement composite nanostructures. Comput Math Appl. https://doi.org/10.1016/j.camwa.2018.12.041
Ebrahimi F, Habibi M, Safarpour H (2018) On modeling of wave propagation in a thermally affected GNP-reinforced imperfect nanocomposite shell. Eng Comput pp 1–15.
Hussain M, Naeem MN, Tounsi A, Taj M (2019) Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity. Adv Nano Res 7:431
Bedia WA, Houari MSA, Bessaim A, Bousahla AA, Tounsi A, Saeed T et al (2019) A new hyperbolic two-unknown beam model for bending and buckling analysis of a nonlocal strain gradient nanobeams. J Nano Res. https://doi.org/10.4028/www.scientific.net/JNanoR.57.175
Karami B, Janghorban M, Tounsi A (2019) On pre-stressed functionally graded anisotropic nanoshell in magnetic field. J Braz Soc Mech Sci Eng 41:495
Karami B, Janghorban M, Tounsi A (2019) Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation. Struct Eng Mech 70:55–66
Karami B, Shahsavari D, Janghorban M, Tounsi A (2019) Resonance behavior of functionally graded polymer composite nanoplates reinforced with graphene nanoplatelets. Int J Mech Sci 156:94–105
Chakrapani SK, Barnard DJ, Dayal V (2016) Nonlinear forced vibration of carbon fiber/epoxy prepreg composite beams: theory and experiment. Compos B Eng 91:513–521
Emam S, Eltaher M (2016) Buckling and postbuckling of composite beams in hygrothermal environments. Compos Struct 152:665–675
Maghamikia S, Jam J (2011) Buckling analysis of circular and annular composite plates reinforced with carbon nanotubes using FEM. J Mech Sci Technol 25:2805–2810
Tahouneh V, Yas M (2014) Influence of equivalent continuum model based on the Eshelby–Mori–Tanaka scheme on the vibrational response of elastically supported thick continuously graded carbon nanotube-reinforced annular plates. Polym Compos 35:1644–1661
Tahouneh V, Eskandari-Jam J (2014) A semi-analytical solution for 3-D dynamic analysis of thick continuously graded carbon nanotube-reinforced annular plates resting on a Two-parameter elastic foundation. Mech Adv Composite Struct 1:113–130
Ansari R, Torabi J, Shojaei MF (2017) Buckling and vibration analysis of embedded functionally graded carbon nanotube-reinforced composite annular sector plates under thermal loading. Compos B Eng 109:197–213
Draiche K, Bousahla AA, Tounsi A, Alwabli AS, Tounsi A, Mahmoud S (2019) Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory. Comput Concrete 24:369–378
Alimirzaei S, Mohammadimehr M, Tounsi A (2019) Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions. Struct Eng Mech 71:485–502
Draoui A, Zidour M, Tounsi A, Adim B (2019) Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT). J Nano Res. https://doi.org/10.4028/www.scientific.net/JNanoR.57.117
Meksi R, Benyoucef S, Mahmoudi A, Tounsi A, Adda Bedia EA, Mahmoud S (2019) An analytical solution for bending, buckling and vibration responses of FGM sandwich plates. J Sandw Struct Materials 21:727–757
Tlidji Y, Zidour M, Draiche K, Safa A, Bourada M, Tounsi A et al (2019) Vibration analysis of different material distributions of functionally graded microbeam. Struct Eng Mech 69:637–649
Medani M, Benahmed A, Zidour M, Heireche H, Tounsi A, Bousahla AA et al (2019) Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate using energy principle. Steel Composite Struct 32:595–610
Berghouti H, Adda Bedia E, Benkhedda A, Tounsi A (2019) Vibration analysis of nonlocal porous nanobeams made of functionally graded material. Adv Nano Res 7:351–364
Karami B, Janghorban M, Tounsi A (2019) Galerkin’s approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions. Eng Comput 35:1297–1316
Bourada F, Bousahla AA, Bourada M, Azzaz A, Zinata A, Tounsi A (2019) Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory. Wind Struct 28:19–30
Abualnour M, Chikh A, Hebali H, Kaci A, Tounsi A, Bousahla AA et al (2019) Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory. Comput Concrete 24:489–498
Khiloun M, Bousahla AA, Kaci A, Bessaim A, Tounsi A, Mahmoud S (2019) Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT. Eng Comput 1–15.
Boutaleb S, Benrahou KH, Bakora A, Algarni A, Bousahla AA, Tounsi A et al (2019) Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT. Adv Nano Res 7:191
Zarga D, Tounsi A, Bousahla AA, Bourada F, Mahmoud S (2019) Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory. Steel Composite Struct 32:389–410
Addou FY, Meradjah M, Bousahla AA, Benachour A, Bourada F, Tounsi A et al (2019) Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT. Comput Concrete 24:347–367
Boulefrakh L, Hebali H, Chikh A, Bousahla AA, Tounsi A, Mahmoud S (2019) The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate. Geomech Eng 18:161–178
Safarpour H, Barooti M, Ghadiri M (2019) Influence of Rotation on Vibration Behavior of a Functionally Graded Moderately Thick Cylindrical Nanoshell Considering Initial Hoop Tension. J Solid Mech 11:254–271
Ebrahimi F, Safarpour H (2018) Vibration analysis of inhomogeneous nonlocal beams via a modified couple stress theory incorporating surface effects. Wind Struct 27:431–438
Mohammadi K, Barouti MM, Safarpour H, Ghadiri M (2019) Effect of distributed axial loading on dynamic stability and buckling analysis of a viscoelastic DWCNT conveying viscous fluid flow. J Braz Soc Mech Sci Eng 41:93
SafarPour H, Hosseini M, Ghadiri M (2017) Influence of three-parameter viscoelastic medium on vibration behavior of a cylindrical nonhomogeneous microshell in thermal environment: an exact solution. J Therm Stresses 40:1353–1367
Safarpour H, Mohammadi K, Ghadiri M, Barooti MM (2018) Effect of porosity on flexural vibration of CNT-reinforced cylindrical shells in thermal environment using GDQM. Int J Struct Stab Dyn 18:1850123
Safarpour H, Mohammadi K, Ghadiri M (2017) Temperature-dependent vibration analysis of a FG viscoelastic cylindrical microshell under various thermal distribution via modified length scale parameter: a numerical solution. J Mech Behav Materials 26:9–24
SafarPour H, Ghanbari B, Ghadiri M (2019) Buckling and free vibration analysis of high speed rotating carbon nanotube reinforced cylindrical piezoelectric shell. Appl Math Model 65:428–442
Shojaeefard M, Mahinzare M, Safarpour H, Googarchin HS, Ghadiri M (2018) Free vibration of an ultra-fast-rotating-induced cylindrical nano-shell resting on a Winkler foundation under thermo-electro-magneto-elastic condition. Appl Math Model 61:255–279
Ghadiri M, Safarpour H (2016) Free vibration analysis of embedded magneto-electro-thermo-elastic cylindrical nanoshell based on the modified couple stress theory. Appl Phys A 122:833
Ghadiri M, SafarPour H (2017) Free vibration analysis of size-dependent functionally graded porous cylindrical microshells in thermal environment. J Therm Stresses 40:55–71
Ghadiri M, Shafiei N, Safarpour H (2017) Influence of surface effects on vibration behavior of a rotary functionally graded nanobeam based on Eringen’s nonlocal elasticity. Microsyst Technol 23:1045–1065
SafarPour H, Ghadiri M (2017) Critical rotational speed, critical velocity of fluid flow and free vibration analysis of a spinning SWCNT conveying viscous fluid. Microfluid Nanofluid 21:22
Barooti MM, Safarpour H, Ghadiri M (2017) Critical speed and free vibration analysis of spinning 3D single-walled carbon nanotubes resting on elastic foundations. Euro Phys J Plus 132:6
Safarpour M, Rahimi A, Alibeigloo A, Bisheh H, Forooghi A (2019) Parametric study of three-dimensional bending and frequency of FG-GPLRC porous circular and annular plates on different boundary conditions. Mech Based Des Struct Mach. https://doi.org/10.1080/15397734.2019.1701491
Bisheh H, Alibeigloo A, Safarpour M, Rahimi A (2019) Three-dimensional static and free vibrational analysis of graphene reinforced composite circular/annular plate using differential quadrature method. Int J Appl Mech 11:1950073
Safarpour M, Rahimi A, Alibeigloo A (2019) Static and free vibration analysis of graphene platelets reinforced composite truncated conical shell, cylindrical shell, and annular plate using theory of elasticity and DQM. Mech Based Des Struct Mach. https://doi.org/10.1080/15397734.2019.1646137
Zhong R, Wang Q, Tang J, Shuai C, Qin B (2018) Vibration analysis of functionally graded carbon nanotube reinforced composites (FG-CNTRC) circular, annular and sector plates. Compos Struct 194:49–67
Yang Y, Wang Z, Wang Y (2018) Thermoelastic coupling vibration and stability analysis of rotating circular plate in friction clutch. J Low Frequency Noise Vib Active Control. https://doi.org/10.1177/1461348418817465
Shojaeefard M, Googarchin HS, Mahinzare M, Ghadiri M (2018) Free vibration and critical angular velocity of a rotating variable thickness two-directional FG circular microplate. Microsyst Technol 24:1525–1543
Wang Z-W, Han Q-F, Nash DH, Liu P-Q (2017) Investigation on inconsistency of theoretical solution of thermal buckling critical temperature rise for cylindrical shell. Thin Walled Struct 119:438–446
Chaabane LA, Bourada F, Sekkal M, Zerouati S, Zaoui FZ, Tounsi A et al (2019) Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation. Struct Eng Mech 71:185–196
Boukhlif Z, Bouremana M, Bourada F, Bousahla AA, Bourada M, Tounsi A et al (2019) A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation. Steel Composite Struct 31:503–516
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 Sandw Struct Materials 21:1906–1929
Semmah A, Heireche H, Bousahla AA, Tounsi A (2019) Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT. Adv Nano Res 7:89
Zaoui FZ, Ouinas D, Tounsi A (2019) New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations. Compos B Eng 159:231–247
Belbachir N, Draich K, Bousahla AA, Bourada M, Tounsi A, Mohammadimehr M (2019) Bending analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings. Steel Composite Struct 33:81–92
Hellal H, Bourada M, Hebali H, Bourada F, Tounsi A, Bousahla AA et al (2019) Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory. J Sandw Struct Materials. https://doi.org/10.1177/1099636219845841
She G-L, Jiang X, Karami B (2019) On thermal snap-buckling of FG curved nanobeams. Materials Res Express 6:115008
Shafiei N, She G-L (2018) On vibration of functionally graded nano-tubes in the thermal environment. Int J Eng Sci 133:84–98
Keleshteri M, Asadi H, Aghdam M (2019) Nonlinear bending analysis of FG-CNTRC annular plates with variable thickness on elastic foundation. Thin-Walled Struct 135:453–462
Ansari R, Torabi J (2019) Nonlinear free and forced vibration analysis of FG-CNTRC annular sector plates. Polym Compos 40:E1364–E1377
Karimiasl M, Ebrahimi F, Akgöz B (2019) Buckling and post-buckling responses of smart doubly curved composite shallow shells embedded in SMA fiber under hygro-thermal loading. Compos Struct 223:110988
Rafiee M, Yang J, Kitipornchai S (2013) Large amplitude vibration of carbon nanotube reinforced functionally graded composite beams with piezoelectric layers. Compos Struct 96:716–725
Ebrahimi F, Habibi S (2018) Nonlinear eccentric low-velocity impact response of a polymer-carbon nanotube-fiber multiscale nanocomposite plate resting on elastic foundations in hygrothermal environments. Mech Adv Mater Struct 25:425–438
Ebrahimi F, Dabbagh A (2019) On thermo-mechanical vibration analysis of multi-scale hybrid composite beams. J Vib Control 25:933–945
Shahgholian-Ghahfarokhi D, Safarpour M, Rahimi A (2019) Torsional buckling analyses of functionally graded porous nanocomposite cylindrical shells reinforced with graphene platelets (GPLs). Mech Based Des Struct Mach. https://doi.org/10.1080/15397734.2019.1666723
Guo H, Zhuang X, Rabczuk T (2019) A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate. CMC-Comput Materials Cont 59:433–456
Bellman R, Casti J (1971) Differential quadrature and long-term integration. J Math Anal Appl 34:235–238
Bellman R, Kashef B, Casti J (1972) Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. J Comput Phys 10:40–52
Gharamohammadi A, Darestani MR, Taghavirashidizadeh A, Abbasi A, Shokouhmand A (2012) Electromagnetic sensor to detect objects by classification and neural networks. Sens Lett 17(9):710–715. https://doi.org/10.1166/sl.2019.4134
Shu C, Richards BE (1992) Application of generalized differential quadrature to solve two-dimensional incompressible Navier–Stokes equations. Int J Numer Meth Fluids 15:791–798
He J-H (1999) Homotopy perturbation technique. Comput Methods Appl Mech Eng 178:257–262
Han J-B, Liew K (1999) Axisymmetric free vibration of thick annular plates. Int J Mech Sci 41:1089–1109
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Safarpour, M., Ebrahimi, F., Habibi, M. et al. On the nonlinear dynamics of a multi-scale hybrid nanocomposite disk. Engineering with Computers 37, 2369–2388 (2021). https://doi.org/10.1007/s00366-020-00949-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00366-020-00949-5