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Erschienen in: Engineering with Computers 2/2021

03.10.2019 | Original Article

Chaotic dynamics and forced harmonic vibration analysis of magneto-electro-viscoelastic multiscale composite nanobeam

verfasst von: Farzad Ebrahimi, Mahsa karimiasl, Vinyas Mahesh

Erschienen in: Engineering with Computers | Ausgabe 2/2021

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Abstract

In this article, the damping forced harmonic vibration characteristics of magneto-electro-viscoelastic (MEV) nanobeam embedded in viscoelastic foundation is evaluated based on nonlocal strain gradient elasticity theory. The viscoelastic foundation consists of Winkler–Pasternak layer. The governing equations of nonlocal strain gradient viscoelastic nanobeam in the framework of refined shear deformable beam theory are obtained using Hamilton’s principle and solved implementing an analytical solution. In addition, a parametric study is presented to examine the effect of the nonlocal strain gradient parameter, magneto-electro-mechanical loadings, and aspect ratio on the vibration characteristics of nanobeam. From the numerical evaluation, it is revealed that the effect of electric and magnetic loading on the natural frequency has a predominant influence.

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Literatur
1.
Zurück zum Zitat van den Boomgard J, Terrell DR, Born RAJ et al (1974) An in situ grown eutectic magnetoelectric composite material. J Mater Sci 9:1705–1709 van den Boomgard J, Terrell DR, Born RAJ et al (1974) An in situ grown eutectic magnetoelectric composite material. J Mater Sci 9:1705–1709
2.
Zurück zum Zitat Zheng H, Wang J, Lofland SE et al (2004) Multiferroic BaTiO3–CoFe2O4 nanostructures. Science 303:661–663 Zheng H, Wang J, Lofland SE et al (2004) Multiferroic BaTiO3–CoFe2O4 nanostructures. Science 303:661–663
3.
Zurück zum Zitat Martin LW, Crane SP, Chu YH et al (2008) Multiferroics and magnetoelectrics: thin films and nanostructures. J Phys Condens Matter 20:434220 Martin LW, Crane SP, Chu YH et al (2008) Multiferroics and magnetoelectrics: thin films and nanostructures. J Phys Condens Matter 20:434220
4.
Zurück zum Zitat Wang Y, Hu JM, Lin YH et al (2010) Multiferroic magnetoelectric composite nanostructures. NPG Asia Mater 2:61–68 Wang Y, Hu JM, Lin YH et al (2010) Multiferroic magnetoelectric composite nanostructures. NPG Asia Mater 2:61–68
5.
Zurück zum Zitat Prashanthi K, Shaibani PM, Sohrabi A et al (2012) Nanoscale magnetoelectric coupling in multiferroic BiFeO3 nanowires. Phys Status Solid R 6:244–246 Prashanthi K, Shaibani PM, Sohrabi A et al (2012) Nanoscale magnetoelectric coupling in multiferroic BiFeO3 nanowires. Phys Status Solid R 6:244–246
6.
Zurück zum Zitat Eringen A (1968) Mechanics of micromorphic continua. In: Kroner E (ed) Mechanics of Generalized Continua. Springer, Berlin, pp 18–35 Eringen A (1968) Mechanics of micromorphic continua. In: Kroner E (ed) Mechanics of Generalized Continua. Springer, Berlin, pp 18–35
8.
Zurück zum Zitat Eringen A (1976) Nonlocal micropolar field theory. In: Eringen AC (ed) Continuum Physics. Academic Press, New York, p 106 Eringen A (1976) Nonlocal micropolar field theory. In: Eringen AC (ed) Continuum Physics. Academic Press, New York, p 106
9.
Zurück zum Zitat Eringen A (2002) Nonlocal continuum field theories. Springer, New York, p 105MATH Eringen A (2002) Nonlocal continuum field theories. Springer, New York, p 105MATH
10.
Zurück zum Zitat Eringen A (2006) Nonlocal continuum mechanics based on distributions. Int J Eng Sci 44(3):141–147MathSciNetMATH Eringen A (2006) Nonlocal continuum mechanics based on distributions. Int J Eng Sci 44(3):141–147MathSciNetMATH
11.
Zurück zum Zitat Eringen AC (1983) On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys 54(9):4703–4710 Eringen AC (1983) On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys 54(9):4703–4710
12.
Zurück zum Zitat Li L, Hu Y, Ling L (2015) Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory. Compos Struct 133:1079–1092 Li L, Hu Y, Ling L (2015) Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory. Compos Struct 133:1079–1092
13.
Zurück zum Zitat Lam DCC, Yang F, Chong ACM, Wang J, Tong P (2003) Experiments and theory in strain gradient elasticity. J Mech Phys Solids 51(8):1477–1508MATH Lam DCC, Yang F, Chong ACM, Wang J, Tong P (2003) Experiments and theory in strain gradient elasticity. J Mech Phys Solids 51(8):1477–1508MATH
14.
Zurück zum Zitat She GL, Ren YR, Yan KM (2019) On snap-buckling of porous FG curved nanobeams. Acta Astronaut 161:475–484 She GL, Ren YR, Yan KM (2019) On snap-buckling of porous FG curved nanobeams. Acta Astronaut 161:475–484
15.
Zurück zum Zitat She GL, Yan KM, Zhang YL, Liu HB, Ren YR (2018) Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory. Euro Phys J Plus 133(9):368 She GL, Yan KM, Zhang YL, Liu HB, Ren YR (2018) Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory. Euro Phys J Plus 133(9):368
16.
Zurück zum Zitat Shafiei N, She GL (2018) On vibration of functionally graded nano-tubes in the thermal environment. Int J Eng Sci 133:84–98MathSciNetMATH Shafiei N, She GL (2018) On vibration of functionally graded nano-tubes in the thermal environment. Int J Eng Sci 133:84–98MathSciNetMATH
17.
Zurück zum Zitat Peddieson J, Buchanan GR, McNitt RP (2003) Application of nonlocal continuum models to nanotechnology. Int J Eng Sci 41(3–5):305–312 Peddieson J, Buchanan GR, McNitt RP (2003) Application of nonlocal continuum models to nanotechnology. Int J Eng Sci 41(3–5):305–312
18.
Zurück zum Zitat Zenkour AM, Sobhy M (2013) Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium. Phys E Low Dimens Syst Nanostruct 53:251–259 (Science 41:305–312) Zenkour AM, Sobhy M (2013) Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium. Phys E Low Dimens Syst Nanostruct 53:251–259 (Science 41:305–312)
19.
Zurück zum Zitat Wang Q (2005) Wave propagation in carbon nanotubes via nonlocal continuum mechanics. J Appl Phys 98:124301 Wang Q (2005) Wave propagation in carbon nanotubes via nonlocal continuum mechanics. J Appl Phys 98:124301
20.
Zurück zum Zitat Wang CM, Kitipornchai S, Lim CW, Eisenberger M (2008) Beam bending solutions based on nonlocal Timoshenko beam theory. J Eng Mech 134:475–481 Wang CM, Kitipornchai S, Lim CW, Eisenberger M (2008) Beam bending solutions based on nonlocal Timoshenko beam theory. J Eng Mech 134:475–481
21.
Zurück zum Zitat Civalek O, Demir C (2011) Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory. Appl Math Model 35:2053–2067MathSciNetMATH Civalek O, Demir C (2011) Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory. Appl Math Model 35:2053–2067MathSciNetMATH
22.
Zurück zum Zitat Murmu T, Pradhan SC (2009) Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM. Physica E 41(7):1232–1239 Murmu T, Pradhan SC (2009) Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM. Physica E 41(7):1232–1239
23.
Zurück zum Zitat Yang J, Ke LL, Kitipornchai S (2010) Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory. Physica E 42(5):1727–1735 Yang J, Ke LL, Kitipornchai S (2010) Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory. Physica E 42(5):1727–1735
24.
Zurück zum Zitat Roque CMC, Ferreira AJM, Reddy JN (2011) Analysis of Timoshenko nanobeams with a nonlocal formulation and meshless method. Int J Eng Sci 49(9):976–984MATH Roque CMC, Ferreira AJM, Reddy JN (2011) Analysis of Timoshenko nanobeams with a nonlocal formulation and meshless method. Int J Eng Sci 49(9):976–984MATH
25.
Zurück zum Zitat Şimşek M, Yurtcu HH (2013) Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory. Compos Struct 97:378–386 Şimşek M, Yurtcu HH (2013) Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory. Compos Struct 97:378–386
26.
Zurück zum Zitat Arefi M, Zenkour AM (2016) A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magneto-thermo-electric environment. J Sandwich Struct Mater 18(5):624–651 Arefi M, Zenkour AM (2016) A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magneto-thermo-electric environment. J Sandwich Struct Mater 18(5):624–651
28.
Zurück zum Zitat Ebrahimi F, Barati MR (2016) Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium. J Brazil Soc Mech Sci Eng 39:1–16 Ebrahimi F, Barati MR (2016) Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium. J Brazil Soc Mech Sci Eng 39:1–16
29.
Zurück zum Zitat Ebrahimi F, Barati MR (2016) Dynamic modeling of a thermo–piezo-electrically actuated nanosize beam subjected to a magnetic field. Appl Phys A 122(4):1–18 Ebrahimi F, Barati MR (2016) Dynamic modeling of a thermo–piezo-electrically actuated nanosize beam subjected to a magnetic field. Appl Phys A 122(4):1–18
30.
Zurück zum Zitat Ebrahimi F, Barati MR (2016) Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment. Int J Smart Nano Mater 7:1–22 Ebrahimi F, Barati MR (2016) Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment. Int J Smart Nano Mater 7:1–22
31.
Zurück zum Zitat Ebrahimi F, Barati MR (2016) An exact solution for buckling analysis of embedded piezoelectro-magnetically actuated nanoscale beams. Adv Innano Res 4(2):65–84 Ebrahimi F, Barati MR (2016) An exact solution for buckling analysis of embedded piezoelectro-magnetically actuated nanoscale beams. Adv Innano Res 4(2):65–84
32.
Zurück zum Zitat Ke LL, Wang YS, Yang J, Kitipornchai S (2014) Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory. Acta Mech Sin 30(4):516–525MathSciNetMATH Ke LL, Wang YS, Yang J, Kitipornchai S (2014) Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory. Acta Mech Sin 30(4):516–525MathSciNetMATH
33.
Zurück zum Zitat Ke LL, Wang YS (2014) Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory. Physica E 63:52–61 Ke LL, Wang YS (2014) Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory. Physica E 63:52–61
34.
Zurück zum Zitat Thostenson ET, Li WZ, Wang {\rm d}z, Ren ZF, Chou TW (2002) Carbon nanotube/carbon fiber hybrid multiscale composites. J Appl Phys 91(9):6034–6037 Thostenson ET, Li WZ, Wang {\rm d}z, Ren ZF, Chou TW (2002) Carbon nanotube/carbon fiber hybrid multiscale composites. J Appl Phys 91(9):6034–6037
35.
Zurück zum Zitat Shen HS (2009) A comparison of buckling and postbuckling behavior of FGM plates with piezoelectric fiber reinforced composite actuators. Compos Struct 91(3):375–384 Shen HS (2009) A comparison of buckling and postbuckling behavior of FGM plates with piezoelectric fiber reinforced composite actuators. Compos Struct 91(3):375–384
36.
Zurück zum Zitat Kim M, Park YB, Okoli OI, Zhang C (2009) Processing, characterization, and modeling of carbon nanotube-reinforced multiscale composites. Compos Sci Technol 69(3):335–342 Kim M, Park YB, Okoli OI, Zhang C (2009) Processing, characterization, and modeling of carbon nanotube-reinforced multiscale composites. Compos Sci Technol 69(3):335–342
37.
Zurück zum Zitat Feng C, Kitipornchai S, Yang J (2017) Nonlinear bending of polymer nanocomposite beams reinforced with non-uniformly distributed graphene platelets (GPLs). Compos B Eng 110:132–140 Feng C, Kitipornchai S, Yang J (2017) Nonlinear bending of polymer nanocomposite beams reinforced with non-uniformly distributed graphene platelets (GPLs). Compos B Eng 110:132–140
38.
Zurück zum Zitat 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 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
39.
Zurück zum Zitat Mantari JL, Bonilla EM, Soares CG (2014) A new tangential-exponential higher order shear deformation theory for advanced composite plates. Compos B Eng 60:319–328 Mantari JL, Bonilla EM, Soares CG (2014) A new tangential-exponential higher order shear deformation theory for advanced composite plates. Compos B Eng 60:319–328
40.
Zurück zum Zitat Leissa AW (1969) Vibration of plates. J Appl Math Mech 51(3):243 Leissa AW (1969) Vibration of plates. J Appl Math Mech 51(3):243
41.
Zurück zum Zitat Ebrahimi F, Salari E (2016) Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams. Mech Adv Mater Struct 23:1379–1397 Ebrahimi F, Salari E (2016) Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams. Mech Adv Mater Struct 23:1379–1397
42.
Zurück zum Zitat Ebrahimi F, Barati MR (2017) Porosity-dependent vibration analysis of piezo-magnetically actuated heterogeneous nanobeams. Mech Syst Signal Process 93:445–459 Ebrahimi F, Barati MR (2017) Porosity-dependent vibration analysis of piezo-magnetically actuated heterogeneous nanobeams. Mech Syst Signal Process 93:445–459
43.
Zurück zum Zitat Shen HS, Chen X, Guo L, Wu L, Huang XL (2015) Nonlinear vibration of FGM doubly curved panels resting on elastic foundations in thermal environments. Aerosp Sci Technol 47:434–446 Shen HS, Chen X, Guo L, Wu L, Huang XL (2015) Nonlinear vibration of FGM doubly curved panels resting on elastic foundations in thermal environments. Aerosp Sci Technol 47:434–446
44.
Zurück zum Zitat Sahmani S, Aghdam MM (2017) Nonlinear instability of axially loaded functionally graded multilayer graphene platelet-reinforced nanoshells based on nonlocal strain gradient elasticity theory. Int J Mech Sci 131:95–106 Sahmani S, Aghdam MM (2017) Nonlinear instability of axially loaded functionally graded multilayer graphene platelet-reinforced nanoshells based on nonlocal strain gradient elasticity theory. Int J Mech Sci 131:95–106
Metadaten
Titel
Chaotic dynamics and forced harmonic vibration analysis of magneto-electro-viscoelastic multiscale composite nanobeam
verfasst von
Farzad Ebrahimi
Mahsa karimiasl
Vinyas Mahesh
Publikationsdatum
03.10.2019
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 2/2021
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-019-00865-3

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