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Nonlinear modeling and dynamic analysis of bioengineering hyper-elastic tubes based on different material models

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Abstract

In this research, nonlinear vibrations of a hyper-elastic tube accounting for large deflection and moderate rotation have been examined. The hyper-elastic tube is assumed to be surrounded by a nonlinear hardening elastic medium. Different types of hyper-elastic material models are presented and discussed including neo-Hookean, Mooney–Rivlin, Ishihara and Yeoh models. The efficacy of these models in nonlinear vibration modeling and analysis of hyper-elastic tubes has been examined. Modified von-Karman strain is used to consider both large deflection and moderate rotation. The governing equations are obtained based on strain energy function of above-mentioned hyper-elastic material models. The nonlinear governing equation of the tube contains cubic and quantic terms which is solved via extended Hamiltonian method leading to a closed form of nonlinear vibration frequency. The effect of hyper-elastic models and their material parameters on nonlinear vibrational frequency of tubes has been studied.

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References

  • Abdelaziz et al (2017) An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions. Steel Compos Struct 25(6):693–704

    MathSciNet  Google Scholar 

  • Ahmed RA, Fenjan RM, Faleh NM (2019) Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections. Geomech Eng 17(2):175–180

    Google Scholar 

  • Ali A, Hosseini M, Sahari BB (2010) A review and comparison on some rubber elasticity models. J Sci Ind Res 69(7):495–500

    Google Scholar 

  • Al-Maliki AF, Faleh NM, Alasadi AA (2019) Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities. Struct Monit Maint 6(2):147–159

    Google Scholar 

  • Bakhadda et al (2018) Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation. Wind Struct 27(5):311–324

    Google Scholar 

  • Barati MR (2018a) Investigating nonlinear vibration of closed circuit flexoelectric nanobeams with surface effects via Hamiltonian method. Microsyst Technol 24(4):1841–1851

    Article  Google Scholar 

  • Barati MR (2018b) Closed-form nonlinear frequency of flexoelectric nanobeams with surface and nonlocal effects under closed circuit electric field. Mater Res Exp 5(2):025008

    Article  Google Scholar 

  • Barati MR, Shahverdi H (2018a) Nonlinear vibration of nonlocal four-variable graded plates with porosities implementing homotopy perturbation and Hamiltonian methods. Acta Mech 229(1):343–362

    Article  MathSciNet  MATH  Google Scholar 

  • Barati MR, Shahverdi H (2018b) Nonlinear thermal vibration analysis of refined shear deformable FG nanoplates: two semi-analytical solutions. J Braz Soc Mech Sci Eng 40(2):64

    Article  Google Scholar 

  • Barati MR, Zenkour AM (2019) Analysis of postbuckling of graded porous GPL-reinforced beams with geometrical imperfection. Mech Adv Mater Struct 26(6):503–511

    Article  Google Scholar 

  • Barforooshi SD, Mohammadi AK (2016) Study neo-Hookean and Yeoh hyper-elastic models in dielectric elastomer-based micro-beam resonators. Latin Am J Solids Struct 13(10):1823–1837

    Article  Google Scholar 

  • Bayat M, Pakar I, Cveticanin L (2014) Nonlinear vibration of stringer shell by means of extended Hamiltonian approach. Arch Appl Mech 84(1):43–50

    Article  MATH  Google Scholar 

  • Beda T (2007) Modeling hyperelastic behavior of rubber: a novel invariant-based and a review of constitutive models. J Polym Sci B Polym Phys 45(13):1713–1732

    Article  Google Scholar 

  • Besseghier A, Heireche H, Bousahla AA, Tounsi A, Benzair A (2015) Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix. Adv Nano Res 3(1):029

    Article  Google Scholar 

  • Bouadi et al (2018) A new nonlocal HSDT for analysis of stability of single layer graphene sheet. Adv Nano Res 6(2):147–162

    Google Scholar 

  • Bouiadjra RB, Bedia EA, Tounsi A (2013) Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory. Struct Eng Mech 48(4):547–567

    Article  Google Scholar 

  • Boukhlif et al (2019) A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation. Steel Compos Struct 31(5):503–516

    Google Scholar 

  • Boulefrakh et al (2019) The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate. Geomech Eng 18(2):161–178

    Google Scholar 

  • Bourada et al (2018) A novel refined plate theory for stability analysis of hybrid and symmetric S-FGM plates. Struct Eng Mech 68(6):661–675

    Google Scholar 

  • Boutaleb et al (2019) Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT. Adv Nano Res 7(3):189–206

    Google Scholar 

  • Breslavsky ID, Amabili M, Legrand M (2014) Nonlinear vibrations of thin hyperelastic plates. J Sound Vib 333(19):4668–4681

    Article  Google Scholar 

  • Chaabane et al (2019) Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation. Struct Eng Mech 71(2):185–196

    Google Scholar 

  • Faleh NM, Ahmed RA, Fenjan RM (2018a) On vibrations of porous FG nanoshells. Int J Eng Sci 133:1–14

    Article  MathSciNet  MATH  Google Scholar 

  • Faleh NM, Fenjan RM, Ahmed RA (2018b) Dynamic analysis of graded small-scale shells with porosity distributions under transverse dynamic loads. Eur Phys J Plus 133(9):348

    Article  Google Scholar 

  • Fenjan RM, Ahmed RA, Alasadi AA, Faleh NM (2019) Nonlocal strain gradient thermal vibration analysis of double-coupled metal foam plate system with uniform and non-uniform porosities. Coupled Syst Mech 8(3):247–257

    Google Scholar 

  • He JH (2010) Hamiltonian approach to nonlinear oscillators. Phys Lett A 374(23):2312–2314

    Article  MathSciNet  MATH  Google Scholar 

  • Horgan CO, Saccomandi G (2006) Phenomenological hyperelastic strain-stiffening constitutive models for rubber. Rubber Chem Technol 79(1):152–169

    Article  Google Scholar 

  • Kadari et al (2018) Buckling analysis of orthotropic nanoscale plates resting on elastic foundations. J Nano Res 55:42–56

    Article  Google Scholar 

  • Li L, Hu Y (2016) Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material. Int J Eng Sci 107:77–97

    Article  MathSciNet  MATH  Google Scholar 

  • Marckmann G, Verron E (2006) Comparison of hyperelastic models for rubber-like materials. Rubber Chem Technol 79(5):835–858

    Article  Google Scholar 

  • Martins PALS, Natal Jorge RM, Ferreira AJM (2006) A comparative study of several material models for prediction of hyperelastic properties: application to silicone-rubber and soft tissues. Strain 42(3):135–147

    Article  Google Scholar 

  • Mohammadi AK, Barforooshi SD (2017) Nonlinear forced vibration analysis of dielectric-elastomer based micro-beam with considering Yeoh hyper-elastic model. Latin Am J Solids Struct 14(4):643–656

    Article  Google Scholar 

  • Mokhtar et al (2018) A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory. Smart Struct Syst 21(4):397–405

    Google Scholar 

  • Ogden RW, Saccomandi G, Sgura I (2004) Fitting hyperelastic models to experimental data. Comput Mech 34(6):484–502

    Article  MATH  Google Scholar 

  • Reddy JN, El-Borgi S (2014) Eringen’s nonlocal theories of beams accounting for moderate rotations. Int J Eng Sci 82:159–177

    Article  MathSciNet  MATH  Google Scholar 

  • Reddy JN, Srinivasa AR (2014) Non-linear theories of beams and plates accounting for moderate rotations and material length scales. Int J Non Linear Mech 66:43–53

    Article  Google Scholar 

  • Shahverdi H, Barati MR, Hakimelahi B (2019) Post-buckling analysis of honeycomb core sandwich panels with geometrical imperfection and graphene reinforced nano-composite face sheets. Mater Res Exp 6(9):095017

    Article  Google Scholar 

  • Shahzad M, Kamran A, Siddiqui MZ, Farhan M (2015) Mechanical characterization and FE modelling of a hyperelastic material. Mater Res 18(5):918–924

    Article  Google Scholar 

  • She GL, Yuan FG, Ren YR, Liu HB, Xiao WS (2018a) Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory. Compos Struct 203:614–623

    Article  Google Scholar 

  • She GL, Ren YR, Xiao WS, Liu HB (2018b) Study on thermal buckling and post-buckling behaviors of FGM tubes resting on elastic foundations. Struct Eng Mech 66(6):729–736

    Google Scholar 

  • Sheng GG, Wang X (2018) Nonlinear vibration of FG beams subjected to parametric and external excitations. Eur J Mech A Solids 71:224–234

    Article  MathSciNet  MATH  Google Scholar 

  • Soares RM, Gonçalves PB (2018) Nonlinear vibrations of a rectangular hyperelastic membrane resting on a nonlinear elastic foundation. Meccanica 53(4–5):937–955

    Article  MathSciNet  MATH  Google Scholar 

  • Steinmann P, Hossain M, Possart G (2012) Hyperelastic models for rubber-like materials: consistent tangent operators and suitability for Treloar’s data. Arch Appl Mech 82(9):1183–1217

    Article  MATH  Google Scholar 

  • Wang Y, Ding H, Chen LQ (2019) Vibration of axially moving hyperelastic beam with finite deformation. Appl Math Model 71:269–285

    Article  MathSciNet  MATH  Google Scholar 

  • Yazid et al (2018) A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium. Smart Struct Syst 21(1):15–25

    Google Scholar 

  • Younsi et al (2018) Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates. Geomech Eng 14(6):519–532

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank Fidar Project Qaem (FPQ) for providing the fruitful and useful help.

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, Qatar University, P.O. Box 2713, Doha, Qatar

    Seyed Sajad Mirjavadi & Masoud Forsat

  2. Department of Electrical Engineering, Qatar University, Doha, Qatar

    Salman Badnava

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  1. Seyed Sajad Mirjavadi
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  2. Masoud Forsat
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  3. Salman Badnava
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Correspondence to Seyed Sajad Mirjavadi.

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Mirjavadi, S.S., Forsat, M. & Badnava, S. Nonlinear modeling and dynamic analysis of bioengineering hyper-elastic tubes based on different material models. Biomech Model Mechanobiol 19, 971–983 (2020). https://doi.org/10.1007/s10237-019-01265-8

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  • DOI: https://doi.org/10.1007/s10237-019-01265-8

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