Vibration Analysis of Vessels Conveying Blood Flow Embedded in Viscous Fluid
الموضوعات :R Bahaadini 1 , M Hosseini 2 , M. A Paparisabet 3
1 - Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran
2 - Department of Mechanical Engineering, Sirjan University of Technology, Sirjan, Iran
3 - Department of Mechanical Engineering, Sirjan University of Technology, Sirjan, Iran
الکلمات المفتاحية: Viscous substrate, Modified strain gradient theory, Vessel, hematocrit, blood,
ملخص المقالة :
Vibration analysis of vessels conveying blood flow embedded in viscous fluid is studied based on the modified strain gradient theory. The viscoelastic vessels are simulated as a non-classical Euler-Bernoulli beam theory. Employing Hamilton’s principle, the governing equations for size-dependent vessels are derived. The Galerkin method is used in order to transform the resulting equations into general eigenvalue equations. The effects of the blood flow profile and its modification factors, red blood cells (RBCs) and hematocrit are considered in the blood flow. Besides, the influences of the constitutional material gradient scale, blood flow, internal pressure, structural damping coefficient, viscous fluid substrate and various boundary conditions on the natural frequencies and critical buckling velocities are studied. It is revealed that as the hematocrit, fluid viscosity of substrate, internal pressure and mass ratio increase, the natural frequencies and critical buckling velocities decrease. Furthermore, the results indicated that the strain gradient theory predicts the highest natural frequencies and critical buckling velocities among others. The results are compared with those available in the literature and good agreement has been observed.
[1] Kakisis J.D., Liapis C.D., Breuer C., Sumpio B.E., 2005, Artificial blood vessel: the holy grail of peripheral vascular surgery, Journal of vascular surgery 41(2): 349-354.
[2] Han H-C., 2008, Nonlinear buckling of blood vessels: a theoretical study, Journal of Biomechanics 41(12): 2708-2713.
[3] Han H-C., 2009, Blood vessel buckling within soft surrounding tissue generates tortuosity, Journal of Biomechanics 42(16): 2797-2801.
[4] Nakamachi E., Uchida T., Kuramae H., Morita Y.,2014, Multiscale finite element analyses for stress and strain evaluations of braid fibril artificial blood vessel and smooth muscle cell, International Journal for Numerical Methods in Biomedical Engineering 30(8): 796-813.
[5] Boileau E., 2015, A benchmark study of numerical schemes for one dimensional arterial blood flow modelling, International Journal for Numerical Methods in Biomedical Engineering 31(10).
[6] Mustapha N., Mandal P.K., Johnston P.R., Amin N., 2010, A numerical simulation of unsteady blood flow through multi-irregular arterial stenosis, Applied Mathematical Modelling 34(6): 1559-1573.
[7] Haghighi A.R., Asl M.S., Kiyasatfar M., 2015, Mathematical modeling of unsteady blood flow through elastic tapered artery with overlapping stenosis, Journal of the Brazilian Society of Mechanical Sciences and Engineering 37(2): 571-578.
[8] Haghighi A.R., Chalak S.A., 2017, Mathematical modeling of blood flow through a stenosed artery under body acceleration, Journal of the Brazilian Society of Mechanical Sciences and Engineering 39(7): 2487-2494.
[9] de Azevedo B.A., Azevedo L.F., Nunes R., Nóbrega A.C., 2015, In vivo blood velocity measurements with particle image velocimetry in echocardiography using spontaneous contrast, Journal of the Brazilian Society of Mechanical Sciences and Engineering 37(2): 559-569.
[10] Han H-C., 2009, The theoretical foundation for artery buckling under internal pressure, Journal of Biomechanical Engineering 131(12): 124501.
[11] Liu Q., Han H-C., 2012, Mechanical buckling of artery under pulsatile pressure, Journal of Biomechanics 45(7): 1192-1198.
[12] Khalafvand S.S., Han H-C., 2015, Stability of carotid artery under steady-state and pulsatile blood flow: A fluid–structure interaction study, Journal of Biomechanical Engineering 137 (6): 061007.
[13] Hosseini M., Paparisabet M., 2016, The effects of blood flow on blood vessel buckling embedded in surrounding soft tissues, International Journal of Applied Mechanics 8(5):1650065.
[14] Xiong G., Figueroa C.A., Xiao N., Taylor C.A., 2011, Simulation of blood flow in deformable vessels using subject specific geometry and spatially varying wall properties, International Journal for Numerical Methods in Biomedical Engineering 27(7): 1000-1016.
[15] Sun Q., Wu G.X., 2013, Coupled finite difference and boundary element methods for fluid flow through a vessel with multibranches in tumours, International Journal for Numerical Methods in Biomedical Engineering 29(3): 309-331.
[16] Bouchnita A., Galochkina T., Kurbatova P., Nony P., Volpert V., 2016, Conditions of microvessel occlusion for blood coagulation in flow, International Journal for Numerical Methods in Biomedical Engineering 00:2-27.
[17] Srivastava V., 2007, A theoretical model for blood flow in small vessels, Applications and Applied Mathematics 2(1): 51-65.
[18] McDonald D., 1960, Blood Flow in Arteries, Edward Arnold Ltd, London.
[19] Fung Y., 1968, Biomechanics, its scope, history and some problems of continuum mechanics in physiology, Applied Mechanics Reviews 21(1): 1-20.
[20] Hall J.E.,2015, Guyton and Hall Textbook of Medical Physiology, Elsevier Health Sciences.
[21] Haynes R.H., Burton A.C., 1959, Role of the non-newtonian behavior of blood in hemodynamics, American Journal of Physiology-Legacy Content 197(5): 943-950.
[22] Hershey D., Byrnes R., Deddens R., Rao A., 1964, Blood Rheology: Temperature Dependence of the Power Law Model, AI Ch. E. Boston.
[23] Hosseini M., Fazelzadeh S., 2011, Thermomechanical stability analysis of functionally graded thin-walled cantilever pipe with flowing fluid subjected to axial load, International Journal of Structural Stability and Dynamics 11(03): 513-534.
[24] Eftekhari M., Hosseini M., 2015, On the stability of spinning functionally graded cantilevered pipes subjected to fluid-thermomechanical loading, International Journal of Structural Stability and Dynamics 16(09):1550062.
[25] Lu P., Sheng H., 2012, Exact eigen-relations of clamped-clamped and simply supported pipes conveying fluids, International Journal of Applied Mechanics 4(03): 1250035.
[26] Wang L., Zhong Z., 2015, Radial basis collocation method for the dynamics of rotating flexible tube conveying fluid, International Journal of Applied Mechanics 7(03): 1550045.
[27] Arani A.G., Rastgoo A., Arani A.G., Kolahchi R., 2016, Vibration analysis of carotid arteries conveying non-newtonian blood flow surrounding by tissues, Journal of Solid Mechanics 8(4): 693-704.
[28] Ma Q., Clarke D.R., 1995, Size dependent hardness of silver single crystals, Journal of Materials Research 10(04): 853-863.
[29] Lam D.C., Chong A., 1999, Indentation model and strain gradient plasticity law for glassy polymers, Journal of Materials Research 14(09): 3784-3788.
[30] McFarland A.W., Colton J.S., 2005, Role of material microstructure in plate stiffness with relevance to microcantilever sensors, Journal of Micromechanics and Microengineering 15(5): 1060.
[31] Ziaee S., 2015, Small scale effect on linear vibration of buckled size-dependent FG nanobeams, Ain Shams Engineering Journal 6(2): 587-598.
[32] Eringen A.C., 2002, Nonlocal Continuum Field Theories, Springer Science & Business Media.
[33] Yang F., Chong A., Lam D.C.C., Tong P., 2002, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures 39(10): 2731-2743.
[34] Lam D.C.C., Yang F., Chong A., Wang J., Tong P., 2003, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids 51(8): 1477-1508.
[35] Hosseini M., Sadeghi-Goughari M., 2016, Vibration and instability analysis of nanotubes conveying fluid subjected to a longitudinal magnetic field, Applied Mathematical Modelling 40(4): 2560-2576.
[36] Bahaadini R., Hosseini M., 2016, Effects of nonlocal elasticity and slip condition on vibration and stability analysis of viscoelastic cantilever carbon nanotubes conveying fluid, Computational Materials Science 114: 151-159.
[37] Bahaadini R., Hosseini M., 2018, Flow-induced and mechanical stability of cantilever carbon nanotubes subjected to an axial compressive load, Applied Mathematical Modelling 59: 597-613.
[38] Bahaadini R., Hosseini M., 2016, Nonlocal divergence and flutter instability analysis of embedded fluid-conveying carbon nanotube under magnetic field, Microfluidics and Nanofluidics 20(7): 108.
[39] Bahaadini R., Saidi A.R., Hosseini M., 2019, Flow-induced vibration and stability analysis of carbon nanotubes based on the nonlocal strain gradient Timoshenko beam theory, Journal of Vibration and Control 25(1): 203-218.
[40] Bahaadini R., Hosseini M., Jamalpoor A., 2017, Nonlocal and surface effects on the flutter instability of cantilevered nanotubes conveying fluid subjected to follower forces, Physica B: Condensed Matter 509: 55-61.
[41] Bahaadini R., Hosseini M., Jamali B., 2018, Flutter and divergence instability of supported piezoelectric nanotubes conveying fluid, Physica B: Condensed Matter 529: 57-65.
[42] Bahaadini R., Saidi A.R., Hosseini M., 2018, Dynamic stability of fluid-conveying thin-walled rotating pipes reinforced with functionally graded carbon nanotubes, Acta Mechanica 229(12): 5013-5029.
[43] Bahaadini R., Hosseini M., Khalili-Parizi Z., 2019, Electromechanical stability analysis of smart double-nanobeam systems, The European Physical Journal 134(7): 320.
[44] Bahaadini R., Dashtbayazi M.R., Hosseini M., Khalili-Parizi Z., 2018, Stability analysis of composite thin-walled pipes conveying fluid, Ocean Engineering 160: 311-323.
[45] Bahaadini R., Saidi A.R., Arabjamaloei Z., Ghanbari-Nejad-Parizi A., 2019, Vibration analysis of functionally graded graphene reinforced porous nanocomposite shells, International Journal of Applied Mechanics 11(7): 1950068.
[46] Bahaadini R., Saidi A.R., 2019, Aerothermoelastic flutter analysis of pre-twisted thin-walled rotating blades reinforced with functionally graded carbon nanotubes, European Journal of Mechanics-A/Solids 75: 285-306.
[47] Bahaadini R., Saidi A.R., 2018, On the stability of spinning thin-walled porous beams, Thin-Walled Structures 132: 604-615.
[48] Bahaadini R., Saidi A.R., 2018, Aeroelastic analysis of functionally graded rotating blades reinforced with graphene nanoplatelets in supersonic flow, Aerospace Science and Technology 80: 381-391.
[49] Bahaadini R., Saidi A.R., 2018, Stability analysis of thin-walled spinning reinforced pipes conveying fluid in thermal environment, European Journal of Mechanics-A/Solids 72: 298-309.
[50] Saidi A.R., Bahaadini R., Majidi-Mozafari K., 2019, On vibration and stability analysis of porous plates reinforced by graphene platelets under aerodynamical loading, Composites Part B: Engineering 164: 778-799.
[51] Mohammadi K., Barouti M.M., Safarpour H., Ghadiri M., Effect of distributed axial loading on dynamic stability and buckling analysis of a viscoelastic DWCNT conveying viscous fluid flow, Journal of the Brazilian Society of Mechanical Sciences and Engineering 41(2): 93.
[52] Cabrera-Miranda J.M., Paik J.K., 2019, Two-phase flow induced vibrations in a marine riser conveying a fluid with rectangular pulse train mass, Ocean Engineering 174: 71-83.
[53] Farajpour A., Farokhi H., Ghayesh M.H., 2019, Chaotic motion analysis of fluid-conveying viscoelastic nanotubes, European Journal of Mechanics-A/Solids 74: 281-296.
[54] Amiri A., Vesal R., Talebitooti R., Flexoelectric and surface effects on size-dependent flow-induced vibration and instability analysis of fluid-conveying nanotubes based on flexoelectricity beam model, International Journal of Mechanical Sciences 156: 474-485.
[55] Ebrahimi F., Hajilak Z.E., 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, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233: 4590-4605.
[56] Mohammadimehr M., Mehrabi M., 2017, Stability and free vibration analyses of double-bonded micro composite sandwich cylindrical shells conveying fluid flow, Applied Mathematical Modelling 47: 685-709.
[57] Arani A.G., Shajari A., Atabakhshian V., Amir S., Loghman A., 2013, Nonlinear dynamical response of embedded fluid-conveyed micro-tube reinforced by BNNTs, Composites Part B: Engineering 44(1): 424-432.
[58] Arani A.T., Ghorbanpour Arani A., Kolahchi R., 2015, Non-newtonian pulsating blood flow-induced dynamic instability of visco-carotid artery within soft surrounding visco-tissue using differential cubature method, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229(16): 3002-3012.
[59] Atashafrooz M., Bahaadini R., Sheibani H.R., 2018, Nonlocal, strain gradient and surface effects on vibration and instability of nanotubes conveying nanoflow, Mechanics of Advanced Materials and Structures 27: 1-13.
[60] Hosseini M., Maryam A.Z.B., Bahaadini R., 2017, Forced vibrations of fluid-conveyed double piezoelectric functionally graded micropipes subjected to moving load, Microfluidics and Nanofluidics 21(8): 134.
[61] Hosseini M., Bahaadini R., Makkiabadi M., 2018, Application of the Green function method to flow-thermoelastic forced vibration analysis of viscoelastic carbon nanotubes, Microfluidics and Nanofluidics 22(1): 6.
[62] Hosseini M., Bahaadini R., Khalili-Parizi Z., 2019, Structural instability of non-conservative functionally graded micro-beams tunable with piezoelectric layers, Journal of Intelligent Material Systems and Structures 30(4): 593-605.
[63] Soleymani T., Arani A.G., 2019, On aeroelastic stability of a piezo-MRE sandwich plate in supersonic airflow, Composite Structures 230: 111532.
[64] Arani A.G., Soleymani T., 2019, Size-dependent vibration analysis of a rotating MR sandwich beam with varying cross section in supersonic airflow, International Journal of Mechanical Sciences 151: 288-299.
[65] Arani A.G., Soleymani T., 2019, Size-dependent vibration analysis of an axially moving sandwich beam with MR core and axially FGM faces layers in yawed supersonic airflow, European Journal of Mechanics-A/Solids 77: 103792.
[66] Yin L., Qian Q., Wang L., 2011, Strain gradient beam model for dynamics of microscale pipes conveying fluid, Applied Mathematical Modelling 35(6): 2864-2873.
[67] Ghavanloo E., Fazelzadeh S.A., 2011, Flow-thermoelastic vibration and instability analysis of viscoelastic carbon nanotubes embedded in viscous fluid, Physica E: Low-dimensional Systems and Nanostructures 44(1): 17-24.
[68] Haynes R.H., 1960, Physical basis of the dependence of blood viscosity on tube radius, American Journal of Physiology-Legacy Content 198(6): 1193-1200.
[69] Benjamin T.B., 1961, Dynamics of a System of articulated pipes conveying fluid. I. Theory, Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences 261(1307): 457-486.
[70] Bahaadini R., Hosseini M., 2016, Nonlocal divergence and flutter instability analysis of embedded fluid-conveying carbon nanotube under magnetic field, Microfluidics and Nanofluidics 20(7): 1-14.
[71] Hosseini M., Bahaadini R., Jamali B., 2016, Nonlocal instability of cantilever piezoelectric carbon nanotubes by considering surface effects subjected to axial flow, Journal of Vibration and Control 24:1908-1825.
[72] Paidoussis M.P., 1998, Fluid-Structure Interactions: Slender Structures and Axial Flow, Academic Press.
[73] Ni Q., Zhang Z.L., Wang L., 2011, Application of the differential transformation method to vibration analysis of pipes conveying fluid, Applied Mathematics and Computation 217(16): 7028-7038.
[74] Guo C., Zhang C., Païdoussis M., 2010, Modification of equation of motion of fluid-conveying pipe for laminar and turbulent flow profiles, Journal of Fluids and Structures 26(5): 793-803.
[75] Qin S., Ferrara K.W., 2007, The natural frequency of nonlinear oscillation of ultrasound contrast agents in microvessels, Ultrasound in Medicine & Biology 33(7): 1140-1148.
