Free Vibration Analysis of Microtubules as Orthotropic Elastic Shells Using Stress and Strain Gradient Elasticity Theory
Subject Areas : Engineering
1 - Faculty of Engineering, Shahrekord University
2 - Nanotechnology Research Center, Shahrekord University
Keywords:
Abstract :
[1] Wada H., 2005, Biomechanics at Micro- and Nanoscale Levels, World Scientific Publishing Company.
[2] Alberts B., Bray D., Lewis J., Raff M., Roberts K., Watson J., 1994, Molecular Biology of the Cell, Garland Publishing, New York.
[3] Faber J., Portugal R., Ros L.P., 2006, Information processing in brain microtubules, Biosystems 83: 1-9.
[4] Hawkins T., Mirigian M., Yasar M.S., Ross J.L., 2010, Mechanics of microtubules, Journal of Biomechanics 43: 23-30.
[5] Pampaloni F., Florin E.L., 2008, Microtubule architecture: inspiration for novel carbon nanotube-based biomimetic materials, Trends in Biotechnology 26(6): 302-310.
[6] Yuanwen G., Ming L.F., 2009, Small scale effects on the mechanical behaviors of protein microtubules based on the nonlocal elasticity theory, Biochemical and Biophysical Research Communications 387: 467- 471.
[7] Tadi Beni Y., Abadyan M., 2013, Size-dependent pull-in instability of torsional nano-actuator, Physica Scripta 88(5): 055801.
[8] Tadi Beni Y., Abadyan M., 2013, Use of strain gradient theory for modeling the size-dependent pull-in of rotational nano-mirror in the presence of molecular force, International Journal of Modern Physics B 27: 1350083-1350101.
[9] TadiBeni Y., Koochi A., Abadyan M., 2011, Theoretical study of the effect of Casmir force, elastic boundary conditions and size dependency on the pull-in instability of beam-type NEMS, Physica E 43: 979-988.
[10] Tadi Beni Y., Koochi A., Kazemi A.S., Abadyan M., 2012, Modeling the influence of surface effect and molecular force on pull-in voltage of rotational Nano–micro mirror using 2-DOF model, Canadian Journal of Physics 90: 963-974.
[11] Sharma P., Zhang X., 2006, Impact of size-dependent non-local elastic strain on the electronic band structure of embedded quantum dots, Journal Nanoengineering and Nanosystems 220: 17403499.
[12] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54: 4703-4710.
[13] Gittes F., Mickey B., Nettleton J., Howard J., 1995, Flexural rigidity of microtubules and actin filaments measured from thermal fluctuation in shape, Journal of Cell Biology 120: 923-934.
[14] Venier P., Maggs A.C., Carlier M.F., Pantaloni D., 1994, Analysis of microtubule rigidity using hydrodynamic flow and thermal fluctuations, Journal of Biological Chemistry 269: 13353-13360.
[15] Vinckier A., Dumortier C., Engelborghs Y., Hellemans L., 1996, Dynamical and mechanical study of immobilized microtubule with atomic force microscopy, Journal of Vacuum Science & Technology B 14: 1427-1431.
[16] Sirenko Y.M., Stroscio M.A., Kim K.W., 1996, Elastic vibration of microtubules in a fluid, Physical Review E 53: 1003-1010.
[17] Wang C.Y., Ru C.Q., Mioduchowski A., 2006, Vibration of microtubules as orthotropic elastic shells, Physica E 35: 48-56.
[18] Wang C.Y., Zhang L.C., 2008, Circumferential vibration of microtubules with long axial wavelength, Journal of Biomechanics 41: 1892-1896.
[19] Shen H.S., 2011, Nonlinear vibration of microtubules in living cells, Current Applied Physics 11: 812-821.
[20] Civalek Ö., Akgöz B., 2010, Free vibration analysis of microtubules as cytoskeleton components: nonlocal euler-bernoulli beam modeling, Transaction B: Mechanical Engineering 17: 367-375.
[21] Heireche H., Tounsi A., Benhassaini H., Benzair A., Bendahmane M., Missouri M., Mokadem S., 2010, Nonlocal elasticity effect on vibration characteristics of protein microtubules, Physica E 42: 2375-2379.
[22] Xiang P., Liew K.M., 2011, Free vibration analysis of microtubules based on an atomistic-continuum model, Journal of Sound and Vibration 331: 213-230.
[23] Karimi Zeverdejani M., Tadi Beni Y., 2013, The nano scale vibration of protein microtubules based on modified strain gradient theory, Current Applied Physics 13: 1566-1576.
[24] Lam D.C.C., Yang F., Chong A.C.M., Wang J., Tong P., 2003, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids 51: 1477-1508.
[25] Fleck N., Muller G., Ashby M., Hutchinson J., 1994, Strain gradient plasticity: theory and experiment, Acta Metallurgica et Materialia 42: 475-487.
[26] Stölken J., Evans A., 1998, A microbend test method for measuring the plasticity length scale, Acta Materialia 46: 5109-5115.
[27] McElhaney K., Vlassak J., Nix W., 1998, Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments, Journal of Materials Research 13: 1300-1306.
[28] Nix W.D., Gao H., 1998, Indentation size effects in crystalline materials: a law for strain gradient plasticity, Journal of the Mechanics and Physics of Solids 46: 411-425.
[29] Chong A., Lam D.C., 1999, Strain gradient plasticity effect in indentation hardness of polymers, Journal of Materials Research 14: 4103-4110.
[30] Tadi Beni Y., Karimi Zeverdejani M., 2015, Free vibration of microtubules as elastic shell model based on modified couple stress theory, Journal of Mechanics in Medicine and Biology 15(3):1550037-1550060.
[31] Askes H., Aifantis E.C., 2011, Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results, International Journal of Solids and Structures 48: 1962-1990.
[32] Tuszynski J.A., Luchko T., Portet S., Dixon J.M., 2005, Anisotropic elastic properties of microtubules, The European Physical Journal E 17: 29-35.
[33] De Pablo P.J., Schaap I..A.T., Mackintosh F.C., Schmidt C.F., 2003, Deformational collapse of microtubules on the nanometer scale, Physical Review Letters 91: 098101.
[34] Sirenko Y. M., Stroscio M. A., Kim K. W., 1996, Elastic vibrations of microtubules in a fluid, Physical Review E 53: 1003.
[35] Askes H., Aifantis E.C., 2009, Gradient elasticity and flexural wave dispersion in carbon Nanotubes, Physical Review B 80: 195412.
[36] Bennett T., Gitman I., Askes H., 2007, Elasticity theories with higher-order gradients of inertia and stiffness for the modeling of wave dispersion in laminates, International Journal of Fracture 148: 185-193.
[37] Gitman I., Askes H., Aifantis E.C., 2005, The representative volume size in static and dynamic micro-macro transitions, International Journal of Fracture 135: 3-9.
[38] Wang Q., 2005, Wave propagation in carbon nanotubes via nonlocal continuum mechanics, Journal of Applied Physics 98: 124301.
[39] Civalek O., Demir C., Akgoz B., 2010, Free vibration and bending analyses of cantilever microtubules based on nonlocal continuum model, Mathematical and Computational Applications 15: 289-298.
[40] Heireche H., Tounsi A., Benhassaini H., Benzair A., Bendahmane M., Missouri M., Mokadem S., 2010, Nonlocal elasticity effect on vibration characteristics of protein microtubules, Physica E 42: 2375-2379.
[41] Shen H. S., 2010, Nonlocal shear deformable shell model for postbuckling of axially compressed microtubules embedded in an elastic medium, Biomechanics and Modeling in Mechanobiology 9: 345-357.
[42] Shen H. S., 2010, Buckling and postbuckling of radially loaded microtubules by nonlocal shear deformable shell model, Journal of Theoretical Biology 264: 386-394.
[43] Park S., Gao X., 2006, Bernoulli–Euler beam model based on a modified couple stress theory, Journal of Micromechanics and Microengineering 16: 2355-2359.
[44] Maranganti R., Sharma P., 2007, A novel atomistic approach to determine strain-gradient elasticity constants: Tabulation and comparison for various metals, semiconductors, silica, polymers and the (ir) relevance for nanotechnologies, Journal of the Mechanics and Physics of Solids 55: 1823-1852.
[45] Duan W., Wang C.M., Zhang Y., 2007, Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics, Journal of Applied Physics 101: 024305-024307.
[46] Chan K., Zhao Y., 2011, The dispersion characteristics of the waves propagating in a spinning single-walled carbon nanotube, Science China Physics, Mechanics & Astronomy 54: 1854-1865.
[47] Shi Y.J., Guo W.L., Ru C.Q., 2008, Relevance of timoshenko-beam model to microtubules of low shear modulus, Physica E 41: 213-219.
