Dynamic Behavior of Anisotropic Protein Microtubules Immersed in Cytosol Via Cooper–Naghdi Thick Shell Theory
محورهای موضوعی : EngineeringM.R Ghorbanpour Arani 1 , Z Khoddami Maraghi 2 , E Haghparast 3
1 - Electrical Engineering Department, Amirkabir University of Technology, Tehran, Iran
2 - Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
3 - Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
کلید واژه: Strain gradient theory, Anisotropic protein MT, Cooper–Naghdi thick shell model, Visco-elastic bio-medium,
چکیده مقاله :
In the present research, vibrational behavior of anisotropic protein microtubules (MTs) immersed in cytosol via Cooper–Naghdi shell model is investigated. MTs are hollow cylindrical structures in the eukaryotic cytoskeleton which surrounded by filament network. The temperature effect on vibration frequency is also taken into account by assuming temperature-dependent material properties for MTs. To enhance the accuracy of results, strain gradient theory is utilized and the motion equations are derived based on Hamilton’s principle. Effects of various parameters such as environmental conditions by considering the surface traction of cytosol, length scale, thickness and aspect ratio on vibration characteristics of anisotropic MTs are studied. Results indicate that vibrational behavior of anisotropic MTs is strongly dependent on longitudinal Young’s modulus and length scale parameters. The results of this investigation can be utilized in the ultrasonic examine of MT organization in medical applications particularly in the treatment of cancers.
[1] Cooper G.M., Hausman R.E., 2007, The Cell: A Molecular Approach, ASM Press, Washington.
[2] 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.
[3] Gao Y., Lei F.M., 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.
[4] Tounsi A., Heireche H., Benhassaini H., Missouri M., 2010, Vibration and length-dependent flexural rigidity of protein microtubules using higher order shear deformation theory, The Journal of Theoretical Biology 266: 250-255.
[5] Fu Y., Zhang J., 2010, Modeling and analysis of microtubules based on a modified couple stress theory, Physica E 42: 1741-1745.
[6] Civalek O., Demir C., 2011, Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory, Applied Mathematical Modelling 35: 2053-2067.
[7] Demir Ç., Civalek Ö., 2013, Torsional and longitudinal frequency and wave response of microtubules based on the nonlocal continuum and nonlocal discrete models, Applied Mathematical Modelling 37: 9355-9367.
[8] Cooper R.M., Naghdi P.M., 1957, Propagation of non-axially symmetric waves in elastic cylindrical shells, Journal of the Acoustical Society of America 29: 1365-1372.
[9] Daneshmand F., Ghavanloo E., Amabili M., 2011, Wave propagation in protein microtubules modeled as orthotropic elastic shells including transverse shear deformations, Journal of Biomechanics 44: 1960-1966.
[10] Gao Y., An L., 2010, A nonlocal elastic anisotropic shell model for microtubule buckling behaviors in cytoplasm, Physica E 42: 2406-2415.
[11] Gheshlaghi B., Hasheminejad S.M., 2011, Surface effects on nonlinear free vibration of nano-beams, Composites: Part B 42: 934-937.
[12] Ghorbanpour Arani A., Kolahchi R., Khoddami Maraghi Z., 2013, Nonlinear vibration and instability of embedded double-walled boron nitride nano-tubes based on nonlocal cylindrical shell theory, Applied Mathematical Modelling 37: 7685-7707.
[13] Ghorbanpour Arani A., Shajari A.R., Amir S., Loghman A., 2012, Electro-thermo-mechanical nonlinear nonlocal vibration and instability of embedded micro-tube reinforced by BNNT, Physica E 45: 109-121.
[14] Ghorbanpour Arani A., Shirali A.A., Noudeh Farahani M., Amir S., Loghman A., 2012, Nonlinear vibration analysis of protein microtubules in cytosol conveying fluid based on nonlocal elasticity theory using differential quadrature method, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227: 137-145.
[15] Gu B., Mai Y. W., Ru C. Q., 2009, Mechanics of microtubules modeled as orthotropic elastic shells with transverse shearing, Acta Mechanica 207: 195-209.
[16] 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.
[17] 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.
[18] Liew K.M., Wang Q., 2007, Analysis of wave propagation in carbon nanotubes via elastic shell theories, International Journal of Engineering Science 45: 227-241.
[19] Shen H.S., 2013, Nonlocal shear deformable shell model for torsional buckling and postbuckling of microtubules in thermal environments, Mechanics Research Communications 54: 83- 95.
[20] Shu C., 2000, Differential Quadrature and its Application in Engineering, Springer, London.
[21] Taj M., Zhang J., 2014, Analysis of wave propagation in orthotropic microtubules embedded within elastic medium by Pasternak model, Journal of the Mechanical Behavior of Biomedical Materials 30: 300-305.
[22] Taj M., Zhang J.Q., 2012. Analysis of vibrational behaviors of microtubules embedded within elastic medium by Pasternak model, Biochemical and Biophysical Research Communications 424: 89-93.
[23] Wang C.Y., Li C.F., Adhikari S., 2009, Dynamic behaviors of microtubules in cytosol, Journal of Biomechanics 42: 1270-1274.
[24] Wang C.Y., Ru C.Q., Mioduchowski A., 2006, Vibration of microtubules as orthotropic elastic shells, Physica E 35: 48-56.
[25] Wang C.Y., Zhang L.C., 2008, Circumferential vibration of microtubules with long axial wavelength, Journal of Biomechanics 41: 1892-1896.
[26] Wang L., 2010, Vibration analysis of fluid-conveying nanotubes with consideration of surface effects, Physica E 43: 437-439.
[27] Wang X., Yang W.D., Xiong J.T., 2014, Coupling effects of initial stress and scale characteristics on the dynamic behavior of bio-liquid-filled microtubules immersed in cytosol, Physica E 56: 342-347.
[28] Zhou X., Wang L., 2012, Vibration and stability of micro-scale cylindrical shells conveying fluid based on modified couple stress theory, Micro & Nano Letters 7: 679-684.
