پایان نامه ارتعاشات غیرخطی و رفتار پس از کمانش میکرو لوله های حاوی جریان بر اساس تئوری های تنش کوپل و تغییرات کرنش

فهرست:

چکیده ‌ز

فصل1. 1

مقدمهای بر نانوتکنولوژی و مروری بر پژوهش­های گذشته. 1

1-1. مقدمه. 2

1-2. تاریخچه­ی نانوتکنولوژی.. 2

1-1. اهمیت نانوتکنولوژی.. 3

1-2. کاربردهای نانوتکنولوژی.. 4

1-2-1. صنایع هوانوردی و اتوماسیون: 5

1-2-2. الکترونیک وارتباطات : 5

1-2-3. مواد شیمیایی و مواد: 5

1-2-4. درمان، بهداشت و علوم زیستی: 5

1-2-5. ساخت وتولید : 5

1-2-6. فناوریهای انرژی: 6

1-2-7. کاوش درفضا : 6

1-2-8. محیط زیست : 6

1-2-9. امنیت ملی : 6

1-1. روش ساخت میکرولوله­ها 6

1-2. پیشینه­ی تحقیق.. 8

فصل2. 12

تحلیل ارتعاشات آزاد غیرخطی و رفتار پس  از کمانش میکرولوله­های حاوی جریان.. 12

2-1. مقدمه. 13

2-2. تئوری تنش کوپل.. 13

2-3. تئوری گرادیان کرنش.... 14

2-4. روابط سینماتیک.... 16

2-5. استخراج معادلات حاکم به روش انرژی.. 19

2-6. روش حل تحلیل هموتوپی.. 27

2-7. اعمال روش تحلیل هموتوپی.. 28

2-8. روش حل ماکزیمم - مینیمم.. 32

2-9. تحلیل رفتار پس از کمانش.... 34

فصل3.. 40

اعتبارسازی و نتایج.. 40

3-1. مقدمه. 41

3-2. اعتبار سنجی.. 41

3-3. ارتعاش غیرخطی میکرولوله­های حاوی جریان.. 43

3-4. رفتار پس از کمانش میکرولوله­های حاوی جریان.. 52

4-1. مقدمه. 57

4-2. ارتعاشات آزاد میکرولوله­ی هدفمند حاوی جریان.. 58

4-3. رفتار پس از کمانش میکرولوله­های هدفمند. 65

4-4. نتایج.. 66

4-4-1. ارتعاشات غیرخطی میکرولوله­های هدفمند حاوی جریان.. 67

4-4-2. رفتار پس از کمانش میکرولوله­های هدفمند. 71

فصل5.. 73

نتیجه­گیری و پیشنهادات... 73

5-1. نتیجه­گیری.. 74

5-2. پیشنهادات... 75

مراجع.. 76

مراجع: 77

Abstract 82

منبع:

[1]   C.-L. Kuo, T. Masuzawa, M. Fujino, A micropipe fabrication process, in:  Micro Electro Mechanical Systems, 1991, MEMS'91, Proceedings. An Investigation of Micro Structures, Sensors, Actuators, Machines and Robots. IEEE, IEEE, 1991, pp. 80-85.

[2]  N. Fleck, G. Muller, M. Ashby, J. Hutchinson, Strain gradient plasticity: theory and experiment, Acta Metallurgica et Materialia, 42 (1994) 475-487.

[3]  J. Stölken, A. Evans, A microbend test method for measuring the plasticity length scale, Acta Materialia, 46 (1998) 5109-5115.

[4]  D. Lam, F. Yang, A. Chong, J. Wang, P. Tong, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids, 51 (2003) 1477-1508.

[5]  A.W. McFarland, J.S. Colton, Role of material microstructure in plate stiffness with relevance to microcantilever sensors, Journal of Micromechanics and Microengineering, 15 (2005) 1060.

[6]  R. Mindlin, H. Tiersten, Effects of couple-stresses in linear elasticity, Archive for Rational Mechanics and Analysis, 11 415-448 (1962).

[7]  R. Toupin, Elastic materials with couple-stresses, Archive for Rational Mechanics and Analysis, 11 (1962) 385-414.

[8]  W. Koiter, Couple stresses in the theory of elasticity, I and II, in:  Nederl. Akad. Wetensch. Proc. Ser. B, 1964, pp. 17-29.

[9]  S. Zhou, Z. Li, Length scales in the static and dynamic torsion of a circular cylindrical micro-bar, Journal of Shandong university of technology, 31 (2001) 401-407.

[10]          X. Kang, Z. Xi, Size effect on the dynamic characteristic of a micro beam based on cosserat theory, Journal of Mechanical Strength, 29 (2007) 1-4.

[11]          F. Yang, A. Chong, D. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39 (2002) 2731-2743.

[12]          S. Kong, S. Zhou, Z. Nie, K. Wang, The size-dependent natural frequency of Bernoulli–Euler micro-beams, International Journal of Engineering Science, 46 (2008) 427-437.

[13]          H. Ma, X.-L. Gao, J. Reddy, A microstructure-dependent Timoshenko beam model based on a modified couple stress theory, Journal of the Mechanics and Physics of Solids, 56 (2008) 3379-3391.

[14]          M. Asghari, M. Kahrobaiyan, M. Ahmadian, A nonlinear Timoshenko beam formulation based on the modified couple stress theory, International Journal of Engineering Science, 48 (2010) 1749-1761.

[15]          E. Jomehzadeh, H. Noori, A. Saidi, The size-dependent vibration analysis of micro-plates based on a modified couple stress theory, Physica E: Low-dimensional Systems and Nanostructures, 43 (2011) 877-883.

[16]          L. Wang, Size-dependent vibration characteristics of fluid-conveying microtubes, Journal of Fluids and Structures, 26 (2010) 675-684.

[17]          W. Xia, L. Wang, Microfluid-induced vibration and stability of structures modeled as microscale pipes conveying fluid based on non-classical Timoshenko beam theory, Microfluidics and nanofluidics, 9 (2010) 955-962.

[18]          S. Ahangar, G. Rezazadeh, R. Shabani, G. Ahmadi, A. Toloei, On the stability of a microbeam conveying fluid considering modified couple stress theory, International Journal of Mechanics and Materials in Design, 7 (2011) 327-342.

[19]          T.-Z. Yang, S. Ji, X.-D. Yang, B. Fang, Microfluid-induced nonlinear free vibration of microtubes, International Journal of Engineering Science, 76 (2014) 47-55.

[20]          R.D. Mindlin, Second gradient of strain and surface-tension in linear elasticity, International Journal of Solids and Structures, 1 (1965) 417-438.

[21]          N. Fleck, J. Hutchinson, A reformulation of strain gradient plasticity, Journal of the Mechanics and Physics of Solids, 49 (2001) 2245-2271.

[22]          N. Fleck, J. Hutchinson, Strain gradient plasticity, Advances in applied mechanics, 33 (1997) 295-361.

[23]          S. Kong, S. Zhou, Z. Nie, K. Wang, Static and dynamic analysis of micro beams based on strain gradient elasticity theory, International Journal of Engineering Science, 47 (2009) 487-498.

[24]          M. Kahrobaiyan, M. Asghari, M. Rahaeifard, M. Ahmadian, A nonlinear strain gradient beam formulation, International Journal of Engineering Science, 49 (2011) 1256-126 7.

[25]          M. Asghari, M. Kahrobaiyan, M. Nikfar, M. Ahmadian, A size-dependent nonlinear Timoshenko microbeam model based on the strain gradient theory, Acta Mechanica, 223 (2012) 1233-1249.

[26]          J. Zhao, S. Zhou, B. Wang, X. Wang, Nonlinear microbeam model based on strain gradient theory, Applied Mathematical Modelling, 36 (2012) 2674-2686.

[27]          S. Ramezani, A micro scale geometrically non-linear Timoshenko beam model based on strain gradient elasticity theory, International Journal of Non-Linear Mechanics 873-863 (2012) 47.

[28]          F. Rajabi, S. Ramezani, A nonlinear microbeam model based on strain gradient elasticity theory with surface energy, Archive of Applied Mechanics, 82 (2012) 363-376.

[29]          M.H. Ghayesh, M. Amabili, H. Farokhi, Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory, International Journal of Engineering Science, 63 (2013) 52-60.

[30]          B. Wang, S. Zhou, J. Zhao, X. Chen, A size-dependent Kirchhoff micro-plate model based on strain gradient elasticity theory, European Journal of Mechanics-A/Solids, 30 (2011) 517-524.

[31]          S. Ramezani, A shear deformation micro-plate model based on the most general form of strain gradient elasticity, International Journal of Mechanical Sciences, 57 (2012) 34-42.

[32]          L. Yin, Q. Qian, L. Wang, Strain gradient beam model for dynamics of microscale pipes conveying fluid, Applied Mathematical Modelling, 35 (2011) 2864-2873.

[33]          A. Farshidianfar, A microstructure-dependent Timoshenko beam model for vibration analysis of micropipes conveying fluid based on strain gradient theory, Journal of Mathematics, (2012).

[34]          M. Païdoussis, F.S. Interactions, Slender Structures and Axial Flow, vol, in, 1Academic Press, London, 1998.

[35]          Y. Zhang, X. Liu, J. Zhao, Influence of temperature change on column buckling of multiwalled carbon nanotubes, Physics Letters A, 372 (2008) 1676-1681.

[36]          T.B. Benjamin, Dynamics of a system of articulated pipes conveying fluid. II. Experiments, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 261 (1961) 487-499.

[37]          A. Nayfeh, D. Mook, Nonlinear oscillations. 1979, John Willey and Sons, New York.

[38]          S. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, in, Ph. D. Thesis, Shanghai Jiao Tong University, 1992.

[39]          S. Liao, Beyond perturbation: introduction to the homotopy analysis method, CRC press, 2003.

[40]          J.-H. He, Max-min approach to nonlinear oscillators, International Journal of Nonlinear Sciences and Numerical Simulation, 9 (2), 207-210, 2008, (2008).

[41]          Y. Wei, X. Wang, X. Wu, Y. Bai, Theoretical and experimental researches of size effect in micro-indentation test, Science in China Series A: Mathematics, 44 (2001) 74-82.

[42]          N. Marakala, R. KADOLI, Thermally induced vibration of a simply supported beam using finite element method, International Journal of Engineering Science & Technology, 2 (2010) 7874-7879.

[43]          A. Witvrouw, A. Mehta, The use of functionally graded poly-SiGe layers for MEMS applications, in:  Materials Science Forum, Trans Tech Publ, 2005, pp. 255-260.

[44]          Z. Lee, C. Ophus, L. Fischer, N. Nelson-Fitzpatrick, K. Westra, S. Evoy, V. Radmilovic, U. Dahmen, D. Mitlin, Metallic NEMS components fabricated from nanocomposite Al–Mo films, Nanotechnology, 17 (2006) 3063.

[45]          M. Rahaeifard, M. Kahrobaiyan, M. Ahmadian, Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials, in, ASME, 2009.

[46]          G. Sheng, X. Wang, Dynamic characteristics of fluid-conveying functionally graded cylindrical shells under mechanical and thermal loads, Composite Structures, 93 (2010) 162-170.

[47]          M. Asghari, M. Rahaeifard, M. Kahrobaiyan, M. Ahmadian, The modified couple stress functionally graded Timoshenko beam formulation, Materials & Design, 32 (2011) 1435-1443.

[48]          [J. Reddy, Microstructure-dependent couple stress theories of functionally graded beams, Journal of the Mechanics and Physics of Solids, 59 (2011) 2382-2399.

[49]          A. Nateghi, M. Salamat-Talab, J. Rezapour, B. Daneshian, Size dependent buckling analysis of functionally graded micro beams based on modified couple stress theory, Applied Mathematical Modelling, 36 (2012) 4971-4987.

[50]          L.-L. Ke, Y.-S. Wang, J. Yang, S. Kitipornchai, Nonlinear free vibration of size-dependent functionally graded microbeams, International Journal of Engineering Science, 50 (2012) 256-267.

[51]          J. Reddy, J. Kim, A nonlinear modified couple stress-based third-order theory of functionally graded plates, Composite Structures, 94 (2012) 1128-1143.

[52]          M. Asghari, Geometrically nonlinear micro-plate formulation based on the modified couple stress theory, International Journal of Engineering Science, 51 (2012) 292-309.

[53]          L.-L. Ke, J. Yang, S. Kitipornchai, M.A. Bradford, Bending, buckling and vibration of size-dependent functionally graded annular microplates, Composite Structures, 94 (2012) 3250-3257.

[54]          S. Sahmani, R. Ansari, R. Gholami, A. Darvizeh, Dynamic stability analysis of functionally graded higher-order shear deformable microshells based on the modified couple stress elasticity theory, Composites Part B: Engineering, (2013).

[55]          R. Ansari, R. Gholami, S. Sahmani, Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory, Composite Structures, 94 (2011) 221-228.

[56]          M. Kahrobaiyan, M. Rahaeifard, S. Tajalli, M. Ahmadian, A strain gradient functionally graded Euler–Bernoulli beam formulation, International Journal of Engineering Science, 52 (2012) 65-76.

[57]          B. Zhang, Y. He, D. Liu, Z. Gan, L. Shen, A novel size-dependent functionally graded curved mircobeam model based on the strain gradient elasticity theory, Composite Structures, 106 (2013) 374-392.

[58]          S. Sahmani, R. Ansari, On the free vibration response of functionally graded higher-order shear deformable microplates based on the strain gradient elasticity theory, Composite Structures, (2012).

[59]          H. Sadeghi, M. Baghani, R. Naghdabadi, Strain gradient elasticity solution for functionally graded micro-cylinders, International Journal of Engineering Science, 50 (2012) 22-30.

[60]          M. Salamat-talab, F. Shahabi, A. Assadi, Size dependent analysis of functionally graded microbeams using strain gradient elasticity incorporated with surface energy, Applied Mathematical Modelling, 37 (2013) 507-526.