فهرست:
فصل اول: مباحث نظری ................................................................................................1
1-1- مقدمهای بر نانوفناوری.. 2
1-1-1- کاربرد فناوری نانو. 3
1-1-2- تئوریهای مختلف اثرات اندازه. 4
1-2- تیر پیچیده شده. 5
1-3- موج.. 8
1-3-1- انواع موج.. 9
1-3-2- کمیتهای امواج مکانیکی.. 9
1-4- پیشینه و هدف تحقیق.. 10
فصل دوم: معادلات حاکمه حرکت نانو تیر پیچیده شده 17
2-1- مقدمه. 18
2-2- میدان جابهجایی.. 18
2-3- روش حداقل انرژی.. 23
2-4- تئوری گرادیان کرنشی.. 24
2-5- معادله حاکمه نانو تیر پیچیده شده. 25
2-6- تئوری غیر موضعی ارینگن.. 32
2-7- انرژی جنبشی.. 35
2-8- کار خارجی.. 36
2-9- معادلات حرکت... 38
3 فصل سوم: نتایج عددی و بحث .....................................................................................43
3-1- بررسی انتشار موج نانو تیر پیچیده شده. 44
3-2- ارتعاشات نانو تیر پیچیده شده. 46
3-3- کمانش.... 48
3-4- نتایج عددی وبحث... 52
3-4-1- تحلیل انتشار موج نانو تیر پیچیده شده. 53
3-4-1-1- سرعت فاز. 53
3-4-1-2- سرعت گروه. 57
3-4-1-3- فرکانس قطع.. 61
3-4-1-4- فرکانس فرار. 63
3-4-2- تحلیل کمانش نانو تیر پیچیده شده. 68
3-4-3- تحلیل ارتعاشات نانو تیر پیچیده شده. 71
فصل چهارم: نتیجهگیری ..................................................................................................75
4-1- بحث و نتیجه گیری.. 76
4-2- پیشنهاد برای ادامه کار. 77
منابع و ماخذ 78
منبع:
1
1.Giannakopoulos A.W., Aravas N., A. Papageorgopoulou A. and Vardoulakis I., A structural gradient theory of torsion, the effects of pretwist, and the tension of pre-twisted DNA, International Journal of Solids and Structures, 50, pp. 3922-3933, 2013.
Ho Sh.H., and Chen Ch.K., Free transverse vibration of an axially loaded non-uniform spinning twisted Timoshenko beam using differential transform, International Journal of Mechanical Sciences, 48, pp. 1323-1331, 2006.
Leung A.Y.T., and Fan J., Natural vibration of pre-twisted shear deformable beam systems subject to multiple kinds of initial stresses, Journal of Sound and Vibration, 329, pp. 1901–1923, 2010.
Yu A.M., Yang X.G. and Nie G.H., Generalized coordinate for warping of naturally curved and twisted beams with general cross-sectional shapes. International Journal of Solids and Structures, 43, pp. 2853-2876, 2006.
Wang Q., and Yu W., A refined model for thermoelastic analysis of initially curvedand twisted composite beams, Engineering Structures, 48, pp. 233-244, 2013.
Mustapha K.B., and Zhong Z.W., Wave propagation characteristics of a twisted micro scale beam, International Journal of Engineering Science, 53, pp. 46–57, 2012.
CˇešarekP., Saje M., and Zupan D., Kinematically exact curved and twisted strain-based beam, International Journal of Solids and Structures, 49, pp. 1802–1817, 2012.
Rao J.S., and Carnegie W., Solution of the equations of motion of coupled-bending bending torsion vibrations of turbine blades by the method of Ritz-Galerkin,International Journal of Mechanical Sciences, 12, pp. 875-882, 1970.
Chen W.R., Effect of local Kelvin-Voigt damping on eigenfrequencies of cantilevered twisted Timoshenko beams, Procedia Engineering, 79, pp. 160-165, 2014.
Subrahmanyam K.B., and Rao J.S., Coupled bending-bending vibrations of pretwisted tapered cantilever beams treated by the reissner method, Journal of Sound and Vibration, 82(4), pp.577-592, 1982.
Chen W.R., On the vibration and stability of spinning axially loaded pre-twisted Timoshenko beams, Finite Elements in Analysis and Design, 46, pp. 1037-1047, 2010.
Sinha S.K., and Turner K.E., Natural frequencies of a pre-twisted blade in a centrifugal force field, Journal of Sound and Vibration, 330, pp. 2655-2681, 2011.
Chen W.R., Hsin S.W. and Chu T.H., Vibration analysis of twisted Timoshenko beams with internal Kelvin-Voigt damping, Procedia Engineering, 67, pp. 525-532, 2013.
Banerjee J. R., Free vibration analysis of a twisted beam using the dynamic stiffness method, 38, pp. 6703-6722, 2001.
Sabuncu M., and Evran K., The dynamic stability of a rotating pre-twisted asymmetric cross-section Timoshenko beam subjected to lateral parametric excitation, International Journal of Mechanical Sciences, 48, pp. 878–888, 2006.
Mohammadimehr M., Saidi A.R., Ghorbanpour Arani A., Arefmanesh A. and Han Q.,Torsional buckling of a DWCNT embedded on Winkler and Pasternak foundations using nonlocal theory, pp.1289-1299, 2010.
Mohammadimehr M., and Mahmoudian M., Bending and free vibration analysis of nonlocal functioonally graded nanocomposite Timoshenko beam modal reinforced by SWBNNT based on modified coupled stress theory, Journal of Nanostructures, Accepted 1 May 2014.
Ghorbanpour Arani A., Amir S., Shajari A.R. and Mozdianfard M.R.,“Electro-thermo-mechanical buckling of DWBNNTs embedded in bundle of CNTs using nonlocal piezoelasticity cylindrical shell theory”, CompositesPart B: Engineering, 225(12), pp. 195-203, 2011.
Ghannadpour S.A.M., Mohammadi B. and Fazilati J., Bending, buckling and vibration problems of nonlocal Euler beams using Ritz method, Composite Structures, 96, pp. 584–589, 2013.
Wang C.M., Zhang Y.Y. and He X.Q., Vibration of nonlocal Timoshenko beams, Nanotechnology, 18, pp. 9-18, 2007.
Salehi-Khojin A., and Jalili N., Buckling of boron nitride nanotube reinforced piezoelectric polymeric composites subject to combined electro–thermo-mechanical loadings, Composites Science and Technology, 68, pp. 1489-1501, 2008.
Murmu T., and Pradhan S.C., Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM, Physica E, 41, pp. 1232-1239, 2009.
Mohammadimehr M. and Salemi M., Bending and buckling analysis of functionally graded mindlin nanao-plate model based on strain gradient elasticity theory, Indian J.Sci.Res, 1(2), pp. 587-594, 2014.
Ghorbanpour Arani A., Kolahchi.R. and Vossough.H., Nonlocal wave propagation in an embedded DWBNNT conveying fluid via strain gradient theory, Physica B, 407, pp. 4281–4286, 2012.
S. Narendar S., Gupta S.S. and Gopalakrishnan S., Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler–Bernoulli beam theory, Applied Mathematical Modelling, 36, pp. 4529-4538, 2012.
Aydogdu M., Longitudinal wave propagation in multiwalled carbon nanotubes, Composite Structures, 107, pp. 578-584, 2014.
Wang L., Wave propagation of fluid-conveying single-walled carbon nanotubes via gradient elasticity theory, Computational Materials Science, 49, pp. 761-766, 2010.
Sun D., Song-Nan Luo S.L., Wave propagation of functionally graded material plates in thermal environments, Ultrasonics, 51, pp. 940-952, 2011.
Liew K.M., Wang Q., Analysis of wave propagation in carbon nanotubes via elastic shell theories, International Journal of Engineering Science, 45, pp. 227-241, 2007.
Reddy JN. Energy principles and variational methods in applied mechanics. John Wiley & Sons; 2002.
Wang B., Zhou Sh., Zhao J. and, Chen X., A size-dependent Kirchhoff micro-plate model based on strain gradient elasticity theory, European Journal of Mechanics A/Solids, 30, pp. 517-524, 2011.
A. L, Vibration of Shells, Ohio State University. pp. 1-175 1993.
Paliwal D.N., Pendey R.K. and Nath T., Free vibrations of circular cylindrical shell on Winkler and Pasternak foundations, International Journal of Pressure Vessels and Piping, 69, pp. 79-89, 1996.
Thai H.T., and Kim S.E., A size-dependent functionally graded Reddy plate model based on a modified couple stress theory, Composites: Part B, 45, pp. 1636-1645, 2013.