Nonlocal Dispersion Analysis of a Fluid – Conveying Thermo Elastic Armchair Single Walled Carbon Nanotube Under Moving Harmonic Excitation
الموضوعات :M Mahaveersree Jayan 1 , R Kumar 2 , R Selvamani 3 , J Rexy 4
1 - Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore, Tamil Nadu, India
2 - Department of Mathematises, Kurukshetra University, Kurukshetra, Haryana, India
3 - Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore, Tamil Nadu, India
4 - Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore, Tamil Nadu, India
الکلمات المفتاحية: Harmonic load, Newmarks’s direct integration method, Armchair, Nonlocal model, Thermo elastic nanotube,
ملخص المقالة :
In this work, the nonlocal elastic waves in a fluid conveying armchair thermo elastic single walled carbon nanotube under moving harmonic load is studied using Eringen nonlocal elasticity theory via Euler Bernoulli beam equation. The governing equations that contains partial differential equations for single walled carbon nanotube is derived by considering thermal and Lorenz magnetic force. The small scale interactions induced by the nano tubes are simulated by the non-local effects. The time domain responses are obtained by using both modal super position method and Newmarks’s direct integration method. The effect of nonlocal parameter, thermal load, magnetic field of the moving harmonic load on the dynamic displacement of SWCNT is discussed. The results obtained show that the dynamic displacement of fluid conveying SWCNT ratio is significantly affected by the load velocity and the excitation frequency. This type of results presented here, will provide useful information for researchers in structural nano science to understand the small scale response of elastic waves coupled with thermo elasticity and some field forces.
[1] Lijima S., 1991, Synthesis of carbon nanotubes, Nature 354: 56-58.
[2] Eringen A.C., 1983, On differential equation of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54: 4703-4710.
[3] Peddieson T., Buchanan G.R., McNitt R.P., 2003, Application of nonlocal continuum model of technology, International Journal of Engineering Sciences 41: 305-312.
[4] Lu P., Lee L.P., Lu C., Zhang P.Q., 2006, Dynamic properties of flexural beams using nonlocal elasticity model , Journal of Applied Physics 99: 073510-9.
[5] Aydogdu M., Arda M., 2016, Torsional vibration analysis of double walled carbon nanotubes using nonlocal elasticity, International Journal of Mechanical Designs 12(1): 71-84.
[6] Civalek O., Demir C., Akgoz B., 2009, Static analysis of single walled carbon nanotubes based on eringen’s nonlocal elasticity theory, Journal of Sound Vibrations 2: 47-50.
[7] Yamabe T., 1995, Recent development of carbon nanotube, Synthetic Metals 70: 1511-1518.
[8] Wu Y., Zhang Y., Leung A.Y., Zhong W., 2006, En energy- equivalent model on studying the mechanical properties of single walled carbon nanotubes, Thin- Walled Structures 44: 667-676.
[9] Baghdadi H., Tounsi A., Zidour A., Benzairi A., 2014, Thermal effect on vibration charecterstics of armchair and zigzag single walled carbon nanotubes using nonlocal parabolic beam theory, Nanotubes and Carbon Nanostructures 23: 266-272.
[10] Naceri M., Zidour M., Semmah A., Houari M.S.A., Benzair A., Tounsi A., 2011, Sound wave propagation in armchair single walled carbon nanotubes under thermal environment, Journal of Applied Physics 110: 124322-7.
[11] Bedia W.A., Benzair A., Semmah A., Tounsi A., Mahmoud S.R., 2015, On the thermal buckling characteristics of armchair single-walled carbon nanotube embedded in an elastic medium based on nonlocal continuum elasticity, Journal of Physics 45(2): 225-233.
[12] Murmu T., Pradhan S.C., 2010, Thermal effect on stability of embedded carbon nanotubes, Computational Materials Science 47: 721-726.
[13] Narender S., Gopalakrishnan S., 2012, Temperature effects on wave propagation in nanoplates, Composites Part -B Engineering 43: 1275-1281.
[14] Ebrahimi F., Mahmoodi F., 2018, Vibration analysis of carbon nanotubes with multiple cracks in thermal environment, Advances in Nano Research 6(1): 2287-2388.
[15] Ebrahimi F., Boreiry M., Shaghaghi G.R., 2018, Nonlinear vibration analysis of electro – hygro - thermally actuated embedded nanobeams with various with various boundary conditions, Microsystem Technologies 24(12): 5037-5054.
[16] Yoon J., Ru C.Q., Mioduchowski A., 2005, Vibration and instability of carbon nanotubes conveying fluid, Composites Science and Technologies 65: 1326-1336.
[17] Yoon J., Ru C.Q., Mioduchowski A., 2006, Flow –induced flutter instability of cantilever carbon nanotubes, International Journal of Solid Structures 43: 3337-3349.
[18] Zhang Y.Q., Liu X., Liu G.R., 2007, Thermal effect on transverse vibration of double walled carbon nanotube, Nanotechnology 18: 445701-7.
[19] Chang T.P., 2012, Thermal- mechanical vibration and instability of a fluid conveying single walled carbon nanotube embedded in a n elastic medium based on nonlocal elasticity theory, Applied of Mathematical Modelling 36: 1964-1973.
[20] Wang L., 2010, Wave propagation of fluid conveying single walled carbon nanotubes via gradient elasticity theory, Computational Materials Sciences 49: 761-766.
[21] Mohammad H., Goughari S., 2016, Vibration and instability analysis of nanotubes conveying fluid subjected to a longitudinal magnetic field, Applied Mathematical Modelling 40: 2560-2576.
[22] Kiani K., Mehri B., 2010, Assessment of nanotubes structures under a moving nanoparticle using nonlocal beam theories, Journal of Sound Vibrations 329(11): 2241 - 2264.
[23] Simsek M., Kocaturk T., 2009, Nonlinear dynamic analysis of an eccentrically prestressed damped beam under a concentrated moving harmonic load, Journal of Sound Vibrations 320: 235-253.
[24] Simsek M., Kocaturk T., 2009, Free and forced vibration of functionally graded beam subjected to concentrated moving harmonic load, Composites Structures 90: 465-473.
[25] Simsek M., 2010, Vibration of a single walled carbon nanotube under action of a moving harmonic load based on nonlocal elasticity theory, Physica E: Low -Dimensional Systems and Nanostructures 43(1): 182-191.
[26] Fryba L., 1972, Vibration of Solids and Structures under Moving Loads, Noordhoff International, Groningen, The Netherlands.
[27] Simsek M., 2011, Nonlocal effect in the forced vibration of an elastically connected double- carbon nanotube system under a moving nanoparticle, Composites Materials Sciences 50: 2112-2123.
[28] Wang Q., Liew K.M., 2007, Application of nonlocal continuum mechanics to static analysis of micro and nano structure, Physics Letters A 363(3): 236-242.
