LONGITUDINAL FORCED VIBRATION ANALYSIS OF POROUS A NANOROD

Year 2019, Volume: 7 Issue: 4, 736 - 743, 19.12.2019

Şeref Doğuşcan Akbaş

https://doi.org/10.21923/jesd.553328

Cited By: 7

Abstract

In this paper, longitudinal
vibration responses of a nanorod subjected to harmonic external load are
investigated with porosity based on Nonlocal Elasticity theory. The governing
equation of the problem is solved by analytically. Frequency equations and the
forced vibration displacements are obtained exactly. In the numerical examples,
effects of the nonlocal, dynamic, geometry and porosity parameters on forced
vibration responses of the nanorod are investigated.

Keywords

Nanorods, Nonlocal Elasticity Theory, Porosity, Forced Vibration

BOŞLUK YAPILI NANO BİR ÇUBUK ELEMANIN BOYUNA ZORLANMIŞ TİTREŞİM ANALİZİ

Abstract

Bu çalışmada, boşluk yapılı nano çubuk bir elemanın harmonik bir
dış kuvvet etkisi altında zorlanmış boyuna titreşim cevapları, yerel olmayan
elastisite teorisi ile incelenmiştir. Probleme ait hareket denklemi analitik
olarak çözülmüş olup, frekans denklemleri ile zorlamış titreşim yer
değiştirmeleri kesin bir analitik değerde elde edilmiştir. Sayısal çalışmada,
yerel olmayan parametre, dinamik, geometrik ve boşluk oranı parametrelerinin,
nano çubuğun zorlanmış titreşim cevaplarına olan etkileri incelenmiştir.

Keywords

Nano Çubuklar, Yerel Olmayan Elastisite Teorisi, Boşluk Oranı, Zorlanmış Titreşim

References

• Ahmed, R. A., Fenjan, R. M., & Faleh, N. M. (2019). Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections. Geomechanics and Engineering, 17(2), 175-180.
• Akbaş, Ş.D. (2014a). Free vibration of axially functionally graded beams in thermal environment. International Journal Of Engineering & Applied Sciences, 6(3), 37-51.
• Akbaş, Ş.D. (2014b). Wave propagation analysis of edge cracked circular beams under impact force. PloS one, 9(6), e100496.
• Akbaş, Ş.D. (2014c). Wave propagation analysis of edge cracked beams resting on elastic foundation. International Journal of Engineering & Applied Sciences, 6(1), 40-52.
• Akbaş, Ş.D. (2015). Free vibration and bending of functionally graded beams resting on elastic foundation. Research on Engineering Structures and Materials, 1(1), 25-37.
• Akbaş, Ş.D., 2016a. Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium. Smart Structures and Systems, 18(6), 1125-1143.
• Akbaş, Ş.D., 2016b. Analytical solutions for static bending of edge cracked micro beams. Structural Engineering and Mechanics, 59(3),579-599.
• Akbaş, Ş.D., 2017a. Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory, International Journal of Structural Stability and Dynamics, 17(3),1750033.
• Akbaş Ş.D., 2017b. Static, Vibration, and Buckling Analysis of Nanobeams, in Nanomechanics, ed. A. Vakhrushev (InTech ), pp.123-137.
• Akbaş, Ş.D., 2017c. Stability of A Non-Homogenous Porous Plate by Using Generalized Differantial Quadrature Method, International Journal of Engineering & Applied Sciences, 9(2), 147-155.
• Akbaş, Ş.D., 2017d. Forced vibration analysis of functionally graded nanobeams, International Journal of Applied Mechanics, 9(07), 1750100.
• Akbaş, Ş.D. (2017e). Thermal effects on the vibration of functionally graded deep beams with porosity. International Journal of Applied Mechanics, 9(05), 1750076.
• Akbaş, Ş.D. 2018a. Forced vibration analysis of cracked functionally graded microbeams, Advances in Nano Research, 6(1), 39-55.
• Akbaş, Ş.D., 2018b. Forced vibration analysis of cracked nanobeams, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40(8), 392.
• Akbaş, Ş.D. (2018c) Investigation on Free and Forced Vibration of a Bi-Material Composite Beam. Journal of Polytechnic, 21(1), 65-73.
• Akbaş, Ş.D. (2018d). Investigation of static and vibration behaviors of a functionally graded orthotropic beam. Journal of Balıkesir University Institute of Science and Technology, 20(1), 69-82.
• Akbaş, Ş D. (2018e). Forced vibration analysis of functionally graded porous deep beams. Composite Structures, 186, 293-302.
• Akgöz, B. and Civalek, Ö., 2013). Free vibration analysis of axially functionally graded tapered Bernoulli-Euler microbeams based on the modified couple stress theory. Composite Structures, 98:314-322.
• Akgöz, B. and Civalek, Ö. (2014a) Thermo-mechanical buckling behavior of functionally graded microbeams embedded in elastic medium. International Journal of Engineering Science, 85:90-104.
• Akgöz, B. and Civalek, Ö., 2014b. Longitudinal vibration analysis for microbars based on strain gradient elasticity theory, Journal of Vibration and Control, 20(4), 606-616.
• Akgöz, B. and Civalek, Ö. (2017). Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams. Composites Part B: Engineering, 129, 77-87.
• Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R., 2015. Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position, Composite Structures, 125, 621-630.
• Ansari, R., Gholami, R. and Sahmani, S., 2011. Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory, Composite Structures, 94(1): 221-228.
• Arda, M. and Aydogdu, M., 2017. Longitudinal Vibration of CNTs Viscously Damped in Span, International Journal Of Engineering & Applied Sciences, 9(2), 22-38.
• Arda, M., 2018. Vibration Analysis of an Axially Loaded Viscoelastic Nanobeam, Int J Eng, 10(3), 252-263.
• Asghari, M., Ahmadian, M.T., Kahrobaiyan, M.H. and Rahaeifard, M., 2010. On the size-dependent behavior of functionally graded micro-beams. Materials and Design, 31(5):2324-2329.
• Avcar, M. (2010). Free Vibration of Randomly and Continuously NonHomogenous Beams with Clamped Edges Resting On Elastic Foundation. Journal of Engineering Science and Design, 1(1), 33-38.
• Avcar, M. and Mohammed, W.K.M. (2017). Examination of The Effects of Winkler Foundation and Functionally Graded Material Properties on The Frequency Parameters of Beam. Journal of Engineering Science and Design, 5(3), 573-580.
• Avcar, M. and Mohammed, W.K.M. (2018). Free vibration of functionally graded beams resting on Winkler-Pasternak foundation. Arabian Journal of Geosciences, 11(10), 232.
• Barati, M. R., & Zenkour, A. M. (2018). Analysis of postbuckling of graded porous GPL-reinforced beams with geometrical imperfection. Mechanics of Advanced Materials and Structures, 1-9.
• Belkorissat, I., Houari, M. S. A., Tounsi, A., Bedia, E. A. and Mahmoud, S. R., 2015. On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model, Steel and Composite Structures, 18(4), 1063-1081.
• Civalek, Ö., Demir, Ç. and Akgöz, B., 2009. Static analysis of single walled carbon nanotubes (SWCNT) based on Eringen’s nonlocal elasticity theory, International Journal Of Engineering & Applied Sciences, 1(2), 47-56.
• Civalek, Ö. and Kiracioglu, O. (2010). Free vibration analysis of Timoshenko beams by DSC method. International Journal for Numerical Methods in Biomedical Engineering, 26(12), 1890-1898.
• Civalek, Ö. and Demir, C. (2011). Buckling and bending analyses of cantilever carbon nanotubes using the euler-bernoulli beam theory based on non-local continuum model. Asian Journal of Civil Engineering, 12(5), 651-661.
• Chaht, F. L., Kaci, A., Houari, M. S. A., Tounsi, A., Bég, O. A. and Mahmoud, S. R., 2015. Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect, Steel and Composite Structures, 18(2), 425-442.
• Demir, Ç. and Civalek, Ö. 2016. Bending and Vibration of Single-Layered Graphene Sheets. Journal of Engineering Science and Design, 4(3), 173-183.
• Demir, Ç. and Civalek, Ö. (2017). A new nonlocal FEM via Hermitian cubic shape functions for thermal vibration of nano beams surrounded by an elastic matrix. Composite Structures, 168, 872-884.
• Ebrahimi, F., Daman, M., & Jafari, A. (2017). Nonlocal strain gradient-based vibration analysis of embedded curved porous piezoelectric nano-beams in thermal environment. Smart Structures & Systems, 20(6), 709-728.
• Ebrahimi, F., & Barati, M. R. (2018a). Stability analysis of porous multi-phase nanocrystalline nonlocal beams based on a general higher-order couple-stress beam model. Structural Engineering and Mechanics, 65(4), 465-476.
• Ebrahimi, F., & Barati, M. R. (2018b). Propagation of waves in nonlocal porous multi-phase nanocrystalline nanobeams under longitudinal magnetic field. Waves in Random and Complex Media, 1-20.
• Eren, M. and Aydogdu, M. 2018. Finite strain nonlinear longitudinal vibration of nanorods. Advances in Nano Research, 6(4), 323-337.
• Eringen, A.C., 1972. Nonlocal polar elastic continua, International Journal of Engineering Science, 10(1),1-16.
• Eringen, A.C., 1983. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics, 54, 4703–10.
• Hasanyan, D.J., Batra, R.C. and Harutyunyan, S., 2008. Pull-in instabilities in functionally graded microthermoelectromechanical systems, J Therm Stresses, 31,1006–21.
• Hasheminejad, B.S.M., Gheshlaghi, B., Mirzaei, Y., Abbasion, S., 2011. Free transverse vibrations of cracked nanobeams with surface effects, Thin Solid Films, 519, 2477-2482.
• Karami, B., Janghorban, M., & Li, L. (2018). On guided wave propagation in fully clamped porous functionally graded nanoplates. Acta Astronautica, 143, 380-390.
• Karličić, D., Cajić, M., Murmu, T., & Adhikari, S., 2015. Nonlocal longitudinal vibration of viscoelastic coupled double-nanorod systems, European Journal of Mechanics-A/Solids, 49, 183-196.
• Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. ,2012. Nonlinear free vibration of size-dependent functionally graded microbeams, International International Journal of Engineering Science, 50(1),256-267.
• Kocatürk, T. and Akbaş, Ş.D. (2013). Wave propagation in a microbeam based on the modified couple stress theory, Structural Engineering and Mechanics, 46(3),417-431.
• Lam, D.C.C., Yang ,F., Chong, A.C.M., Wang J. and Tong P., 2003. Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids, 51(8),1477–508.
• Li, L., Tang, H., & Hu, Y. (2018). Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature. Composite Structures, 184, 1177-1188.
• Liu, P. and Reddy, J.N., 2011. A Nonlocal curved beam model based on a modified couple stress theory, International Journal of Structural Stability and Dynamics, 11(3),495-512.
• Liu, S.J., Qi, S.H. Zhang, W.M., 2013. Vibration behavior of a cracked micro-cantilever beam under electrostatic excitation, Zhendong yu Chongji/Journal of Vibration and Shock, 32,41-45.
• Loya, J., López-Puente, J., Zaera, R. and Fernández-Sáez, J., 2009. Free transverse vibrations of cracked nanobeams using a nonlocal elasticity model, Journal of Applied Physics, 105(4),044309.
• Mercan, K. and Civalek, Ö. (2017). Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface effect and nonlocal elasticity using the method of HDQ. Composites Part B: Engineering, 114, 34-45.
• Mindlin, R.D. and Tiersten H.F., 1962. Effects of couple-stresses in linear elasticity, Archive for Rational Mechanics and Analysis, 11(1),415–48.
• Mindlin, R.D., 1963. Influence of couple-stresses on stress concentrations, Experimental mechanics, 3(1),1–7.
• Park, S.K. and Gao, X.L., 2006. Bernoulli–Euler beam model based on a modified couple stress theory, Journal of Micromechanics and Microengineering, 16(11),2355-2359.
• Peng, X.-L., Li. X.-F., Tang, G.-J., Shen, Z.-B., 2015. Effect of scale parameter on the deflection of a nonlocal beam and application to energy release rate of a crack, ZAMM - Journal of Applied Mathematics and Mechanics, 95,1428–1438.
• Radić, N. (2018). On buckling of porous double-layered FG nanoplates in the Pasternak elastic foundation based on nonlocal strain gradient elasticity. Composites Part B: Engineering, 153, 465-479.
• Reddy, J.N., 2010. Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates, International Journal of Engineering Science, 48(11), 1507-1518.
• Reddy, J.N., 2011. Microstructure-dependent couple stress theories of functionally graded beams, Journal of the Mechanics and Physics of Solids, 59(11), 2382-2399.
• Roostai, H. and Haghpanahi, M., 2014. Vibration of nanobeams of different boundary conditions with multiple cracks based on nonlocal elasticity theory, Applied Mathematical Modelling, 38,1159–1169.
• Sahmani, S., & Aghdam, M. M. (2018). Nonlinear primary resonance of micro/nano-beams made of nanoporous biomaterials incorporating nonlocality and strain gradient size dependency. Results in physics, 8, 879-892.
• Sahmani, S., Aghdam, M. M., & Rabczuk, T. (2018). Nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets based upon nonlocal strain gradient theory. Composite Structures, 186, 68-78.
• Sedighi, H.M. 2014, The influence of small scale on the pull-in behavior of nonlocal nanobridges considering surface effect, Casimir and Van der Waals attractions, International Journal of Applied Mechanics, 6(03),1450030.
• Shafiei, N., & Kazemi, M. (2017). Buckling analysis on the bi-dimensional functionally graded porous tapered nano-/micro-scale beams. Aerospace Science and Technology, 66, 1-11.
• Şimşek, M., 2016, Axial Vibration Analysis of a Nanorod Embedded in Elastic Medium Using Nonlocal Strain Gradient Theory, Journal of Cukurova University Faculty of Engineering, 31(1), 213-222.
• Toupin, R.A., 1962. Elastic materials with couple stresses. Archive for Rational Mechanics and Analysis, 11(1),385–414.
• Wang, C.M., Xiang, Y., Yang, J. and Kitipornchai, S. 2012. Buckling of nano-rings/arches based on nonlocal elasticity. International Journal of Applied Mechanics, 4(03),1250025.
• Yang, F., Chong, A., Lam, D. and Tong, P., 2002. Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures. 39(10),2731-2743.
• Yayli, M.Ö., 2014. On the axial vibration of carbon nanotubes with different boundary conditions, Micro & Nano Letters, 9(11), 807-811.
• Yayli, M.Ö., Yanik, F. and Kandemir, S.Y., 2015. Longitudinal vibration of nanorods embedded in an elastic medium with elastic restraints at both ends, Micro & Nano Letters, 10(11), 641-644.
• Yaylı, M.Ö. (2018), Free vibration analysis of a rotationally restrained carbon nanotube via nonlocal Timoshenko beam theory, Journal of Balıkesir University Institute of Science and Technology, 20(2), 8-21.
• Zerin, Z. (2012), The Stability Of The Non-Homogenous Cylindrical Shell In The Elastic Medium Subjected To Uniform Hydrostatıc Pressure. Journal of Engineering Science and Design, 2(1), 37-41.