Free tangential vibration of cracked nanotubes incorporating scale effects using doublet mechanics
Subject Areas : Analytical and Numerical Methods in Mechanical Design
Alireza Fatahi-Vajari
1
,
Zahra Azimzadeh
2
1 -
2 -
Keywords: Tangential vibration, Cracked nanotube, Doublet mechanics, Natural frequency, Crack severity.,
Abstract :
This paper investigates the free tangential vibration of cracked nanotubes with considering scale parameter under various boundary conditions. The cracked nanotube is modeled by dividing it into two segments connected by a linear spring. The stiffness of the spring is dependent to the crack severity and obtained using fracture mechanics principles. Governing equations and corresponding boundary conditions are derived with the aid of doublet mechanics (DM). The natural frequencies are obtained analytically with solving characteristics equation and the influence of the crack severity, boundary conditions, tube chirality, and the dimensions of nanotube on the free tangential vibration of cracked nanotubes is studied in detail. It was shown that the frequency decreases with increase of the crack severity and scale parameter. This reduction is more apparent when the boundaries of the beam are changed from free end to clamped one. In addition, when the crack location is near the support, a larger decrease in the frequency can be observed. To validate accuracy and efficiency of the present method, the results obtained herein are compared with the available results in the literatures and good agreement is observed.
[1] Ahmed Saimi, Ismail Bensaid and Ömer Civalek, "A study on the crack presence effect on dynamical behaviour of bi-directional compositionally imperfect material graded micro beams", Compos. Struct., Vol. 316, No. 15, pp. 1170302, (2023).
[2] K. Larkin, M. Ghommem, A. Hunter and A. Abdelkefi, "Crack severity and size dependent effects on the effectiveness and operability of micro/nanogyroscopes", Int. J. Solids Struct., Vol. 216, pp. 94-107, (2021).
[3] A. Fatahi-Vajari, A. Imam, "Axial vibration of single-walled carbon nanotubes using doublet mechanics", Indian J. Phys., Vol. 90, No. 4, pp. 447–455, (2016).
[4] Aleksandar Nikolić and Slaviša Šalinić, "Free vibration analysis of cracked beams by using rigid segment method", Appl. Math. Modell. , Vol. 84, pp. 158-172, (2020).
[5] A. Fatahi-Vajari and Z. Azimzadeh , "Analysis of nonlinear axial vibration of single-walled carbon nanotubes using Homotopy perturbation method", Indian J. Phys., November Vol. 92, No. 11, pp. 1425–1438, (2018).
[6] Seyyed Sajad Mousavi Nejad Souq, Faramarz Ashenai Ghasemi and Mir Masoud Seyyed Fakhrabadi, "A comparative study of crack detection in nanobeams using molecular dynamics, analytical and finite element methods", Journal of Computational Applied Mechanics, Vol. 52, No. 3, pp. 408-422, (2021).
[7] Siva Sankara Babu Chinka, Srinivasa Rao Putti and Bala Krishna Adavi, "Modal testing and evaluation of cracks on cantilever beam using mode shape curvatures and natural frequencies", Struct., Vol. 32, pp. 1386-1397, (2021).
[8] Alireza Fatahi-Vajari and Zahra Azimzadeh, "Axial vibration of single-walled carbon nanotubes with fractional damping using doublet mechanics", Indian J. Phys., Vol. 94, No. 7, pp. 975-986, (2019).
[9] Linda J. Johnston a, Norma Gonzalez-Rojano b, Kevin J. Wilkinson c and Baoshan Xing, "Key challenges for evaluation of the safety of engineered nanomaterials", NanoImpact, Vol. 18, pp. 100219, (2020).
[10] Md. Shumon Miaa, Md. Shahidul Islam, Udayan Ghosh, "Modal Analysis of Cracked Cantilever Beam by Finite Element Simulation", Procedia Eng., Vol. 194, pp. 509 – 516, (2017).
[11] Swapnil Dokhe and Shailesh Pimpale, "Effects of crack on modal frequency of cantilever beam", International journal of research in aeronautical and mechanical engineering, Vol.3, No. 8, pp. 24-38, (2015).
[12] P. Y. Ghodke, D. H. Tupe and G. R. Gandhe, "Modal Analysis Of Cracked Continuous Beam Using ANSYS", International Research Journal of Engineering and Technology (IRJET), Vol. 04, No. 02, pp. 86-93, (2017).
[13] Qiang Lua & Baidurya Bhattacharya, "Fracture resistance of zigzag single walled carbon nanotubes, Nanotechnology", Institute of Physics, vol. 17, pp. 1323 - 1332, (2006).
[14] Aleksandar Nikolić and Slaviša Šalinić, "Free vibration analysis of cracked beams by using rigid segment method", Appl. Math. Modell., Vol. 84, pp. 158-172, (2020).
[15] A. Fatahi-Vajari and A. Imam, "Lateral Vibrations of Single-Layered Graphene Sheets Using Doublet Mechanics", Journal of Solid Mechanics, Vol. 8, No. 4, pp. 875-894, (2016).
[16] A Fatahi-Vajari and A Imam, "Analysis of radial breathing mode of vibration of single-walled carbon nanotubes via doublet mechanics", ZAMM. Vol. 96, No. 9, pp. 1020-1032, (2016).
[17] Sri Aurobindo Panda, Sumita Choudhary, Sushil Barala, Arnab Hazra, Suchit Kumar Jena and Subhashis Gangopadhyay, "Surface energy and stress driven growth of extremely long and high-density ZnO nanowires using a thermal step-oxidation process", RSC Adv., Vol. 14, pp. 28086–28097, (2024).
[18] Bingsen Fan, Xiaolong Li, Shengjie Xu, Yanhui Zhong, Bei Zhang and Xiaofeng Liu, "Experimental Study on the Mechanical Properties of NanoSilicon Modified Polyurethane Crack Repair Materials", Processes, Vol. 12, No. 8, pp. 1735.1-1735.17, (2024).
[19] Abbas Rahi and Hamed Petoft, "Free vibration analysis of multi-cracked micro beams based on Modified Couple Stress Theory", Journal of Theoretical and Applied Vibration and Acoustics, Vol. 4, No. 2, pp. 205-222, (2018).
[20] L. Anitha and J. Sudha, "Size-dependent vibration analysis of cracked micro beams reinforced with functionally graded boron nitride nanotubes in composite structures", journal of mechanics of continua and mathematical sciences, Vol. 19, No. 3, pp. 22-39, (2024).
[21] R. Nazemnezhad and P. Fahimi, "Free torsional vibration of cracked nanobeams incorporating surface energy effects", Appl. Math. Mech. -Engl. Ed., Vol. 38, No. 2, pp. 217–230, (2017).
[22] Mustafa Ö Yayli, Suheyla Y Kandemir, and Ali E Çerçevik, "Torsional vibration of cracked carbon nanotubes with torsional restraints using Eringen’s nonlocal differential model", J. Low Freq. Noise Vibr. Act. Control., Vol. 38, No. 1, pp. 70-87, (2019).
[23] O. Ifayefunmi and S.H. Sheikh Md Fadzullah, "Buckling behaviour of imperfect axially compressed cylinder with an axial crack", International Journal of Automotive and Mechanical Engineering, Vol. 14, No. 1, pp. 3837-3848, (2017).
[24] K. Yazdchi and A. R. Gowhari Anaraki, "Carrying capacity of edge-cracked columns under concentric vertical loads", Acta Mech, Vol. 198, pp. 1–19, (2008).
[25] Seyyed M. Hasheminejad, Behnam Gheshlaghi, Yaser Mirzaei and Saeed Abbasion, "Free transverse vibrations of cracked nanobeams with surface effects", Thin Solid Films, Vol. 519, No.8, pp. 2477-2482, (2011).
[26] W. Zhang, R. C. Picu, and N. Koratkar, "Suppression of fatigue crack growth in carbon nanotube composites", Appl. Phys. Lett. , Vol. 91, pp. 193109.1-193109.3, (2007).
[27] H. S. Rane, R.B. Barjibhe and A.V. Patil, "Free Vibration Analysis of Cracked Structure", International Journal on Mechanical Engineering and Robotics (IJMER), Vol. 2, No. 6, pp. 34-41, (2014).
[28] Jung-Chang Hsu, Haw-Long Lee and Win-Jin Chang, "Longitudinal vibration of cracked nanobeams using nonlocal elasticity theory", Curr. Appl Phys., Vol. 11, pp. 1384-1388 (2011).
[29] K.V. Singh, "Transcendental inverse eigenvalue problems in damage parameter estimation", Mech. Syst. Signal Process., Vol. 23, No. 6, pp. 1870-1883, (2009).
[30] Mustafa Özgür Yaylı and Ali Erdem Çerçevik, "Axial vibration analysis of cracked nanorods with arbitrary boundary conditions", J. Vibroeng., Vol. 17, No. 6, pp. 2907-2921, (2015).
[31] Masih Loghmani and Mohammad Reza Hairi Yazdi, "An analytical method for free vibration of multi cracked and stepped nonlocal nanobeams based on wave approach", Results Phys., Vol. 11, pp. 166-181, (2018).
[32] Farzad Ebrahimi and Fatemeh Mahmoodi , "Vibration analysis of carbon nanotubes with multiple cracks in thermal environment", Adv. Nano Res., Vol. 6, No. 1, pp 57-80, (2018).
[33] M. Dilena and A. Morassi, "The use of antiresonances for crack detection in beams", J. Sound Vib., Vol. 276, pp. 195–214, (2004).
[34] H. Tada, P.C.Paris and G.R.Irwin, The stress analysis of cracks handbook, ASME press, Newyork, (2000).
