Analytical Study on Longitudinal Vibration of Viscoelastic Cracked Rod under Magnetic Field.

Authors

Department of Mechanical Engineering/Tabriz Branch/ Islamic Azad University/Tabriz/Iran.

Abstract

Rods are one of the most important members in engineering structures and due to the wide application in different mechanical equipments, vibration analysis of them have great importance. Uderstanding the longitudinal vibration of the rod in different support conditions and in the presence of crack is very useful. In this study, vibration analysis of cracked viscoelastic rod in magnetic field is studied. The crack is modeled as the local stiffness reduction of the structure. To consider the more realistic assumptions, in this study and for the first time, viscoelastic behavior is considered for crack. Newton's second law and structural damping are used to obtain the governing equations. Then boundary and inter-boundary conditions are applied at the crack location and characteristic equation of the system is derived. By solving the characteristic equation, the natural frequencies of the rod which in turn depends on boundary conditions and geometrical characteristics, including location and depth of crack, are obtained. To evaluate the accuracy and validity of the mention method, the results are compared with the literature. Finally, The effect of different parameters on the vibration characteristics of the rod is studied.

Keywords

References

[1] سام پور س، معین خواه ح، رحمانی ح (2019)         حل تحلیلی پاسخ گذرای غیرخطی میکروتیر ویسکوالاستیک با تحریک الکتریکی بر اساس تئوری الاستیسیته ریز قطبی. مجله مکانیک سازه­ها و شاره­ها 138-125 :(3)9.
[2] جلیلی م، درعلی­زاده م م (2017) مدلسازی وتحلیل ارتعاشات غیرخطی میکروسکوپ نیروی اتمی در محیط مایع به روش تحلیلی. مجله مدل­سازی در مهندسی 224-209 :(51)15.
[3] قنبری م، حسین­پور س، رضازاده ق (2015) اثرات محیط سیال روی ارتعاشات رزوناتور میکروتیر با استفاده ازتئوری میکروپولار. مجله مهندسی مکانیک مدرس 210-205 :(10)14.
[4] اندخشیده ع، مالکی س، مرعشی س ص (2018) بررسی پدیده‌ی غیرخطی ولتاژ کشیدگی در میکروتیر‌های هدفمند تحت بارگذاری الکترواستاتیک. مجله مکانیک سازه­ها و شاره­ها 151-135 :(3)8.
[5] عطار ع، طهماسبی­پور م، دهقان م (2018) بررسی تاثیر پارامترهای هندسی بر جابه جایی خارج از صفحه میکروتیر پیزوالکتریکی با سطح مقطع T شکل. مجله مکانیک سازه­ها و شاره­ها 9-1 :(4)8.
[6] رهایی فرد م (2019) بررسی اثر تحریک الکترواستاتیک بر رفتار الکترومکانیکی میکرو حسگرهای فشار خازنی. مجله مکانیک سازه­ها و شاره­ها 152-141 :(2)9.
 [7] Lakes R (2009) Viscoelastic materials. Cambridge university press.
[8] Łabędzki P, Pawlikowski R,  Radowicz A (2018)  Axial vibration of bars using fractional viscoelastic material models. Vib Phys Syst 15: 43-65.
[9] McDowell T, Xu X, Warren C, Welcome D, Dong R (2018)  The effects of feed force on rivet bucking bar vibrations. Int J Ind Ergon 67: 145-158.
[10] Zhao W, Yang Y, Niu P (2018)  Frequency and buckling load analysis of an axial compressive bar resting on an elastic foundation. IJLCPE 2(3-4): 210-222.
[11] Liu X, Liu Q, Wu S, Li R, Gao H (2018)  Analysis of the vibration characteristics and adjustment method of boring bar with a variable stiffness vibration absorber. Int J Adv Manuf Technol 98: 95-105.
[12] Nayfeh A (1975) Finite-amplitude longitudinal waves in non-uniform bars. J Sound Vib 42(3): 357-361.
[13] Raman V (1983)  On analytical solutions of vibrations of rods with variable cross sections. Appl 7(5): 356-361.
[14] Li Q, Li G, Liu D (2000)  Exact solutions for longitudinal vibration of rods coupled by translational springs. Int J Mech Sci 42(6): 1135-1152.
[15] Mousavi S, Fariborz S (2012)  Free vibration of a rod undergoing finite strain. J Phys Conf Ser  382: 1-8.
[16] Baghestani A, Fariborz S, Mousavi S (2014) Low-frequency free vibration of rods with finite strain. J Appl Nonlinear Dyn 3(1): 85-93.
]17[ پورجعفری م، فتوحی ع، جلیلی م م (2019) ارتعاشات آزاد طولی میله با سطح مقطع متغییر تحت کرنش محدود. مهندسی مکانیک مدرس 437-429 :(2)19.
 [18] Soleimani Roody B, Fotuhi A, Jalili M (2018)  Nonlinear longitudinal free vibration of a rod undergoing finite strain. Amirkabir J Mech Eng 50(5): 353-356.
[19] Narendar S (2016) Wave dispersion in functionally graded magneto-electro-elastic nonlocal rod. Aerosp Sci Technol 51:42-51.
[20] Güven U (2016) Longitudinal vibration of cracked beams under magnetic field. Mech Syst Signal Process 81: 308-317.
[21] Il’gamo M (2017)  Longitudinal vibrations of a bar with incipient transverse cracks. Mech Solids 52(1): 18-24.
[22] Soleimani Roody B,  Fotuhi R, Jalili M   (2018) Nonlinear longitudinal forced vibration of a rod undergoing finite strain. Proc. Inst Mech Eng Part C 232(12): 2229-2243.
]23[ رضایی م، عرب ملکی و (2019) ارائه حل تحلیلی برای مطالعه رفتار دینامیکی لوله‌های ویسکوالاستیک حامل سیال با اعمال فرم کلی مدل ساختاری. نشریه پژوهشی مهندسی مکانیک ایران 29-6 :(1)21.
 [24] Loghmani M, Yazdi M,  Nikkhah Bahrami M (2018)  Longitudinal vibration analysis of nanorods with multiple discontinuities based on nonlocal elasticity theory using wave approach. Microsyst Technol 24(5): 2445-2461.
[25] Arani A, Maboudi M, Arani A.G, Amir S (2013) 2D-magnetic field and biaxiall in-plane pre-load effects on the vibration of double bonded orthotropic graphene sheets. J Solid Mech 5(2): 193-205.
[26] Kiani K (2014)  Magnetically affected single-walled carbon nanotubes as nanosensors. Mech Res Commun 60: 33-39.
[27] Murmu T, McCarthy M, Adhikari S (2012) Vibration response of double-walled carbon nanotubes subjected to an externally applied longitudinal magnetic field: A nonlocal elasticity approach. J Sound Vib 331(23): 5069-5086.
[28] Murmu T, McCarthy M.A, Adhikari S  (2012) Nonlocal elasticity based magnetic field affected vibration response of double single-walled carbon nanotube systems. J Appl Phys 111(11): 113-121.
[29] Karličić D, Cajić M, Murmu T, Kozić P, Adhikari S (2015) Nonlocal effects on the longitudinal vibration of a complex multi-nanorod system subjected to the transverse magnetic field. Meccanica 50(6): 1605-1621.
[30] Satish N, Narendar S, Raju K.B (2017)  Magnetic field and surface elasticity effects on thermal vibration properties of nanoplates. Compos Struct 180: 568-580.
[31] Narendar S, Gupta S, Gopalakrishnan S (2012) Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler–Bernoulli beam theory. Appl Math Model 36(9): 4529-4538.
[32] Wang H, Dong K, Men F, Yan Y, Wang X (2010)  Influences of longitudinal magnetic field on wave propagation in carbon nanotubes embedded in elastic matrix. Appl Math Model 34(4): 878-889.
[33] Bahaadini R, Hosseini M (2016) Nonlocal divergence and flutter instability analysis of embedded fluid-conveying carbon nanotube     under magnetic field. Microfluid Nanofluidics 20(7): 1-14.
[34] Hsu JC, Lee HL, Chang WJ (2011) Longitudinal vibration of cracked nanobeams using nonlocal elasticity theory. Curr Appl Phys 11(6): 1384-1388.
[35] Anderson TL (2017) Fracture mechanics: fundamentals and applications. CRC press.
[36] Hai T, Nguyen K, Lien P (2019) Characteristic equation for antiresonant frequencies of multiple cracked bars and application for crack detection. Nondestruct. Test Evaluation 34(3): 299-323.
Journal of Solid and Fluid Mechanics
Volume 10, Issue 4
December 2021
Pages 275-286

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