Nonlinear Free Vibration Analysis of Functionally Graded Sandwich Beam with Magnetorheological Fluid Core Using Timoshenko Beam Theory

Subject Areas : Applied Mechanics

O Miraliyari ¹ (Department of Mechanical Engineering, Islamic Azad University, Arak Branch, Arak, Iran)
S Jafari Mehrabadi ² (Department of Mechanical Engineering, Islamic Azad University, Arak Branch, Arak, Iran)
M.M Najafizadeh ³ (Department of Mechanical Engineering, Islamic Azad University, Arak Branch, Arak, Iran)

Received: 2023-02-10 Accepted : 2023-03-25 Published : 2023-06-01

Keywords: Nonlinear free vibration, Functionally graded sandwich beam, Magnetorheological fluid core, Euler Bernoulli and Timoshenko beam theories,

Abstract :

In this paper, the analysis of nonlinear free vibrations of beams made of functionally graded materials with magnetorheological fluid as core is investigated. It is assumed that the beam is made of three layers including constraining layer, magnetorheological fluid and base layer and is located on Simply-Simply, Clamped-Simply and Clamped–Clamped supports. The governing equations of the beam are derived using the Hamilton’s principle. To obtain the vibrational frequencies, the theory of Timoshenko beam is used by the Generalized Differential Quadrature method. The effects of magnetic field intensity, power law exponents, core thickness and constraining layer thickness and the length of the beam on natural frequency and modal loss factor related to different frequencies modes for the three boundary conditions have been investigated. The results show the effects of physical and geometrical parameters regarding the natural frequency and modal loss factor of the sandwich beam with different modes. Also, the frequency and loss factor values obtained from Generalized Differential Quadrature method are very close to the results obtained by the Finite Element method. This shows the accuracy and precision of this method.

References:

1. Ashtiani M., Hashemabadi S.H., Ghaffari A., 2015, A review on the magnetorheological fluid preparation and stabilization, Journalof Magnetism and Magnetic Materials 374: 711-715. 


2. Allahverdizadeh A., Eshraghi I., Mahjoob M.J., Nasrollahzadeh N., 2014, Nonlinear vibration analysis of FGER sandwich beams, International Journal of Mechanical Sciences 78:167-176.


3. Aguib S., Nour A., Benkoussas B., Tawfiq I., Djedid T., Chikh N., 2016, Numerical simulation of the nonlinear static behavior of composite sandwich beams with a magnetorheological elastomer core, Composite Structures 139:111-119.


4. Acharya S., Allien V.J., Kumar H., 2021, Dynamic behavior of sandwich beams with different compositions of magnetorheological fluid core, International Journalof Smart and Nano Materials 12:88-106.


5. Nayak B., Dwivedy S.K., Murthy K.S.R.K., 2013, Vibration analysis of a three-layer magnetorheological elastomer embedded sandwich beam with conductive skins using finite element method, Proceedings of the Institutionof Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227: 714-729.


6. Navazi H.M., Bornassi S., Haddadpour H., 2017, Vibration analysis of a rotating magnetorheological tapered sandwich beam, International Journal of Mechanical Sciences 122: 308-317.


7. Marynowski K., 2012, Dynamic analysis of an axially moving sandwich beam with viscoelastic core, Composite Structures 94: 2931-2936.


8. Wei K., Bai Q., Meng G., Ye L., 2011, Vibration characteristics of electrorheological elastomer sandwich beams, Smart Materialsand Structures 20: 055012.


9. Allahverdizadeh A., Mahjoob M.J., Eshraghi I., Asgharifard-S. P., 2012, Effects of electrorheological fluid core and functionally graded layers on the vibration behavior of a rotating composite beam, Meccanica 47: 1945-1960.


10. Allahverdizadeh A., Mahjoob M.J., Eshraghi I., Nasrollahzadeh N., 2013, On the vibration behavior of functionally graded electrorheological sandwich beams, International Journal of Mechanical Sciences 70: 130-139.


11. Ke L.L., Yang J., Kitipornchai S., 2010, An analytical study on the nonlinear vibration of functionally graded beams, Meccanica 45: 743-752.


12. Elmaguiri M.N., Haterbouch M., Bouayad A., Oussouaddi O., 2015, Geometrically nonlinear free vibration of functionally graded beams, Journalof Materials and Environmental Science 6: 3620-3633.


13. Taeprasartsit S., 2015, Nonlinear free vibration of thin functionally graded beams using the finite element method, Journalof Vibration and Control 21: 29-46.


14. Sheng G.G., Wang X., 2018, Nonlinear vibration of FG beams subjected to parametric and external excitations, European Journal of Mechanics; A/Solids 71: 224-234.


15. Barari A., Kaliji H.D., Ghadimi M., Domairry G., 2011, Non-linear vibration of Euler-Bernoulli beams, Latin American Journal of Solids and Structures 8(2):139-148.


16. Sınır S., Çevik M., Sınır B.G., 2018, Nonlinear free and forced vibration analyses of axially functionally graded Euler-Bernoulli beams with non-uniform cross-section, Composites Part B: Engineering 148: 123-131.


17. Hemmatnezhad M., Ansari R., Rahimi G.H., 2013, Large-amplitude free vibrations of functionally graded beams by means of a finite element formulation, Applied MathematicalModelling 37: 8495-84504.


18. Gunda J.B., Gupta R.K., Janardhan G.R., Rao G.V., 2010, Large amplitude free vibration analysis of Timoshenko beams using a relatively simple finite element formulation, International Journal of Mechanical Sciences 52: 1597-1604.


19. Ebrahimi F., Zia M., 2015, Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities, ActaAstronautica 116: 117-125.


20. Chen D., Kitipornchai S., Yang J., 2016, Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core, Thin-walled Structures 107: 39-48.


21. Ghorbanpour Arani A., Kolahchi R., Haghighi S., Mosallaie Barzoki A.A., 2013, Nonlinear viscose flow induced nonlocal vibration and instability of embedded DWCNC via DQM, Journalof Mechanical Science and Technology 27: 21-31.


22. Ghaitani M.M., Ghorbanpourarani A., Khademizadeh H., 2014, Nonlinear vibration and instability of embedded viscose-fluid-conveying pipes using DQM, Advanced Design and Manufacturing Technology 7: 45-51.


23. Yeh J.Y., 2013, Vibration analysis of sandwich rectangular plates with magnetorheological elastomer damping treatment, Smart Materialsand Structures 22: 035010.


24. Rajamohan V., Rakheja S., Sedaghati R., 2010, Vibration analysis of a partially treated multi-layer beam with magnetorheological fluid, Journal of Soundand Vibration 329: 3451-3469.


25. Zhong Z., Wu L., Chen W., 2012, Mechanics of Functionally Graded Materials and Structures,


26. Kang J.H., 2014, An exact frequency equation in closed form for Timoshenko beam clampled at both ends, Journal of Soundand Vibration 333: 3332-3337.


27. Shafiei N., Kazemi M., Ghadiri M., 2016, Nonlinear vibration behavior of a rotating nanobeam under thermal stress using Eringen’s nonlocal elasticity and DQM, Applied Physics A: Materials Science & Processing 122: 123265759.


28. Rajamohan V., Sundararaman V., Govindarajan B., 2013, Finite element vibration analysis of a magnetorheological fluid sandwich beam, Procedia Engineering 64: 603-612.


29. Rajamohan V., Sedaghati R., Rakheja S., 2010, Vibration analysis of a multi-layer beam containing magnetorheological fluid, Smart Materialsand Structures 19: 015013.


30. Bilasse M., Daya E.M., Azrar L., 2010, Linear and nonlinear vibrations analysis of viscoelastic sandwich beams, Journal of Soundand Vibration 329: 4950-4969.