علوم و فناوری کامپوزیت

کنترل ارتعاشات تیر ساندویچی با لایه‌ی مغناطیسی بر پایه‌ی منطق فازی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی کارشناسی ارشد، مهندسی مکانیک، دانشگاه فردوسی مشهد، مشهد، ایران

2 استادیار، مهندسی مکانیک، دانشگاه فردوسی مشهد، مشهد، ایران

چکیده

در این مقاله به بررسی تاثیر استفاده از لایه‌ی هوشمند مغناطیسی در کاهش و سرکوب ارتعاشات ناخواسته‌ در تیرهای هوشمند پرداخته شده است. تیری سه‌لایه متشکل از یک لایه‌ی الاستومر مگنتورئولوژیکال که به‌صورت ساندویچی بین دو لایه‌ی الاستیک قرار دارد، در نظر گرفته شده است. با مدل‌سازی رفتار لایه‌ی مگنتورئولوژیکال به‌صورت ماده‌ی ویسکوالاستیک در ناحیه‌ی قبل از تسلیم، معادلات حاکم بر حرکت تیر ساندویچی به‌همراه شرایط مرزی متناظر با استفاده از اصل همیلتون به‌دست آمده است. به‌علت وابسته‌بودن مدول برشی لایه‌ی مگنتورئولوژیکال به میدان مغناطیسی، با تغییر میدان وارد بر هسته‌، سختی و میرایی تیر هوشمند می‌تواند به سرعت تغییر ‌کند و از این قابلیت برای کنترل و میراسازی ارتعاشات ناخواسته‌ی وارد بر سیستم استفاده شده است. انتخاب میدان مغناطیسی مناسب برای رسیدن به پاسخ گذرای مطلوب، توسط یک کنترلر فازی با استفاده از جابه‌جایی و سرعت مودال، به‌عنوان ورودی‌های کنترلر انجام می‌شود. پارامترهای مودال تیر ساندویچی شامل فرکانس‌های طبیعی و شکل‌مودهای متناظر به‌دست آمده و با نتایج موجود مقایسه و صحه‌گذاری شده است. در ادامه از روش گلرکین برای رسیدن به معادله‌ی زمانی حاکم بر تیر، با در نظرگرفتن اثر میدان مغناطیسی، استفاده شده است. نتایج حاصل از شبیه‌سازی نشان می‌دهد که لایه‌ی هوشمند مغناطیسی به‌همراه کنترلر طراحی شده بر اساس منطق فازی می‌تواند به‌طور موثری در میراسازی ارتعاشات ناخواسته‌ی وارد بر سیستم مورد استفاده قرار گیرد. نتایج حاصل از این پژوهش می‌تواند در طراحی و تحلیل تیرهای هوشمند، به‌عنوان اجزای اصلی سازه‌های پیشرفته‌ی مهندسی ‌برای بهبود عملکرد دینامیکی این سیستم‌ها استفاده شود.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Vibration suppression of MR sandwich beams based on fuzzy logic

نویسندگان [English]

  • Hasan Maleeke 1
  • Hamid Moeenfard 2

1 Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

2 Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

چکیده [English]

In this paper, the vibration suppression capabilities of magnetorheological layer in smart beams is investigated. A three-layered beam including magnetorheological elastomer layer sandwiched between two elastic layers is considered. By assuming the properties of magnetorheological layer in the pre-yield region as viscoelastic materials behavior, the governing equations of motion and the corresponding boundary conditions are derived using Hamilton’s principle. Due to field-dependent shear modulus of magnetorheological layer, the stiffness and damping properties of the smart beam can be changed by application of magnetic field. This feature is utilized to suppress the unwanted vibration of the system. The appropriate magnetic field applied over the beam is chosen through a fuzzy controller for improving the transient response. The designed fuzzy controller uses the modal displacement and velocity of the beam as its inputs. The modal parameters of the sandwich beam including the natural frequencies and mode shapes are obtained and validated with existing results. Using the Galerkin method, the temporal equation governing beam’s motion is obtained and then the vibration of smart sandwich beam is investigated using numerical simulations. The results show that the magnetorheological layer along with the designed fuzzy controller can be effectively used to suppress the unwanted vibration of the system. The qualitative and quantitative knowledge resulting from this research is expected to enable the analysis, design and synthesis of smart beams for improving the dynamic performance of smart engineering structures.
 

 
 

کلیدواژه‌ها [English]

  • Magnetorheological layer
  • Unwanted vibrations
  • Sandwich beam
  • Fuzzy Controller
مراجع
[1]    Carlson, J. D., “Portable controllable fluid rehabilitation devices,” Google Patents, 1998.
[2]    Carlson, J. D. Catanzarite, D. and Clair, K. St., “Commercial magneto-rheological fluid devices,” International Journal of Modern Physics B, Vol. 10, No. 23-24, pp. 2857-2865, 1996.
[3]    Carlson, J. D., Chrzan, M. J. and James, F. O., “Magnetorheological fluid devices,” Google Patents, 1995.
[4]    Ginder, J. Clark, S. Schlotter, W. and Nichols, M., "Magnetostrictive phenomena in magnetorheological elastomers," International Journal of Modern Physics B, Vol. 16, pp. 2412-2418, 2002.
[5]    Han, Y. Hong, W. and Faidley, L. E., "Field-stiffening effect of magneto-rheological elastomers," International Journal of Solids and Structures, Vol. 50, pp. 2281-2288, 2013.
[6]    Danas, K. Kankanala, S. and Triantafyllidis, N., "Experiments and modeling of iron-particle-filled magnetorheological elastomers," Journal of the Mechanics and Physics of Solids, Vol. 60, pp. 120-138, 2012.
[7]    Eshaghi, M. Sedaghati, R. and Rakheja, S., "Dynamic characteristics and control of magnetorheological/electrorheological sandwich structures: A state-of-the-art review," Journal of Intelligent Material Systems and Structures, pp. 1045389X15620041, 2015.
[8]    DiTaranto, R., “Theory of vibratory bending for elastic and viscoelastic layered finite-length beams, ” Journal of Applied Mechanics, Vol. 32, No. 4, pp. 881-886, 1965.
[9]    Mead, D. and Markus, S., “The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary conditions,” Journal of sound and vibration, Vol. 10, No. 2, pp. 163-175, 1969.
[10] Yalcintas, M. and Dai, H., “Magnetorheological and electrorheological materials in adaptive structures and their performance comparison,” Smart Materials and Structures, Vol. 8, No. 5, pp. 560, 1999.
[11]Sun, Q. Zhou, J.-X. and Zhang, L., “An adaptive beam model and dynamic characteristics of magnetorheological materials,” Journal of Sound and Vibration, Vol. 261, No. 3, pp. 465-481, 2003.
[12] Rajamohan, V. Sedaghati, R. and Rakheja, S., "Vibration analysis of a multi-layer beam containing magnetorheological fluid," Smart Material Structures, Vol. 19, p. 5013, 2010.
[13] Rajamohan, V. Rakheja, S. and Sedaghati, R., "Vibration analysis of a partially treated multi-layer beam with magnetorheological fluid," Journal of Sound and Vibration, Vol. 329, pp. 3451-3469, 2010.
[14] Rajamohan, V. and Ramamoorthy, M., "Dynamic characterization of non-homogeneous magnetorheological fluids based multi-layer beam," in Applied Mechanics and Materials, 2012, pp. 105-112.
[15] Asgari, M. Payganeh, Gh. Malekzade Fard, K. and Rashed Saghavaz, F., “A parametric study of the free vibration analysis of composite sandwich plate with magneto-rheological smart core,” (In Persian), Modares Mechanical Engineering, Vol. 15, No. 11, pp. 396-404, 2015.
[16] Malekzade Fard, K. Payganeh, Gh. Rashed and Saghavaz, F., “Free vibration and Low velocity impact Analysis of sandwich plates with Smart Flexible cores,” Modares Mechanical Engineering, Vol. 14, No. 13, pp. 191-200, 2015 (In Persian).
[17] Nayak, B. Dwivedy, S. and Murthy, K., "Multi-frequency excitation of magnetorheological elastomer-based sandwich beam with conductive skins," International Journal of Non-Linear Mechanics, Vol. 47, pp. 448-460, 2012.
[18] Nayak, B. Dwivedy, S. and Murthy, K., "Dynamic stability of a rotating sandwich beam with magnetorheological elastomer core," European Journal of Mechanics-A/Solids, Vol. 47, pp. 143-155, 2014.
[19] Rahn, C. D. and Joshi, S., “Modeling and control of an electrorheological sandwich beam,” Journal of vibration and acoustics, Vol. 120, No. 1, pp. 221-227, 1998.
[20] Wang K., Kim Y. and Shea D., “Structural vibration control via electrorheological-fluid-based actuators with adaptive viscous and frictional damping,” Journal of Sound and Vibration, Vol. 177, No. 2, pp. 227-237, 1994.
[21] Chrzan, M. J. and Carlson, J. D., “MR fluid sponge devices and their use in vibration control of washing machines,” in Proceeding of, pp.370-378, 2001.
[22] Hu, G. Guo, M. Li, W. Du, H. and Alici, G., "Experimental investigation of the vibration characteristics of a magnetorheological elastomer sandwich beam under non-homogeneous small magnetic fields," Smart materials and structures, Vol. 20, p. 127001, 2011.
[23] Sun, Q. Zhou, J.-X. and Zhang, L., "An adaptive beam model and dynamic characteristics of magnetorheological materials," Journal of Sound and Vibration, Vol. 261, pp. 465-481, 2003.
[24] Ni, Y. Ying, Z. and Chen, Z., "Micro-vibration suppression of equipment supported on a floor incorporating magneto-rheological elastomer core," Journal of Sound and Vibration, Vol. 330, pp. 4369-4383, 2011.
[25] Dyniewicz, B. Bajkowski, J. M. and Bajer, C. I., "Semi-active control of a sandwich beam partially filled with magnetorheological elastomer," Mechanical Systems and Signal Processing, Vol. 60, pp. 695-705, 2015.
[26] S. S., Rao, “Vibration of continuous system”, John Wiley & Sons, pp. 320-356, 2007.
[27]Li, W. Du, H. Chen, G. Yeo, S. and Guo, N., “Nonlinear rheological behavior of magnetorheological fluids: step-strain experiments,” Smart materials and structures, Vol. 11, No. 2, pp. 209, 2002.
[28] Christensen, R., “Theory of viscoelasticity: an introduction”, Elsevier, pp. 141-152, 2012.
[29] Nayfeh, A. H. and Mook, D. T. “Nonlinear oscillations”: John Wiley & Sons, 2008.
[30] Nayak, B. Dwivedy, S. and Murthy, K., "Dynamic analysis of magnetorheological elastomer-based sandwich beam with conductive skins under various boundary conditions," Journal of Sound and Vibration, Vol. 330, pp. 1837-1859, 2011.
[31] Ray, K. and Kar, R., "Parametric instability of a sandwich beam under various boundary conditions," Computers & structures, Vol. 55, pp. 857-870, 1995.
[32] Yager, R. R. and Zadeh, L. A., “An introduction to fuzzy logic applications in intelligent systems,” Springer Science & Business Media, Vol. 165: 2012.
[33] Wang, L.-X., A course in fuzzy systems: Prentice-Hall press, USA, 1999.
علوم و فناوری کامپوزیت
دوره 3، شماره 4
اسفند 1395
صفحه 359-368
فایل ها
هم رسانی
ارجاع به این مقاله
آمار