پیوندهای مفید
آمار
| تعداد نشریات | 9 |
| تعداد شمارهها | 446 |
| تعداد مقالات | 5,719 |
| تعداد مشاهده مقاله | 8,018,459 |
| تعداد دریافت فایل اصل مقاله | 6,527,290 |
ارتعاشات آزاد خطی و غیرخطی صفحه مدرج تابعی مگنتو-الکترو-الاستیک مستطیلی شکل براساس نظریۀ تغییر شکل برشی مرتبه سوم | ||
| نشریه مهندسی مکانیک امیرکبیر | ||
| مقاله 9، دوره 49، شماره 4، اسفند 1396، صفحه 743-758 اصل مقاله (2.03 M) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22060/mej.2016.763 | ||
| نویسندگان | ||
| علیرضا شوشتری* ؛ رامین منتشلو | ||
| گروه مهندسی مکانیک، دانشکده مهندسی دانشگاه بوعلی سینا، همدان، ایران | ||
| چکیده | ||
| در این مقاله ارتعاشات آزاد غیرخطی ورق مستطیل شکل مدرج تابعی با خواص مگنتو-الکترو-الاستیک مورد بررسی قرار گرفته است. شرایط مرزی ساده برای کلیه لبه های ورق در نظر گرفته شده است. همچنین معادلات حرکت بر اساس تئوری برشی مرتبه سوم به دست آمده اند. در این مساله فرض شده است که سطوح بالا و پایین ورق تحت اختلاف پتانسیلهای الکتریکی و مغناطیسی قرار دارند که با استفاده از قوانین گاوس برای حالتهای الکترواستاتیک و مگنتواستاتیک، رفتار الکتریکی و مغناطیسی ورق مدل شده است. همچنین خواص مدرجی بودن تابعی ورق بر اساس تابع توانی در نظر گرفته شده است.پس از تعیین معادلات حرکت با استفاده از روش گلرکین معادلات دیفرانسیل جزئی حرکت به معادلات دیفرانسیل معمولی تبدیل شده است. سپس با استفاده از تئوری پرتوربیشن مساله حل شده است و رابطهای تحلیلی برای فرکانس طبیعی، نسبت فرکانس غیرخطی به فرکانس طبیعی خطی به دست آمدهاند. نتایج بدست آمده از روابط تحلیلی بدست آمده با نتایج بدست آمده از سایر منابع مرتبط صحهگذاری شده است و نشان میدهد مدل پیشنهادی دارای دقت بسیار خوبی می باشد. سپس با استفاده از نتایج موجود، تعدادی مثل عددی برای بررسی اثر پارامترهای مختلف بر روی رفتار ارتعاشی غیرخطی ورقهای مدرج تابعی مگنتو-الکترو-الاستیک ارائه شده است. | ||
| کلیدواژهها | ||
| ورق هوشمند مدرج تابعی؛ نظریۀ تغییر شکل برشی مرتبه سوم؛ قوانین گاوس؛ روش لیندشتات پوانکاره؛ ارتعاشات آزاد | ||
| عنوان مقاله [English] | ||
| Linear and Nonlinear free vibration of a Functionally Graded Magneto-electro-elastic Rectangular Plate Based on the Third Order Shear Deformation Theory | ||
| نویسندگان [English] | ||
| A. Shooshtari؛ R. Mantashloo | ||
| Mechanical Engineering Department, Bu-Ali Sina University, Hamedan, Iran | ||
| چکیده [English] | ||
| In this paper, linear and nonlinear free vibration of one functionally graded magnetoelectro- elastic rectangular plate is studied. The boundary conditions in all side of plate have been considered as simply supported. Also the equations of motions have been derived calculation the kinetic energy and potential energy based on the third order shear deformation theory using Hamilton principle. Considering the top surface of the plate as an pizeomagnetic material and the bottom surface as a piezoelectric material, the bottom and upper surfaces of the plate are subjected to electric and magnetic potentials. The electric and magnetic behaviors of the plate are modeled by using Gauss’s laws. Then, the equations of motions have been transformed from partial differential equations to ordinary differential equations by using Galerkin Method. Then, Using Lindeshtot- Poincare method a closed form expression for linear and nonlinear natural frequency has been obtained. for validation of the proposed model, some numerical examples have been presented and comparisons between the obtained results with the results in literature have been down. It is shown that good agreement exist between obtained results and previous works. Then, to study the effects of several parameters on the nonlinear vibration response of functionally graded magneto-electro-elastic rectangular plates | ||
| کلیدواژهها [English] | ||
| Functionally graded smart plate, Third order shear deformation theory, Gauss’s laws, Perturbation method, free vibration | ||
|
سایر فایل های مرتبط با مقاله
|
||
| مراجع | ||
|
[1] A. Ferreira, R. Batra, C. Roque, L. Qian, R. Jorge, Natural frequencies of functionally graded plates by a meshless method, Composite Structures, 75(1-4) (2006) 593-600. [2] S. Hosseini-Hashemi, M. Fadaee, S.R. Atashipour, A new exact analytical approach for free vibration of Reissner–Mindlin functionally graded rectangular plates, International Journal of Mechanical Sciences, 53(1)(2011) 11-22. [3] S. Hosseini-Hashemi, M. Fadaee, S.R. Atashipour,Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure, Composite Structures, 93(2) (2011) 722-735. [4] A. Allahverdizadeh, R. Oftadeh, M. Mahjoob, M. Naei, Homotopy perturbation solution and periodicity analysis of nonlinear vibration of thin rectangular functionally graded plates, Acta Mechanica Solida Sinica, 27(2)(2014) 210-220. [5] N.D. Duc, P.H. Cong N.D. Tuan, P. Tran, V.M. Anh,V.D. Quang, Nonlinear vibration and dynamic response of imperfect eccentrically stiffened shear deformable sandwich plate with functionally graded material in thermal environment, Journal of Sandwich Structures &Materials, 18(4) (2016) 445-473. [6] P. Malekzadeh, A. Alibeygi Beni, Nonlinear free vibration of in-plane functionally graded rectangular plates, Mechanics of Advanced Materials and Structures,22(8) (2015) 633-640. [7] J. Reddy, Z.-Q. Cheng, Three-dimensional solutions of smart functionally graded plates, Journal of Applied Mechanics, 68(2) (2001) 234-241. [8] K. Liew, J. Yang, S. Kitipornchai, Postbuckling of piezoelectric FGM plates subject to thermo-electromechanical loading, International Journal of Solids and Structures, 40(15) (2003) 3869-3892. [9] P. Cupiał, Three-dimensional natural vibration analysis and energy considerations for a piezoelectric rectangular plate, Journal of sound and vibration, 283(3-5) (2005) 1093-1113. [10] H.-S. Shen, Postbuckling of axially loaded FGM hybrid cylindrical shells in thermal environments, Composites Science and Technology, 65(11-12) (2005) 1675-1690. [11] X. Chen, Z. Zhao, K.M. Liew, Stability of piezoelectric FGM rectangular plates subjected to non-uniformly distributed load, heat and voltage, Advances in Engineering software, 39(2) (200 8) 121-131. [12] V. Fakhari, A. Ohadi, P. Yousefian, Nonlinear free and forced vibration behavior of functionally graded plate with piezoelectric layers in thermal environment, Composite Structures, 93(9) (2011) 2310-2321. [13] S. Panda, D. Chakraborty, Piezo-viscoelastically damped nonlinear frequency response of functionally graded plates with a heated plate-surface, Journal of Vibration and Control, 22(2) (2016) 320-343. [14] S. Panda, D. Chakraborty, Harmonically exited nonlinear vibration of heated functionally graded plates integrated with piezoelectric composite actuator, Journal of Intelligent Material Systems and Structures, 26(8)(2015) 931-951. [15] H.-S. Shen, Nonlinear bending analysis of unsymmetric cross-ply laminated plates with piezoelectric actuators in thermal environments, Composite Structures, 63(2)(2004) 167-177. [16] X.-L. Huang, H.-S. Shen, Nonlinear free and forced vibration of simply supported shear deformable laminated plates with piezoelectric actuators, International Journal of Mechanical Sciences, 47(2) (2005) 187-208. [17] H.-S. Shen, Nonlinear thermal bending response of FGM plates due to heat conduction, Composites Part B:Engineering, 38(2) (2007) 201-215. [18] E. Pan, Exact solution for simply supported and multilayered magneto-electro-elastic plates, Journal of applied Mechanics, 68(4) (2001) 608-618. [19] R.K. Bhangale, N. Ganesan, Static analysis of simply supported functionally graded and layered magnetoelectro-elastic plates, International Journal of Solids and Structures, 43(10) (2006) 3230-3253. [20] R.K. Bhangale, N. Ganesan, Free vibration of simply supported functionally graded and layered magnetoelectro-elastic plates by finite element method, Journal of sound and vibration, 294(4-5) (2006) 1016-1038. [21] T.-P. Chang, Deterministic and random vibration analysis of fluid-contacting transversely isotropic magneto-electro-elastic plates, Computers & Fluids, 84(2013) 247-254. [22] Z. Lang, L. Xuewu, Buckling and vibration analysis of functionally graded magneto-electro-thermo-elastic circular cylindrical shells, Applied Mathematical Modelling, 37(4) (2013) 2279-2292. [23] J. Chen, P. Heyliger, E. Pan, Free vibration of threedimensional multilayered magneto-electro-elastic plates under combined clamped/free boundary conditions, Journal of Sound and Vibration, 333(17) (2014) 4017-4029. [24] Y. Li, J. Zhang, Free vibration analysis of magnetoelectroelastic plate resting on a Pasternak foundation, Smart materials and structures, 23(2) (2013)025002. [25] S. Razavi, A. Shooshtari, Free vibration analysis of a magneto-electro-elastic doubly-curved shell resting on a Pasternak-type elastic foundation, Smart Materials and Structures, 23(10) (2014) 105003. [26] R. Ansari, R. Gholami, H. Rouhi, Size-dependent nonlinear forced vibration analysis of magneto-electrothermo-elastic Timoshenko nanobeams based upon the nonlocal elasticity theory, Composite Structures, 126(2015) 216-226. [27] R. Ansari, E. Hasrati, R. Gholami, F. Sadeghi, Nonlinear analysis of forced vibration of nonlocal third-order shear deformable beam model of magneto–electro–thermos elastic nanobeams, Composites Part B: Engineering, 83(2015) 226-241. [28] S. Kattimani, M. Ray, Smart damping of geometrically nonlinear vibrations of magneto-electro-elastic plates,Composite structures, 114 (2014) 51-63. [29] A. Milazzo, Large deflection of magneto-electro-elastic laminated plates, Applied Mathematical Modelling, 38(5-6) (2014) 1737-1752. [30] M. Rao, R. Schmidt, K.- U. Schröder, Geometrically nonlinear static FE-simulation of multilayered magnetoelectro-elastic composite structures, Composite Structures, 127 (2015) 120-131. [31] S. Razavi, A. Shooshtari, Nonlinear free vibration of magneto-electro-elastic rectangular plates, Composite Structures, 119 (2015) 377-384. [32] A. Shooshtari, S. Razavi, Linear and nonlinear free vibration of a multilayered magneto-electro-elastic doubly-curved shell on elastic foundation, Composites Part B: Engineering, 78 (2015) 95-108. [33] A. Shooshtari, S. Razavi, Large amplitude free vibration of symmetrically laminated magneto-electroelastic rectangular plates on Pasternak type foundation,Mechanics Research Communications, 69 (2015) 103-113. [34] S. Kattimani, M. Ray, Control of geometrically nonlinear vibrations of functionally graded magneto-electro-elastic plates, International Journal of Mechanical Sciences, 99(2015) 154-167. [35] E. Pan, F. Han, Exact solution for functionally graded and layered magneto-electro-elastic plates, International Journal of Engineering Science, 43(3-4) (2005) 321-339. [36] J.Y. Li, Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials, International Journal of Engineering Science, 38(18) (2000) 1993-2011. [37] J.N. Reddy, An introduction to the finite element method, McGraw-Hill New York, 1993. [38] A.H. Nayfeh, D.T. Mook, Nonlinear oscillations, John Wiley & Sons, 2008. [39] J.M.S. Moita, C.M.M. Soares, C.A.M. Soares, Analyses of magneto-electro-elastic plates using a higher order finite element model, Composite structures, 91(4) (2009)421-426. | ||
|
آمار تعداد مشاهده مقاله: 1,993 تعداد دریافت فایل اصل مقاله: 2,304 |
||
