پیوندهای مفید
آمار
| تعداد نشریات | 7 |
| تعداد شماره‌ها | 399 |
| تعداد مقالات | 5,389 |
| تعداد مشاهده مقاله | 5,288,209 |
| تعداد دریافت فایل اصل مقاله | 4,882,946 |
تحلیل خمش و ارتعاش آزاد نانو ورق مدرج تابعی با استفاده از نظریه ورق مرتبه بالای مثلثاتی | ||
| نشریه مهندسی مکانیک امیرکبیر | ||
| مقاله 10، دوره 50، شماره 5، آذر و دی 1397، صفحه 1039-1050 اصل مقاله (635.78 K) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22060/mej.2017.12173.5274 | ||
| نویسندگان | ||
| علی عزیزی؛ علیرضا ستوده* | ||
| دانشکده مهندسی مکانیک، دانشگاه صنعتی شیراز، شیراز، ایران | ||
| چکیده | ||
| در این مقاله خمش و ارتعاش آزاد نانو ورق مدرج تابعی با استفاده از یک نظریۀ ورق مرتبه بالای مثلثاتی جدید بررسی شده است. معادلات حاکمه با استفاده از اصل همیلتون استخراج گردیده و سپس حل دقیق خمش و ارتعاش آزاد نانو ورق مستطیلی با شرط مرزی ساده به کمک روش ناویر به دست آمده است. همچنین ازنظریۀ غیرمحلی برای لحاظ اثرات اندازه استفاده شده است. خواص مکانیکی نانو ورق مدرج تابعی با تابع توانی در راستای ضخامت تغییر می‌کند. به منظور تأیید دقت نظریۀ ارائه شده، نتایج حاصل از حل حاضر با نتایج موجود مقایسه شده است و مطابقت بسیار خوبی حاصل گردیده است. همچنین، اثرات نسبت طول به ضخامت، نسبت ابعادی درون صفحه ای و پارامتر غیرمحلی روی رفتار خمشی و ارتعاش آزاد نانو ورق بررسی شده است. نتایج نشان می‌دهد که لحاظ پارامتر غیرمحلی در معادلۀ حاکمه یا افزایش مقدار شاخص توانی، باعث کاهش بسامد طبیعی و افزایش خیز نانو ورق می‌شود و به عبارت دیگر موجب کاهش سفتی نانو ورق می‌گردد. در ضمن با افزایش طول نانو ورق یا نسبت ابعادی، تأثیر پارامتر غیرمحلی و اثرات اندازه کاهش می‌یابد. همچنین، نظریه ارائه شده علاوه بر ارائه جوا بهای دقیق خمش و ارتعاش آزاد برای نانو ورق ضخیم و نسبتاً ضخیم با هزینه محاسباتی کم، توزیع سهمیوار تنش برشی درون ضخامت را پیش بینی می‌کند. | ||
| کلیدواژه‌ها | ||
| نانو ورق مدرج تابعی؛ نظریه ورق مرتبه بالای مثلثاتی جدید؛ نظریه غیر محلی؛ خمش؛ ارتعاش آزاد | ||
| عنوان مقاله [English] | ||
| Bending and Free Vibration Analysis of Functionally Graded Nano-plate Using Trigonometric Higher-Order Plate Theory | ||
| نویسندگان [English] | ||
| A. Azizi؛ A. Setoodeh | ||
| Department of Mechanical and Aerospace Engineering, Shiraz University of Technology, Shiraz, Iran | ||
| چکیده [English] | ||
| In this paper, bending and free vibration analyses of functionally graded nano-plates are investigated using a new trigonometric higher-order plate theory. The governing equations are developed by employing Hamilton’s principle and then a Navier-type analytical solution for bending and free vibration of simply supported rectangular FG nano-plates is obtained. Furthermore, the nonlocal theory of elasticity is used to take into account the small scale effects. The mechanical properties of the functionally graded nano-plates are assumed to vary by a power law function through the thickness. In order to confirm the accuracy of the present theory, the obtained results from the present solution are compared with the existed results, and a very good agreement is achieved. Moreover, the effects of length-to-thickness ratio, aspect ratio and nonlocal parameter on the bending and free vibration solutions are investigated. The results demonstrate that the inclusion of nonlocal parameter in governing equations or increasing the power index, leads to reduction of the natural frequency and increasing of the deflection and in another word the nano-plate stiffness is reduced. Also, the impact of the nonlocal parameter and size effects is reduced by increasing the length of the nano-plate or aspect ratio. Furthermore, the present theory not only provides exact solution for the bending and free vibration of thick and moderately thick functionally graded nano-plates with minimum computational cost, but also exhibits the parabolic distribution of the shear stress through the thickness. | ||
| کلیدواژه‌ها [English] | ||
| Functionally graded nano-plate, Trigonometric higher-order theory, Nonlocal theory, Bending, Free vibration | ||
|
سایر فایل های مرتبط با مقاله
|
||
| مراجع | ||
|
[1] H. Rafieipour, A. Lotfavar, S. Hamzeh Shalamzari, Nonlinear vibration analysis of functionally graded beam on Winkler-Pasternak foundation under mechanical and thermal loading via homotopy analysis method, Modares Mechanical Engineering, 12(5) (2013) 87–101. (In Persian) [2] M. Kadkhodayan, H. Zafarmand, An investigation into the three dimensional dynamic analysis and stress wave propagation in thick functionally graded plates under impact loading, Modares Mechanical Engineering, 14(11) (2015) 89–96. (In Persian) [3] P. Malekzadeh, M. Shojaee, Free vibration of nanoplates based on a nonlocal two-variable refined plate theory, Composite Structures, 95 (2013) 443–452. [4] P. Malekzadeh, M. Shojaee, A two-variable first-order shear deformation theory coupled with surface and nonlocal effects for free vibration of nanoplates, Journal of Vibration and Control, 21 (2015) 2755-2772. [5] A. Ghorbanpour Arani, E. Haghparast, H. Baba AkbarZarei, Nonlocal vibration of axially moving graphene sheet resting on orthotropic visco-Pasternak foundation under longitudinal magnetic field, Physica B: Physics of Condensed Matter, 495 (2016) 35-49. [6] M. Mohammadimehr, B. Rousta Navi, A. Ghorbanpour Arani, Free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method, Composite Structures, 131 (2015) 654-671. [7] H.T. Thai, D.H. Choi, Size dependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory, Composite Structures, 95 (2012) 142-153. [8] Sh. Hosseini Hashemi, R. Bedroud, M. Nazemnezhad, An exact analytical solution for free vibration of functionally graded circular annular Mindlin nanoplates via nonlocal elasticity, Composite Structures, 103 (2013) 108-118. [9] W.Y. Jung, S.C. Han, Analysis of Sigmoid Functionally Graded Material (S-FGM) Nanoscale Plates Using the Nonlocal Elasticity Theory, Mathematical Problems in Engineering, 2013 (2013) 1–10. [10] W.Y. Jung, S.C. Han, W.T. Park, A modified couple stress theory for buckling analysis of S-FGM nanoplates embedded in Pasternak elastic medium, Composites: Part B, 60 (2014) 746-756. [11] W.Y. Jung, S.C. Han, Static and Eigenvalue problems of Sigmoid Functionally Graded Materials S-FGM micro-scale plates using the Modified Couple Stress Theory, Applied Mathematical Modeling, 39(12) (2014) 3506–3524. [12] H. Salehipour, H. Nahvi, A.R. Shahidi, Exact analytical solution for free vibration of functionally graded micro-nano plates via three-dimensional nonlocal elasticity, Physica E: Low-dimensional Systems and Nanostructures, 66 (2015) 350–358. [13] M.R. Nami, M. Janghorban, Resonance behavior of FG rectangular micro-nano plate based on nonlocal elasticity theory and SGT with one gradient constant, Composite Structures, 111 (2014) 349-353. [14] M.R. Nami, M. Janghorban, Free vibration of functionally graded size-dependent nanoplates based on second order shear deformation theory using nonlocal elasticity theory, Transactions of Mechanical Engineering, 39(M1) (2015) 15-28. [15] L. He, J. Lou, E. Zhang, Y. Wang, Y. Bai, A size-dependent four variable refined plate model for functionally graded microplates based on modified couple stress theory, Composite Structures, 130(M1) (2015) 107-115. [16] H. Salehipour, A.R. Shahidi, H. Nahvi, Modified nonlocal elasticity theory for functionally graded materials, International Journal of Engineering Science, 90 (2015) 44-57. [17] H. Salehipour, A.R.Shahidi, H. Nahvi, Closed-form elasticity solution for three-dimensional deformation of functionally graded micronano plates on elastic foundation, Latin American Journal of Solids and Structures, 12 (2015) 747-762. [18] H. Salehipour, A.R.Shahidi, H. Nahvi, Exact closed-form free vibration analysis for functionally graded micronano plates based on modified couple stress and three-dimensional elasticity theories, Composite Structures, 124 (2015) 283-291. [19] M. Zare, R. Nazemnezhad, Sh. Hosseini Hashemi, Natural frequency analysis of functionally graded rectangular nanoplates with different boundary conditions via an analytical method, Meccanica, 50 (2015) 2391-2408. [20] A. Daneshmehr, A. Rajabpoor, A. Hadi, Size dependent free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory with high order theories, International Journal of Engineering Science, 95 (2015) 23-35. [21] M.R. Nami, M. Janghorban, M. Damadan, Thermal buckling analysis of functionally graded rectangular nanoplates base on nonlocal third-ordershear deformation theory, Aerospace Science and Technology, 41 (2015) 7-15. [22] R. Ansari, M.F. Shojaei, A. Shahabodini, M. Bazdid- Vahdati, Three-dimensional bending and vibration analysis of functionally graded nanoplates by a novel differential quadrature-based approach, Composite Structures, 131 (2015) 753-764. [23] A.C. Eringen, Nonlocal continuum field theories, Springer, New York, 2002. [24] A. Mahi, E.A.A. Bedia, A. Tounsi, A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic functionally graded sandwich and laminated composite plates, Applied Mathematical Modelling, 39 (2015) 2489-2508. [25] E. Jomehzadeh, A.R. Saidi, Decoupling the nonlocal elasticity equations for three dimensional vibration analysis of nano-plates, Composite Structures, 93 (2011) 1015-1020. [26] R. ghababaei, J.N. Reddy, Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates, Journal of Sound and Vibration, 326 (2009) 277-289. [27] G. Jin, Z. Su, S. Shi, T. Ye, S. Gao, Three-dimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions, Composite Structures, 108 (2014) 567-577. [28] C.P. Wu, K.H. Chiu, Y.M. Wang, RMVT-based meshless collocation and element-free Galerkin methods for the quasi-3D analysis of multilayered composite and FGM plates, Composite Structures, 93 (2011) 923-943. [29] M. Sobhy, A comprehensive study on FGM nanoplates embedded in an elastic medium, Composite Structures, 134 (2015) 966-980. | ||
|
آمار تعداد مشاهده مقاله: 904 تعداد دریافت فایل اصل مقاله: 917 |
||
