تعداد نشریات | 7 |
تعداد شمارهها | 399 |
تعداد مقالات | 5,389 |
تعداد مشاهده مقاله | 5,288,027 |
تعداد دریافت فایل اصل مقاله | 4,882,769 |
رهیافت فضای حالت برای تحلیل خمش ورق پیزوالکتریک مدرج تابعی به کمک تئوری ورق اصلاح شده پنج متغیره | ||
نشریه مهندسی مکانیک امیرکبیر | ||
مقاله 4، دوره 55، شماره 2، اردیبهشت 1402، صفحه 213-234 اصل مقاله (1.47 M) | ||
نوع مقاله: مقاله پژوهشی | ||
شناسه دیجیتال (DOI): 10.22060/mej.2023.21600.7476 | ||
نویسندگان | ||
نیلوفر سلمانپور؛ سید جعفر روزگار* | ||
دانشکده مهندسی مکانیک، دانشگاه صنعتی شیراز، شیراز، ایران | ||
چکیده | ||
در این مقاله، یک حل تحلیلی برای خمش ورق پیزوالکتریک مدرج تابعی تحتبار جانبی گسترده یکنواخت با شرایط مرزی دلخواه ارایه میشود. تئوری اصلاح شده پنج متغیره برای بیان میدان جابجایی به کار میرود که تنشها و کرنشهای برشی در راستای ضخامت را به صورت سهموی پیشبینی میکند و تأثیر کشش در راستای ضخامت ورق را نیز در نظر میگیرد. معادلات حاکم با استفاده از اصل همیلتون و معادلات ماکسول، به دست آمده و از روش لوی و فضای حالت برای حل این معادلات کوپل استفاده میشود. نتایج به دست آمده با سایر تئوریهای برشی مرتبه بالا و نرم افزار آباکوس مقایسه شده که بدین ترتیب دقت روش پیشنهادی تایید میگردد. مشاهده میشود که برای نسبت طول به ضخامت 10 و شاخص توانی 0/5، مقدار تغییرمکان بیبعد ورق با شرط مرزی گیردار 0/3327 است که دارای بیشترین میزان سفتی و کمترین مقدار خیز میباشد در حالیکه مقدار تغییرمکان بیبعد ورق با شرط مرزی آزاد2/2036 میباشد و در نتیجه کمترین میزان سفتی و بیشترین مقدار خیز را دارد. همچنین برای ورق با تکیهگاه گیردار و طول به ضخامت 10 با افزایش شاخص توانی از 0/5 به 10 مقدار تغییرمکان از 0/3327 به 0/3545 یعنی حدود 6 درصد افزایش مییابد. | ||
کلیدواژهها | ||
رهیافت فضای حالت؛ تأثیر کشیدگی ضخامت؛ تئوری ورق اصلاحشده؛ پیزوالکتریک مدرج تابعی؛ حل لوی | ||
عنوان مقاله [English] | ||
State-space approach for bending analysis of functionally graded piezoelectric plate using five-variable refined plate theory | ||
نویسندگان [English] | ||
Niloufar Salmanpour؛ Seyed Jafar Rouzegar | ||
Department of Mechanical Engineering, Shiraz University of Technology, Shiraz, Iran | ||
چکیده [English] | ||
In this paper, an analytical solution for bending analysis of functionally-graded piezoelectric plate with two simply-supported parallel edges and two other arbitrary boundary conditions under uniformly-distributed transverse loading is presented. The five-variable refined plate theory is employed for describing the displacement field. This theory, despite the few numbers of unknown variables, predicts a parabolic distribution for transverse shear stresses across the thickness and also considers the thickness-stretching effect. The governing equations are obtained using Hamilton’s principle and Maxwell's equation. The Levy-type solution in conjunction with the state-space approach is used to solve them. Comparing the results with those obtained by the higher-order shear theories and Abaqus finite element simulation confirms the accuracy and efficiency of the proposed method. It can be seen that for the length-to-thickness ratio of 10 and the power-law index of 0.5, the value of non-dimensional deflection of the plate with the clamped boundary condition is 0.3327, which has the largest amount of stiffness, while the value of the non-dimensional deflection of the plate with two parallel free boundary condition edges having the lowest amount of stiffness is 2.2036. In addition, for the plate with a clamped boundary condition and length-to-thickness ratio of 10, with the increase of the power index from 0.5 to 10, the value of displacement changes from 0.3327 to 0.3545, which means an increase of about 6%. | ||
کلیدواژهها [English] | ||
State-space approach, thickness stretching effect, refined plate theory, functionally-graded piezoelectric plate, levy solution | ||
سایر فایل های مرتبط با مقاله
|
||
مراجع | ||
[1] M. Benchohra, H. Driz, A. Bakora, A. Tounsi, E. Adda Bedia, S.R. Mahmoud, A new quasi-3D sinusoidal shear deformation theory for functionally graded plates, Structural engineering and mechanics: An international journal, 65(1) (2018) 19-31. [2] S.-H. Chi, Y.-L. Chung, Mechanical behavior of functionally graded material plates under transverse load—Part I: Analysis, International Journal of Solids and Structures, 43(13) (2006) 3657-3674. [3] M. Shariati, M. Shishehsaz, R. Mosalmani, Stress-driven Approach to Vibrational Analysis of FGM Annular Nano-plate based on First-order Shear Deformation Plate Theory, Journal of Applied and Computational Mechanics, in-press (2023) 1-23. [4] J. Reddy, Analysis of functionally graded plates, International Journal for numerical methods in engineering, 47(1‐3) (2000) 663-684. [5] P.V. Vinh, Analysis of bi-directional functionally graded sandwich plates via higher-order shear deformation theory and finite element method, Journal of Sandwich Structures & Materials, 24(2) (2022) 860-899. [6] M. Li, C.G. Soares, R. Yan, A novel shear deformation theory for static analysis of functionally graded plates, Composite Structures, 250 (2020) 112559. [7] R.P. Shimpi, Refined plate theory and its variants, AIAA journal, 40(1) (2002) 137-146. [8] R. Shimpi, H. Patel, A two variable refined plate theory for orthotropic plate analysis, International Journal of Solids and Structures, 43(22-23) (2006) 6783-6799. [9] S.-E. Kim, H.-T. Thai, J. Lee, A two variable refined plate theory for laminated composite plates, Composite Structures, 89(2) (2009) 197-205. [10] H.-T. Thai, D.-H. Choi, Improved refined plate theory accounting for effect of thickness stretching in functionally graded plates, Composites Part B: Engineering, 56 (2014) 705-716. [11] M. Bennoun, M.S.A. Houari, A. Tounsi, A novel five-variable refined plate theory for vibration analysis of functionally graded sandwich plates, Mechanics of Advanced Materials and Structures, 23(4) (2016) 423-431. [12] Y. Li, J. Ren, W. Feng, Bending of sinusoidal functionally graded piezoelectric plate under an in-plane magnetic field, Applied Mathematical Modelling, 47 (2017) 63-75. [13] M. Arefi, E.M.-R. Bidgoli, R. Dimitri, M. Bacciocchi, F. Tornabene, Application of sinusoidal shear deformation theory and physical neutral surface to analysis of functionally graded piezoelectric plate, Composites Part B: Engineering, 151 (2018) 35-50. [14] A.M. Zenkour, Z.S. Hafed, Bending analysis of functionally graded piezoelectric plates via quasi-3D trigonometric theory, Mechanics of Advanced Materials and Structures, 27(18) (2020) 1551-1562. [15] Y. Xue, J. Li, F. Li, Z. Song, Active control of plates made of functionally graded piezoelectric material subjected to thermo-electro-mechanical loads, International Journal of Structural Stability and Dynamics, 19(09) (2019) 1950107. [16] N.T. Dung, P.V. Minh, H.M. Hung, D.M. Tien, The third-order shear deformation theory for modeling the static bending and dynamic responses of piezoelectric bidirectional functionally graded plates, Advances in Materials Science and Engineering, 2021 (2021) 1-15. [17] P. Kumar, S.P. Harsha, Response analysis of functionally graded piezoelectric plate resting on elastic foundation under thermo-electro environment, Journal of Composite Materials, 56(24) (2022) 3749-3767. [18] J.S. Lee, L.Z. Jiang, Exact electroelastic analysis of piezoelectric laminae via state space approach, International Journal of Solids and Structures, 33(7) (1996) 977-990. [19] H. Sheng, H. Wang, J. Ye, State space solution for thick laminated piezoelectric plates with clamped and electric open-circuited boundary conditions, International Journal of Mechanical Sciences, 49(7) (2007) 806-818. [20] A. Alibeigloo, R. Madoliat, Static analysis of cross-ply laminated plates with integrated surface piezoelectric layers using differential quadrature, Composite Structures, 88(3) (2009) 342-353. [21] A. Alibeigloo, Coupled thermoelasticity analysis of FGM plate integrated with piezoelectric layers under thermal shock, Journal of Thermal Stresses, 42(11) (2019) 1357-1375. [22] M. Feri, M. Krommer, A. Alibeigloo, Three-dimensional static analysis of a viscoelastic rectangular functionally graded material plate embedded between piezoelectric sensor and actuator layers, Mechanics Based Design of Structures and Machines, (2021) 1-25. [23] J.-m. ZHANG, Z.-h. MAO, F. Xin, L.-l. ZHANG, G. Yang, Free Vibration of Three-Dimensional Piezoelectric Cubic Quasicrystal Plates, in: 2020 15th Symposium on Piezoelectrcity, Acoustic Waves and Device Applications (SPAWDA), IEEE, 2021, pp. 253-257. [24] A. Alibeigloo, M. Talebitooti, Three dimensional transient coupled thermoelasticity analysis of FGM cylindrical panel embedded in piezoelectric layers, Mechanics of Smart Structures, in-press (2021) 1-20. [25] J. Rouzegar, N. Salmanpour, F. Abad, L. Li, An analytical state-space solution for free vibration of sandwich piezoelectric plate with functionally graded core, Scientia Iranica, 29(2) (2022) 502-533. [26] M.H. Sadd, Elasticity: theory, applications, and numerics, 2nd Edition, Academic Press, 2009. [27] S. Shiyekar, T. Kant, Higher order shear deformation effects on analysis of laminates with piezoelectric fibre reinforced composite actuators, Composite structures, 93(12) (2011) 3252-3261. [28] M.A. Farsangi, A. Saidi, R. Batra, Analytical solution for free vibrations of moderately thick hybrid piezoelectric laminated plates, Journal of Sound and Vibration, 332(22) (2013) 5981-5998. [29] M.A. Farsangi, A. Saidi, Levy type solution for free vibration analysis of functionally graded rectangular plates with piezoelectric layers, Smart materials and structures, 21(9) (2012) 094017. [30] J. Rouzegar, R. Koohpeima, F. Abad, Dynamic analysis of laminated composite plate integrated with a piezoelectric actuator using four-variable refined plate theory, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 44 (2020) 557-570. [31] J. Rouzegar, F. Abad, Free vibration analysis of FG plate with piezoelectric layers using four-variable refined plate theory, Thin-Walled Structures, 89 (2015) 76-83. [32] P.A. Demirhan, V. Taskin, Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach, Composites Part B: Engineering, 160 (2019) 661-676. [33] J.N. Franklin, Matrix theory, 1st Edition, Courier Corporation, 2012. [34] A.M. Zenkour, Generalized shear deformation theory for bending analysis of functionally graded plates, Applied Mathematical Modelling, 30(1) (2006) 67-84. [35] H.-T. Thai, D.-H. Choi, Efficient higher-order shear deformation theories for bending and free vibration analyses of functionally graded plates, Archive of Applied Mechanics, 83 (2013) 1755-1771. [36] P.A. Demirhan, V. Taskin, Levy solution for bending analysis of functionally graded sandwich plates based on four variable plate theory, Composite Structures, 177 (2017) 80-95. [37] M. Bodaghi, M. Shakeri, An analytical approach for free vibration and transient response of functionally graded piezoelectric cylindrical panels subjected to impulsive loads, Composite Structures, 94(5) (2012) 1721-1735. | ||
آمار تعداد مشاهده مقاله: 279 تعداد دریافت فایل اصل مقاله: 428 |