ارتعاشات ورق‌های بیضوی از جنس مواد هدفمند تابعی واقع بر بستر کشسان وینکلر تحت پیش بار داخل صفحه‌ای

حسینی, مهدی; غیاثوند, حسن

doi:10.22065/jsce.2021.254420.2276

ارتعاشات ورق‌های بیضوی از جنس مواد هدفمند تابعی واقع بر بستر کشسان وینکلر تحت پیش بار داخل صفحه‌ای

نوع مقاله : علمی - پژوهشی

نویسندگان

¹ استادیار، گروه مهندسی مکانیک، دانشکده فنی و مهندسی،دانشگاه ملایر، ملایر، ایران

² کارشناسی ارشد، گروه مهندسی مکانیک، دانشکده فنی و مهندسی،دانشگاه ملایر، ملایر، ایران

10.22065/jsce.2021.254420.2276

چکیده

در این مقاله، رفتار ارتعاشات آزاد ورقهای بیضوی نازک مدرج تابعی با شرایط مرزی ساده و گیردار بر مبنای تئوری کلاسیک صفحات لایه‌ای بررسی می گردد. برخلاف مطالعات پیشین، هندسه ورق به صورت بیضوی و در حالت کلی تری، به شکل سوپر بیضوی در نظر گرفته می شود. همچنین، فرض می گردد که ورق مورد بررسی، تحت اعمال پیش بار داخل صفحه‌ای مرزی باشد و بر روی بستر کشسان از نوع وینکلر قرار گرفته باشد. فرض می شود که خواص مکانیکی ورق مدرج تابعی در راستای ضخامت به صورت پیوسته و براساس قانون توانی کسر حجمی مواد سازنده تغییر کند. با بکارگیری رویکرد حساب تغییرات، معادلات حاکم بر حرکت استخراج می گردند، برای حل معادلات حاصله، از روش ریتز استفاده می شود. علاوه بر مدلسازی تحلیلی، به منظور انجام مقایسه، مسئله به روش عددی و با استفاده از نرم افزار اجزاء محدود آباکوس نیز مدلسازی و تحلیل می گردد. صحت و دقت رهیافت تحلیلی حاضر از طریق مقایسه نتایج تحلیلی حاضر با نتایج موجود در ادبیات موضوع و همچنین نتایج عددی حاضر تایید می گردد. در ادامه، با انجام مطالعه پارامتری، اثرات برخی پارامترهای مهم همچون شرایط مرزی، نیروهای درون صفحه ای، هندسه ورق و توان کسر حجمی بر روی رفتار ارتعاشی ورق مطالعه و بحث می گردد. نتایج ارائه شده در این پژوهش می تواند در طراحی و کاربرد ورقهای بیضوی از جنس مدرج تابعی حائز اهمیت فراوان باشد.

کلیدواژه‌ها

موضوعات

مکانیک سازه

عنوان مقاله [English]

Vibration of functionally graded elliptical plates resting on Winkler-type elastic foundation subjected to initial in-plane loading

نویسندگان [English]

Mehdi Hosseini ¹
Hasan Ghiasvand ²

¹ Assistant Professor, Department of mechanical engineering, Malayer University, Malayer, Iran

² MSc Graduate, Department of Mechanical Engineering, Malayer University, Malayer, Iran

چکیده [English]

In this paper, the free vibration behavior of functionally graded thin elliptical plates with simply supported and clamped boundary conditions is investigated using classical laminated plate theory. In contrast to previous studies, the geometry of the plate is considered to be as elliptical and in a more general form as super elliptical. Also, it is assumed that the considered plate is subjected to boundary in-plane preload and is rested on Winkler-type elastic foundation. It is assumed that the mechanical properties of the functionally graded plate vary continuously through the thickness according to a power law of the volume fraction of the constituents. The governing equations of motions are derived by employing the variational approach. The obtained equations are solved using Ritz method. In addition to the analytical modeling, for comparison, the problem is also modeled and analyzed numerically by using finite element software Abaqus. Correctness and accuracy of the present analytical model is confirmed through comparing the present analytical results by the results existed in the literature and by the present numerical results. After that, doing parametric study, the effects of some important parameters such as the boundary conditions, the in-plane forces, the plate geometry and the power-law index on the vibration behavior of the plate are studied and discussed. The results presented in this research are of great importance in design and application of the functionally graded elliptical plates.

کلیدواژه‌ها [English]

Vibration
Elliptical plate
Functionally graded material
Winkler foundation
Initial in-plane load

مراجع

[1] Miyamoto, Y. Kaysser, W. A. Rabin, B. H. Kawasaki, A. and Ford, R. G. (1999). Functionally Graded Materials: Desing, Processing and Applications. New York: Springer US.

[2] Yamanouchi, M. Koizumi, M. Hirai, T. and Shiota, I. (1990). Proceedings of First International Symposium on Functionally Gradient Materials, Sendai: Japan.

[3] Koizumi, M. (1993). The Concept of FGM. Ceramic Transactions, Functionally Gradient Materials, Vol. 34, pp. 3-10.

[4] Yang, J. and Shen, H.S. (2001). Dynamic response of initially stressed functionally graded rectangular thin plates. Composite Structures, Vol. 54, pp. 497-508.

[5] Shen, H.S. (2002). Nonlinear bending response of functionally graded plates subjected to transverse loads and in thermal environments. International Journal of Mechanical Sciences, Vol. 44, pp. 561-584.

[6] Yang, J. and Shen, H.S. (2003). Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads under various boundary conditions. Composites Part B: Eng, Vol. 34, pp. 103-115.

[7] Allahverdizadeh, A. Naei, M.H. and Bahrami, M.N. (2008). Nonlinear free and forced vibration analysis of thin circular functionally graded plates, Journal of Sound and Vibration, Vol. 310, pp. 966-984.

[8] Lijun, Y. and Xueliang, J. (2014). Nonlinear vibration of rectangular orthotropic plates resting on the three-parameter foundations in thermal environments. Electronic Journal of Geotechnical Engineering, Vol. 19, pp. 4215-4226.

[9] Lal, R. and Ahlawat, N. (2015). Axisymmetric vibrations and buckling analysis of functionally graded circular plates via differential transform method. European Journal of Mechanics - A/Solids, Vol. 52, pp. 85-94.

[10] Abolghasemi, S. Eipakchi, H. R. and Shariati, M. (2016). An analytical procedure to study vibration of rectangular plates under non-uniform in-plane loads based on first-order shear deformation theory, Archive of Applied Mechanics, vol. 86, pp. 853–867.

[11] Zhao, J. Xie, F. Wang, A. Shuai, C. Tang, J. and Wang, Q. (2019). Dynamics analysis of functionally graded porous (FGP) circular, annular and sector plates with general elastic restraints, Composites Part B: Engineering, Vol. 159, pp. 20-43.

[12] Lal, R. and Ahlawat, N. (2019). Buckling and vibrations of two-directional FGM Mindlin circular plates under hydrostatic peripheral loading, Mechanics of Advanced Materials and Structures, Vol. 26(3), pp. 199-214.

[13] Ceribasi, S. and Altay, G. (2009). Free vibration of super elliptical plates with constant and variable thickness by Ritz method. Journal of Sound and Vibration, Vol. 319, pp. 668-680.

[14] Wang, C.M. Wang, L. and Liew, K.M. (1994). Vibration and buckling of super elliptical plates. J. Sound Vibration., vol. 171(3), pp. 301–314.

[15] Ceribasi, S. (2012). Static and Dynamic Analyses of Thin Uniformly Loaded Super Elliptical FGM Plates. Mechanics of Advanced Materials and Structures, 19(5), pp. 323–335.

[16] Abrate, S .(2008). Functionally Graded Plates Behave Like Homogeneous Plates.Composites Part B:Engineering, Vol. 39, pp. 151–158.

[17] Yang, H.S. Dong, C.Y. Wu, Y.H. (2020). Postbuckling analysis of multi-directional perforated FGM plates using NURBS-based IGA and FCM, Applied Mathematical Modelling, Vol. 84, pp. 466-500.

[18] Reddy, J. N. (2007). Theory and Analysis of Elastic Plates and Shells. New York: CRC Press.

[19] Kirchhoff, G. (1850). Uber Das Gleichgewicht Und Die Bewegung Einer Elatischen Scheibl. Mathematik, Vol. 40, pp. 51-88.

[20] Kumar, A. (2018). Free Transverse Vibration Analysis of thin rectangular plates having arbitrarily varying non-homogeneity along two concurrent edge. Ms.C. Thesis. Department of Mechanical Engineering, National Institute of Technology, Rourkela Odisha.

[21] Teng, M. W. and Wang, Y. Q. (2020). Nonlinear free vibration of rectangular plates reinforced with 3D graphene foam: Approximate analytical solution. Results in Physics, Vol. 17, 103147.

[22] Chinwuba Ike, Ch. (2017). Variational Formulation of the Mindlin Plate on Winkler Foundation Problem, Electronic Journal of Geotechnical Engineering, Vol. 22, Bund. 12, pp. 4829-4846.

[23] Ghiasvand, H. and Hosseini, M. (2019). Buckling analysis of functionally graded elliptical plates resting on Winkler-type elastic foundation. In: 3^rd national conference of materials engineering. Malayer: Malayer university.

[24] Benferhat, R. Daouadji, T. H. Mansour, M. S. (2016). Free vibration analysis of FG plates resting on an elastic foundation and based on the neutral surface concept using higher-order shear deformation theory, Comptes Rendus Mécanique, Vol. 344(9), pp. 631-641.