ارتعاش ورقهای مدرج تحت جرم گسترده با استفاده از تئوری تغییرشکل برشی مرتبۀ سوم

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشگاه بوعلی سینا همدان

2 دانشگاه آزاد اسلامی واحد علوم و تحقیقات همدان

3 دانشگاه آزاد اسلامی واحد ساوه

چکیده

در این مقاله ارتعاش آزاد یک ورق مدرج مستطیلی تحت اثر جرم گستردۀ موضعی بررسی شده است. خواص ورق های مدرج مانند مدول یانگ و چگالی در راستای ضخامت ورق به‌صورت پیوسته متغیر است. ورق بهحالت مدرج توانی، سیگموید و یا نمایی تعریف می شود. تکیه گاه ورق ساده در نظر گرفته میشود و معادلات حرکت با استفاده از اصل همیلتون و براساس تئوری تغییرشکل برشی مرتبۀ سوم به‌دست می آیند. اثر پارامترهای مختلفی مانند ابعاد ورق و جرم گسترده و نسبت جرم روی فرکانس های طبیعی آن بررسی شده است. با مقایسۀ نتایج به‌دست آمده با نتایج ارائهشدۀ قبلی نشان داده شده است که نتایج حاضر از دقت خوبی برخوردار است.

کلیدواژه‌ها


عنوان مقاله [English]

Vibration of FGM Plates With Distributed Mass Using Third Order Shear Deformation Theory

نویسندگان [English]

  • alireza shooshtari 1
  • Reza Motahari 2
  • Mohamadreza Kari 3
1 Bu-Ali Sina university
2 Islamic Azad University, Hamedan
3 Islamic Azad university, Saaveh
چکیده [English]

In this paper, free vibration of rectangular functionally graded material (FGM) plates with distributed patch mass is analyzed. Properties of these plates like Young’s modulus and density vary continuously throughout the thickness direction. The plate is defined by power-law, sigmoid or exponential function. The boundary condition of the plate is assumed to be simply supported and the equation of motion is obtained by using of Hamilton principle and third order shear deformation theory. The effects of different parameters such as the plate and mass dimensions and mass ratio on the natural frequencies of the plate are analyzed. Compared to previous results, our results are very accurate in similar cases.

کلیدواژه‌ها [English]

  • Free Vibration
  • rectangular plate
  • Distributed Patch Mass
  • Third Order Shear Deformation Theory
Stavsky, Y., "On the theory of symmetrically heterogeneous plates having the same thickness variation of the elastic moduli", Topics App. Mech., New York: American Elsevier, pp. 105, (1965).
2. Bert, C. W. and Chen, T.L.C., "Effect of shear deformation on vibration of antisymmetric angle-ply laminated rectangular plates", Int. J. Solids Struct., Vol. 14, pp. 465-473, (1978).
3. Reddy, J.N., "Free vibration of antisymmetric angle-ply laminated plates including transverse shear deformation by the finite element method", J. Sound Vib., Vol. 66(4), pp. 565-576, (1979).
4. Reddy, J.N. and Khdeir, A.A., "Buckling and vibration of laminated composite plates using various plate theories", America. Inst. Aeronaut. Astornaut. J., Vol. 27(12), pp. 1808-1817, (1989).
5. Reddy, J.N., "Mechanics of Laminated Composite Plates", Second Edition, New York: CRC Press. (1997).
6. Khdeir, A.A. and Reddy, J.N., "Free vibration of laminated composite plates using second-order shear deformation theory", Compos. Struct., Vol. 71, pp. 617-626, (1999).
7. Singh, B.N., Yadav, D. and Iyengar, N.G.R., "Natural frequencies of composite plates with random material properties using higher-order shear deformation theory", Int. J. Mech. Sci., Vol. 43,
pp. 2193-2214, (2001).
8. Kant, T. and Swaminathan, K., "Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory", Compos. Struct., Vol. 53, pp. 73-85, (2001).
9. Rastgaar, A., Mahinfalah, M. and Nakhaie Jazar, G., "Natural frequencies of laminated composite plates using third order shear deformation theory", Compos. Struct., Vol. 72, pp. 273-279, (2006).
10. Kompaz, O. and Telli, S., "Free vibration of a rectangular plate carrying distributed mass", J. Sound Vib., Vol. 251(1), pp. 39-57, (2002).
11. Wong, W.O., "The effects of distributed mass loading on plate vibration behavior", J. Sound Vib., Vol. 252(3), pp. 577-583, (2002).
12. Alibeigloo, A., Shakeri, M. and Kari, M.R., "Free vibration analysis of antisymmetric laminated rectangular plates with distributed patch mass using third-order shear deformation theory", Ocean Eng., Vol. 35, pp. 183–190, (2008).
13. Chi, S.H. and Chung, Y.L., "Mechanical behavior of functionally graded material plates under transverse load-Part I: analysis", Int. J. Solids Struct., Vol. 43, pp. 3657-3674, (2006).
14. Vel, S.S. and Batra, R.C., "Three-dimensional exact solution for the vibration of functionally graded rectangular plates", J. Sound Vib., Vol. 272, pp. 703-730, (2004).
15. Qian, L.F., Batra, R.C. and Chen, L.M., "Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local Petrov–Galerkin method", Compos., Part B, Vol. 35, pp. 685–697, (2004).
16. Zenkour, A.M., "A comprehensive analysis of functionally graded sandwich plates: Part 2—Buckling and free vibration", Int. J. Solids Struct., Vol. 42, pp. 5243–5258, (2005).
17. Ferreira, A.J.M., Batra, R.C., Roque, C.M.C., Qian, L.F. and Jorge, R.M.N., "Natural frequencies of functionally graded plates by a meshless method", Compos. Struct., Vol. 75, pp. 593–600, (2006).
18. Hosseini, Sh., Hashemi, H., Rokni Damavandi, T., Akhavan, H. and Omidi, M., "Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory", Appl. Math. Model., Vol. 34, pp. 1276–1291, (2010).
19. Talha, M. and Singh, B.N., "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Model., Vol. 34, pp. 3991–4011, (2010).
20. Efraim, E., "Accurate formula for determination of natural frequencies of FGM plates basing on frequencies of isotropic plates", Proce. Eng., Vol. 10, pp. 242–247, (2011).
21. Uymaz, B., Aydogdu, M. and Filiz, S., "Vibration analyses of FGM plates with in-plane material in-homogeneity by Ritz method", Compos. Struct., Vol. 94, pp. 1398–1405, (2012).
22. Dogan, V., "Nonlinear vibration of FGM plates under random excitation", Compos. Struct., Vol. 95, pp. 366–374, (2013).
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