Free vibration analysis of FGM plates with opening and stiffener

Document Type : Research Article


1 Civil Structural Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad.

2 Civil Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad,Mashhad, Iran

3 Master of Civil Structural Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran


Functionally Graded Materials (FGMs) are kinds of composite materials that due to the continuity of mixture of constituent materials as Functionally Graded, have more effective mechanical properties than multilayered composite materials. The most common use of these materials is in thin[1]walled structures such as plates and shells. Due to some executive needs, make opening and stiffener in plates might be necessary. Free vibration of a system is performed only under the influence of initial conditions and without any external excitation. A system under free vibration situation vibrates with one or more its natural frequencies. If the frequency of vibration caused by the effect of external excitation is equal to the one of the natural frequencies of the system, resonance state occurs. In this case, there will be a large amplitude fluctuation that can cause fracture of huge structures such as bridges and wings of aircrafts. Therefore, in the present study, the effective parameters on free vibration of FGM plates with opening and stiffener have been studied.


Main Subjects

[1]Miyamoto, Y. A., Kaysser, W., Rabin, B. H., kawasaki, A., and Ford, R. G., Functionally Graded Material: Desing, Processing and Applications, United States, 1999.
[2]M. Yamanouchi, M. Koizumi, T. Hirai, and I. Shiota, "FGM-90," in Proceedings of the First International Symposium on Functionally Gradient Materilas, FGM Forum, Tokyo, Japan, 1990.
[3]Koizumi,  M., “The  Concept of  FGM”, Ceramic Transactions, Functionally Gradient Materials, Vol. 34, pp. 3-10, 1993.
[4]S. Srinivas, C. J. Rao, A. J. J. o. s. Rao, and vibration, "An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates," vol. 12, no. 2, pp. 187-199, 1970.
[5]S. Srinivas, A. J. I. J. o. S. Rao, and Structures, "Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates," vol. 6, no. 11, pp. 1463-1481, 1970.
[6]M. J. J. o. S. Levinson and Vibration, "Free vibrations of a simply supported, rectangular plate: an exact elasticity solution," vol. 98, no. 2, pp. 289-298, 1985.
[7]A. K. Noor and W. S. J. J. o. A. M. Burton, "Threedimensional solutions for antisymmetrically laminated anisotropic plates," vol. 57, no. 1, pp. 182-188, 1990.
[8]C.-C. Lin and W. J. J. o. S. V. King, "Free transverse vibrations of rectangular unsymmetrically laminated plates," vol. 36, pp. 91-103, 1974.
[9]D. J. J. o. s. Gorman and vibration, "An exact analytical approach to the free vibration analysis of rectangular plates with mixed boundary conditions," vol. 93, no. 2, pp. 235-247, 1984.
[10]J. Reddy, N. J. J. o. s. Phan, and vibration, "Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory," vol. 98, no. 2, pp. 157-170, 1985.
[11]M. J. J. o. S. Di Sciuva and Vibration, "Bending, vibration and buckling of simply supported thick multilayered orthotropic plates: an evaluation of a new displacement model," vol. 105, no. 3, pp. 425-442, 1986.
[12]A. Ferreira, R. Batra, C. Roque, L. Qian, and R. J. C. S. Jorge, "Natural frequencies of functionally graded plates by a meshless method," vol. 75, no. 1-4, pp. 593-600, 2006.
[13]S. Hosseini-Hashemi, M. Fadaee, and S. R. J. I. J. o. M. S. Atashipour, "A new exact analytical approach for free vibration of Reissner–Mindlin functionally graded rectangular plates," vol. 53, no. 1, pp. 11-22, 2011.
[14]S. Hosseini-Hashemi, M. Fadaee, and S. R. J. C. S. Atashipour, "Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure," vol. 93, no. 2, pp. 722-735, .1102
[15]A. Allahverdizadeh, R. Oftadeh, M. Mahjoob, and M. J. A. M. S. S. Naei, "Homotopy perturbation solution and periodicity analysis of nonlinear vibration of thin rectangular functionally graded plates," vol. 27, no. 2, pp. 210-220, 2014.
[16]P. Malekzadeh, A. J. M. o. A. M. Alibeygi Beni, and Structures, "Nonlinear free vibration of in-plane functionally graded rectangular plates," vol. 22, no. 8, pp.336-640-2015.
[17]A. J. A. M. Alibeigloo, "Free vibration analysis of nanoplate using three-dimensional theory of elasticity," vol. 222, no. 1-2, p. 149, 2011.
[18]A. Setoodeh, P. Malekzadeh, and A. J. P. o. t. I. o. M. E.Vosoughi, Part C: Journal of Mechanical Engineering Science, "Nonlinear free vibration of orthotropic graphene sheets using nonlocal Mindlin plate theory," vol. 226, no. 7, pp. 1896-1906, 2012.
[19]P. A. Sharabiani and M. R. H. J. C. P. B. E. Yazdi, "Nonlinear free vibrations of functionally graded nanobeams with surface effects," vol. 45, no. 1, pp. 581-586, 2013.
[20]M. Talebitooti, M. Ghayour, S. Ziaei-Rad, and R. J. A. o. A. M. Talebitooti, "Free vibrations of rotating composite conical shells with stringer and ring stiffeners," vol. 80, no. 3, pp. 201-215, 2010.
[21]S. Kidane, G. Li, J. Helms, S.-S. Pang, and E. J. C. P. B. E. Woldesenbet, "Buckling load analysis of grid stiffened composite cylinders," vol. 34, no. 1, pp. 1-9, 2003.
[22]B. Mustafa, R. J. C. Ali, and structures, "An energy method for free vibration analysis of stiffened circular cylindrical shells," vol. 32, no. 2, pp. 355-363, 1989.
[23]J. N. Reddy, Mechanics of laminated composite plates and shells: theory and analysis. CRC press, 2004.
[24]W.-Y. Jung and S.-C. J. A. M. M. Han, "Static and eigenvalue problems of sigmoid functionally graded materials (S-FGM) micro-scale plates using the modified couple stress theory," vol. 39, no. 12, pp. 3506-3524, 2015.
[25]X.-L. Huang, H.-S. J. I. J. o. S. Shen, and Structures, "Nonlinear vibration and dynamic response of functionally graded plates in thermal environments," vol. 41, no. 9-10, pp. 2403-2427, 2004.
[26]H.-S. Shen, Functionally graded materials: nonlinear analysis of plates and shells. CRC press, 2016.
[27]R. Gunes, M. Aydin, M. K. Apalak, and J. J. C. S. Reddy, "The elasto-plastic impact analysis of functionally graded circular plates under low-velocities," vol. 93, no. 2, pp. 860-869, 2011.
[28]T. J. I. J. o. I. E. Hause, "Advanced functionally graded plate-type structures impacted by blast loading," vol. 38, no. 5, pp. 314-321, 2011.
[29]Abaqus Analysis User’s Manual Version 6.14. Dassault Systemes Simulia Crop.: Providence, RI, USA, 2014.
[30]R. Jome Manzari and F. Shahabian, "The Geometrically nonlinear dynamic response of metal-ceramic FGM plates under the blast loading", Journal of Structural and Construction Engineering, [online] vol. 5, pages 16, 2018, (in Persian).
[31]Ramu, I. and Mohanty, S.C., 2012. Study on free vibration analysis of rectangular plate structures using finite element method. Procedia engineering, 38, pp.2758-2766
[32]C. Aksoylar, A. Ömercikoğlu, Z. Mecitoğlu, and M. H. J. C. S. Omurtag, "Nonlinear transient analysis of FGM and FML plates under blast loads by experimental and mixed FE methods," vol. 94, no. 2, pp. 731-744, 2012.
[33]A. S. Nowak and K. R. Collins, Reliability of structures. CRC Press, 2012.