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Applied Mathematics and Mechanics >

2022 , Vol. 43 >Issue 4: 523 - 536

DOI: https://doi.org/10.1007/s10483-022-2834-7

Articles

Static and free vibration analysis of four-parameter continuous grading elliptical sandwich plates

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  • 1. Department of Mechanical Engineering, Razi University, Kermanshah 6734667149, Iran;
    2. Department of Mechanical Engineering, Ilam Branch, Islamic Azad University, Ilam 6714414971, Iran;
    3. Department of Mechanical Engineering, Amir-Kabir University of Technology, Tehran 158754413, Iran

Received date: 2021-10-02

  Revised date: 2021-12-21

  Online published: 2022-03-29

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Abstract

In the present study, the static and dynamic analyses of elliptical functionally graded sandwich (FGS) plates are investigated. The constituent materials of the sandwich plates are ceramic and metal so that the core is made of pure metal, while the face sheets consist of a combination of metal and ceramic according to a four-parameter power-law distribution. Different material profiles such as classic, symmetric, and asymmetric can be obtained using the applied generalized power-law distribution relation. The analysis is performed based on the classical laminated plate theory (CLPT) and the Ritz method. The effects of four parameters in the material distribution relation as well as different geometric parameters on the deflection and natural frequencies of elliptical FGS plates are studied. The results of this study show that with a proper distribution of materials, the optimal static and dynamic behavior can be achieved. The results also indicate that the generalized power-law distribution has significant effects on the natural frequencies of elliptical FGS plates. For example, although the frequency parameter of a plate with ceramic face sheets is more than the one with metal face sheets, the use of larger amounts of ceramic does not necessarily increase the natural frequency of the structure.

Key words： elliptical plate; sandwich plate; four-parameter power-law distribution; static analysis; free vibration analysis; Ritz method

Cite this article

M. H. YAS, F. AKHLAGHI, S. KAMARIAN, A. H. YAS . Static and free vibration analysis of four-parameter continuous grading elliptical sandwich plates[J]. Applied Mathematics and Mechanics, 2022 , 43(4) : 523 -536 . DOI: 10.1007/s10483-022-2834-7

References

[1] BIRMAN, V. and KARDOMATEAS, G. A. Review of current trends in research and applications of sandwich structures. Composites Part B: Engineering, 142, 221-240(2018)
[2] RAMNATH, B. V., ALAGARRAJA, K., and ELANCHEZHIAN, C. Review on sandwich composite and their applications. Materials Today: Proceedings, 16, 859-864(2019)
[3] SAYYAD, A. S. and GHUGAL, Y. M. On the free vibration analysis of laminated composite and sandwich plates: a review of recent literature with some numerical results. Composite Structures, 129, 177-201(2015)
[4] SAYYAD, A. S. and GHUGAL, Y. M. Bending, buckling and free vibration of laminated composite and sandwich beams: a critical review of literature. Composite Structures, 171, 486-504(2017)
[5] CAO, D., GAO, Y., YAO, M., and ZHANG, W. Free vibration of axially functionally graded beams using the asymptotic development method. Engineering Structures, 173, 442-448(2018)
[6] MAO, J. J., KE, L. L., YANG, J., KITIPORNCHAI, S., and WANG, Y. S. Thermoelastic instability of functionally graded coating with arbitrarily varying properties considering contact resistance and frictional heat. Applied Mathematical Modelling, 43, 521-537(2017)
[7] ZENKOUR, A. M. A comprehensive analysis of functionally graded sandwich plates: part 1, deflection and stresses. International Journal of Solids and Structures, 42(18-19), 5224-5242(2005)
[8] ZENKOUR, A. M. A comprehensive analysis of functionally graded sandwich plates: part 2, buckling and free vibration. International Journal of Solids and Structures, 42(18-19), 5243-5258 (2005)
[9] ABDELAZIZ, H. H., HASSEN, A. A., ISMAIL, M., LAKHDAR, B., ABDELOUAHED, T., and ADDA, B. E. A. Static analysis of functionally graded sandwich plates using an e–cient and simple refined theory. Chinese Journal of Aeronautics, 24(4), 434-448(2011)
[10] XIANG, S., KANG, G. W., YANG, M. S., and ZHAO, Y. Natural frequencies of sandwich plate with functionally graded face and homogeneous core. Composite Structures, 96, 226-231(2013)
[11] BESSAIM, A., HOUARI, M. S., TOUNSI, A., MAHMOUD, S. R., and BEDIA, E. A. A. A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets. Journal of Sandwich Structures & Materials, 15(6), 671-703(2013)
[12] KAMARIAN, S., YAS, M. H., and POURASGHAR, A. Free vibration analysis of three-parameter functionally graded material sandwich plates resting on Pasternak foundations. Journal of Sandwich Structures & Materials, 15(3), 292-308(2013)
[13] NGUYEN, V. H., NGUYEN, T. K., THAI, H. T., and VO, T. P. A new inverse trigonometric shear deformation theory for isotropic and functionally graded sandwich plates. Composites Part B: Engineering, 66, 233-246(2014)
[14] THAI, H. T., NGUYEN, T. K., VO, T. P., and LEE, J. Analysis of functionally graded sandwich plates using a new first-order shear deformation theory. European Journal of Mechanics-A=Solids, 45, 211-225(2014)
[15] MAHI, A. and TOUNSI, A. 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(9), 2489-2508(2015)
[16] BENNOUN, M., HOUARI, M. S. A., and TOUNSI, A. A novel five-variable refined plate theory for vibration analysis of functionally graded sandwich plates. Mechanics of Advanced Materials and Structures, 23(4), 423-431(2016)
[17] AKAVCI, S. S. Mechanical behavior of functionally graded sandwich plates on elastic foundation. Composites Part B: Engineering, 96, 136-152(2016)
[18] MENASRIA, A., BOUHADRA, A., TOUNSI, A., BOUSAHLA, A. A., and MAHMOUD, S. R. A new and simple HSDT for thermal stability analysis of FG sandwich plates. Steel and Composite Structures, 25(2), 157-175(2017)
[19] DO, T. V., BUI, T. Q., YU, T. T., PHAM, D. T., and NGUYEN, C. T. Role of material combination and new results of mechanical behavior for FG sandwich plates in thermal environment. Journal of Computational Science, 21, 164-181(2017)
[20] ZENKOUR, A. M. A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities. Composite Structures, 201, 38-48(2018)
[21] MEKSI, R., BENYOUCEF, S., MAHMOUDI, A., TOUNSI, A., ADDA-BEDIA, E. A., and MAHMOUD, S. R. An analytical solution for bending, buckling and vibration responses of FGM sandwich plates. Journal of Sandwich Structures & Materials, 21(2), 727-757(2019)
[22] MAHMOUDI, A., BENYOUCEF, S., TOUNSI, A., BENACHOUR, A., ADDA-BEDIA, E. A., and MAHMOUD, S. R. A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations. Journal of Sandwich Structures & Materials, 21(6), 1906-1929(2019)
[23] NIKBAKHT, S., KAMARIAN, S., and SHAKERI, M. A review on optimization of composite structures, part II: functionally graded materials. Composite Structures, 214, 83-102(2019)
[24] TORNABENE, F. and VIOLA, E. Free vibrations of four-parameter functionally graded parabolic panels and shells of revolution. European Journal of Mechanics-A=Solids, 28(5), 991-1013(2009)
[25] ARAGH, B. S. and YAS, M. H. Three-dimensional analysis of thermal stresses in four-parameter continuous grading fiber reinforced cylindrical panels. International Journal of Mechanical Sciences, 52(8), 1047-1063(2010)
[26] KAMARIAN, S., SADIGHI, M., SHAKERI, M., and YAS, M. H. Free vibration response of sandwich cylindrical shells with functionally graded material face sheets resting on Pasternak foundation. Journal of Sandwich Structures & Materials, 16(5), 511-533(2014)
[27] FESHARAKI, J. J. and ROGHANI, M. Thermo-mechanical behavior of a functionally graded hollow cylinder with an elliptic hole. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 42(1), 1-15(2020)
[28] LEISSA, A. W. Vibration of a simply-supported elliptical plate. Journal of Sound and Vibration, 6(1), 145-148(1967)
[29] LEISSA, A. W. Vibration of Plates, Scientific and Technical Information Division, National Aeronautics and Space Administration, 67-68(1969)
[30] BERES, D. P. Vibration analysis of a completely free elliptical plate. Journal of Sound and Vibration, 34(3), 441-443(1974)
[31] LIM, C. W., KITIPORNCHAI, S., and LIEW, K. M. A free-vibration analysis of doubly connected super-elliptical laminated composite plates. Composites Science and Technology, 58(3-4), 435-445 (1998)
[32] ALTEKIN, M. and ALTAY, G. Static analysis of point-supported super-elliptical plates. Archive of Applied Mechanics, 78(4), 259-266(2008)
[33]ÇERIBAŞI, S. Static and dynamic analyses of thin uniformly loaded super elliptical FGM plates. Mechanics of Advanced Materials and Structures, 19(5), 323-335(2012)
[34] HOSSEINI-HASHEMI, S. and ATASHIPOUR, S. R. Free vibration analysis of functionally graded elliptical plates. Journal of Marine Engineering, 8(15), 43-60(2012)
[35] ZHANG, D. G. and ZHOU, H. M. Nonlinear symmetric free vibration analysis of super elliptical isotropic thin plates. Computers; Materials & Continua, 40(1), 21-34(2014)
[36] ALTEKIN, M. Bending of super-elliptical Mindlin plates by finite element method. Teknik Dergi, 29(4), 8469-8496(2018)
[37] MAO, J. J., ZHANG, W., and LU, H. M. Static and dynamic analyses of graphene-reinforced aluminium-based composite plate in thermal environment. Aerospace Science and Technology, 107, 106354(2020)
[38] MAO, J. J., LAI, S. K., ZHANG, W., and LIU, Y. Comparisons of nonlinear vibrations among pure polymer plate and graphene platelet reinforced composite plates under combined transverse and parametric excitations. Composite Structures, 265, 113767(2021)
[39] MAO, J. J. and ZHANG, W. Linear and nonlinear free and forced vibrations of graphene reinforced piezoelectric composite plate under external voltage excitation. Composite Structures, 203, 551- 565(2018)
[40] FANTUZZI, N., TORNABENE, F., and VIOLA, E. Four-parameter functionally graded cracked plates of arbitrary shape: a GDQFEM solution for free vibrations. Mechanics of Advanced Materials and Structures, 23(1), 89-107(2016)
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