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http://dx.doi.org/10.12989/sem.2021.79.4.401

Vibration of two types of porous FG sandwich conical shell with different boundary conditions  

Rahmani, Mohsen (Department of Mechanics, Tuyserkan Branch, Islamic Azad University)
Mohammadi, Younes (Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University)
Publication Information
Structural Engineering and Mechanics / v.79, no.4, 2021 , pp. 401-413 More about this Journal
Abstract
In this paper, in various boundary conditions, the vibration behavior of the two types of porous FG truncated conical sandwich shells is investigated based on the improved high order sandwich shells theory. Two types of porosity are considered in the power law rule to model the FGM properties. In the first type, FG face sheets cover a homogeneous core, and in the second one, the FG core is covered by the homogeneous face sheets. All materials are temperature dependent. By utilizing the Hamilton's energy principle, using the nonlinear von Karman strains in the layers and considering the in-plane stresses and thermal stresses in the core and the face sheets, the governing equations are obtained. A Galerkin method is used to solve the equations with clamped-clamped, clamped-free, and free-free boundary conditions. To validate the results, a FEM software is used and some results are validated with the results in the literatures. Also, Some geometrical parameters, temperature variations and porosity effects are studied. By increasing the length to thickness ratio, temperature, the semi-vertex angle and the radius to thickness ratio, the fundamental frequency parameter decreases in all boundary conditions. In both types of sandwiches for both porosity distributions, by increasing the porosity volume fraction, the fundamental frequency parameters increase. Frequency variation of type-II is lower than type-I in the thermal conditions. And the fundamental frequencies of the clamped-clamped (C-C) and clamped-free (C-F) boundary conditions have the highest and lowest values, respectively.
Keywords
boundary condition; conical shell; FGM; free vibration; porosity; sandwich structure;
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Times Cited By KSCI : 3  (Citation Analysis)
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1 Kang, J.H. (2015), "Vibrations of truncated shallow and deep conical shells with non-uniform thickness", Struct. Eng. Mech., 55(1), 29-46. https://doi.org/10.12989/sem.2015.55.1.029.   DOI
2 Kiani, Y., Dimitri, R. and Tornabene, F. (2018), "Free vibration study of composite conical panels reinforced with FG-CNTs", Eng. Struct., 172, 472-82. https://doi.org/10.1016/j.engstruct.2018.06.006.   DOI
3 Lam, K.Y. and Hua, L. (1999), "Influence of boundary conditions on the frequency characteristics of a rotating truncated circular conical shell", J. Sound, Vib., 223(2), 171-195. https://doi.org/10.1006/jsvi.1998.1432.   DOI
4 Li, F.M., Kishimoto, K. and Huang, W.H. (2009), "The calculations of natural frequencies and forced vibration responses of conical shell using the Rayleigh-Ritz method", Mech. Res. Commun., 36(5), 595-602. https://doi.org/10.1016/j.mechrescom.2009.02.003.   DOI
5 Mohammadi, Y. and Rahmani, M. (2020), "Temperature-dependent buckling analysis of functionally graded sandwich cylinders", J. Solid Mech., 12(1), 1-15. https://doi.org/10.22034/jsm.2020.670341.   DOI
6 Sofiyev, A.H. (2016), "Parametric vibration of FGM conical shells under periodic lateral pressure within the shear deformation theory", Compos. Part B-Eng., 89, 282-294. https://doi.org/10.1016/j.compositesb.2015.11.017.   DOI
7 Song, Z., Cao, Q. and Dai, Q. (2019), "Free vibration of truncated conical shells with elastic boundary constraints and added mass", Int. J. Mech. Sci., 155, 286-294. https://doi.org/10.1016/j.ijmecsci.2019.02.039.   DOI
8 Najafov, A.M., Sofiyev, A.H. and Kuruoglu, N. (2014), "On the solution of nonlinear vibration of truncated conical shells covered by functionally graded coatings", Acta Mech., 225(2), 563-80. https://doi.org/10.1007/s00707-013-0980-5.   DOI
9 Rahmani, M., Mohammadi, Y. and Kakavand, F. (2019a), "Vibration analysis of different types of porous FG circular sandwich plates", ADMT J., 12(3), 63-75.
10 Rahmani, M., Mohammadi, Y., Kakavand, F. and Raeisifard, H. (2020b), "Vibration analysis of different types of porous FG conical sandwich shells in various thermal surroundings", J. Appl. Comput. Mech., 6(3), 416-432. https://doi.org/10.22055/jacm.2019.29442.1598.   DOI
11 Tornabene, F., Viola, E. and Inman, D.J. (2009), "2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures", J. Sound. Vib., 328(3), 259-290. https://doi.org/10.1016/j.jsv.2009.07.031.   DOI
12 Kwak, M.K., Koo, J.R. and Bae, C.H. (2011), "Free vibration analysis of a hung clamped-free cylindrical shell partially submerged in fluid", J. Fluid. Struct., 27(2), 283-296. https://doi.org/10.1016/j.jfluidstructs.2010.11.005.   DOI
13 Su, Z., Jin, G., Shi, S., Ye, T. and Jia, X. (2014a), "A unified solution for vibration analysis of functionally graded cylindrical, conical shells and annular plates with general boundary conditions", Int. J. Mech. Sci., 80, 62-80. https://doi.org/10.1016/j.ijmecsci.2014.01.002.   DOI
14 Singha, T.D., Rout, M., Bandyopadhyay, T. and Karmakar, A. (2020), "Free vibration analysis of rotating pretwisted composite sandwich conical shells with multiple debonding in hygrothermal environment", Eng. Struct., 204, 110058. https://doi.org/10.1016/j.engstruct.2019.110058.   DOI
15 Sofiyev, A.H. (2019), "Review of research on the vibration and buckling of the FGM conical shells", Compos. Struct., 211, 301-317. https://doi.org/10.1016/j.compstruct.2018.12.047.   DOI
16 Sofiyev, A.H. and Osmancelebioglu, E. (2017), "The free vibration of sandwich truncated conical shells containing functionally graded layers within the shear deformation theory", Compos. Part B-Eng., 120, 197-211. https://doi.org/10.1016/j.compositesb.2017.03.054.   DOI
17 Soureshjani, A.H., Talebitooti, R. and Talebitooti, M. (2020), "A semi-analytical approach on the effect of external lateral pressure on free vibration of joined sandwich aerospace composite conical-conical shells", Aerosp. Sci. Technol., 99, 105559. https://doi.org/10.1016/j.ast.2019.105559.   DOI
18 Su, Z., Jin, G. and Ye, T. (2014b), "Three-dimensional vibration analysis of thick functionally graded conical, cylindrical shell and annular plate structures with arbitrary elastic restraints", Compos. Struct., 118, 432-447. https://doi.org/10.1016/j.compstruct.2014.07.049.   DOI
19 Talebitooti, M. (2018), "Thermal effect on free vibration of ring-stiffened rotating functionally graded conical shell with clamped ends", Mech. Adv. Mater. Struct., 25(2), 155-165. https://doi.org/10.1080/15376494.2016.1255809.   DOI
20 Sofiyev, A.H. (2018), "Application of the first order shear deformation theory to the solution of free vibration problem for laminated conical shells", Compos. Struct., 188, 340-346. https://doi.org/10.1016/j.compstruct.2018.01.016.   DOI
21 Qin, B., Zhong, R., Wang, T., Wang, Q., Xu, Y. and Hu, Z. (2020), "A unified Fourier series solution for vibration analysis of FG-CNTRC cylindrical, conical shells and annular plates with arbitrary boundary conditions", Compos. Struct., 232, 111549. https://doi.org/10.1016/j.compstruct.2019.111549.   DOI
22 Shakouri, M. (2019), "Free vibration analysis of functionally graded rotating conical shells in thermal environment", Compos. Part B-Eng., 163, 574-584. https://doi.org/10.1016/j.compositesb.2019.01.007.   DOI
23 Viswanathan, K.K., Saira J. and Abdul Aziz, Z. (2013), "Free vibration of symmetric angle-ply layered conical shell frusta of variable thickness under shear deformation theory", Struct. Eng. Mech., 45(2), 259-275. https://doi.org/10.12989/sem.2013.45.2.259.   DOI
24 Xiang, P., Xia, Q., Jiang, L.Z., Peng, L., Yan, J.W. and Liu, X. (2021), "Free vibration analysis of FG-CNTRC conical shell panels using the kernel particle Ritz element-free method", Compos. Struct., 255, 112987. https://doi.org/10.1016/j.compstruct.2020.112987.   DOI
25 Xie, X., Jin, G., Ye, T. and Liu, Z. (2014), "Free vibration analysis of functionally graded conical shells and annular plates using the Haar wavelet method", Appl. Acoust., 85, 130-142. https://doi.org/10.1016/j.apacoust.2014.04.006.   DOI
26 Ng, T.Y., Li, H. and Lam, K.Y. (2003), "Generalized differential quadrature for free vibration of rotating composite laminated conical shell with various boundary conditions", Int. J. Mech. Sci., 45(3), 567-587. https://doi.org/10.1016/S0020-7403(03)00042-0.   DOI
27 Mouli, B.C., Kar, V.R., Ramji, K. and Rajesh, M. (2018), "Free vibration of functionally graded conical shell", Mater. Today: Proc., 5(6), 14302-14308. https://doi.org/10.1016/j.matpr.2018.03.012.   DOI
28 Amabili, M. and Balasubramanian, P. (2020), "Nonlinear vibrations of truncated conical shells considering multiple internal resonances", Nonlin. Dyn., 6, 1-17. https://doi.org/10.1007/s11071-020-05507-8.   DOI
29 Zhao, J., Choe, K., Shuai, C., Wang, A. and Wang, Q. (2019), "Free vibration analysis of functionally graded carbon nanotube reinforced composite truncated conical panels with general boundary conditions", Compos. Part B: Eng., 160, 225-240. https://doi.org/10.1016/j.compositesb.2018.09.105.   DOI
30 Permoon, M.R., Shakouri, M. and Haddadpour, H. (2019), "Free vibration analysis of sandwich conical shells with fractional viscoelastic core", Compos. Struct., 214, 62-72. https://doi.org/10.1016/j.compstruct.2019.01.082.   DOI
31 Rahmani, M., Mohammadi, Y. and Kakavand, F. (2020a), "Buckling analysis of different types of porous FG conical sandwich shells in various thermal surroundings", J. Brazil. Soc. Mech. Sci., 42(4), 1-16. https://doi.org/10.1007/s40430-020-2200-2.   DOI
32 Zarei, M., Rahimi, G.H. and Hemmatnezhad, M. (2020), "Free vibrational characteristics of grid-stiffened truncated composite conical shells", Aerosp. Sci. Technol., 99, 105717. https://doi.org/10.1016/j.ast.2020.105717.   DOI
33 Bahrami, M.N. (2004), "Vibration theory and its application in engineering", University of Tehran, Tehran.
34 Bakhtiari, M., Lakis, A.A. and Kerboua, Y. (2020), "Nonlinear vibration of truncated conical shells: Donnell, Sanders and Nemeth theories", Int. J. Nonlin. Sci. Numer. Simul., 21(1), 83-97. https://doi.org/10.1515/ijnsns-2018-0377.   DOI
35 Rahmani, M. and Dehghanpour, S. (2020), "Temperaturedependent vibration of various types of sandwich beams with porous FGM layers", Int. J. Struct. Stab. Dyn., 21(02), 2150016. https://doi.org/10.1142/S0219455421500164.   DOI
36 Rahmani, M., Mohammadi, Y. and Kakavand, F. (2019b), "Vibration analysis of sandwich truncated conical shells with porous FG face sheets in various thermal surroundings", Steel. Compos. Struct., 32(2), 239-352. https://doi.org/10.12989/scs.2019.32.2.239.   DOI
37 Aris, H. and Ahmadi, H. (2020), "Nonlinear vibration analysis of FGM truncated conical shells subjected to harmonic excitation in thermal environment", Mech. Res. Commun., 104, 103499. https://doi.org/10.1016/j.mechrescom.2020.103499.   DOI
38 Fard, K.M. and Livani, M. (2015), "New enhanced higher order free vibration analysis of thick truncated conical sandwich shells with flexible cores", Struct. Eng. Mech., 55(4), 719-742. https://doi.org/10.12989/sem.2015.55.4.719.   DOI
39 Fazzolari, F.A. (2017), "Sandwich structures.", Stab. Vib. Thin Wall. Compos. Struct., 49-90. https://doi.org/10.1016/B978-0-08-100410-4.00002-8.   DOI
40 Frostig, Y.B., Baruch, M., Vilnay, O. and Sheinman, I. (1992), "High-order theory for sandwich-beam behavior with transversely flexible core", J. Eng. Mech., 118(5), 1026-43. https://doi.org/10.1061/(ASCE)0733-9399(1992)118:5(1026).   DOI
41 Javed, S., Viswanathan, K.K., Aziz, Z.A. and Lee, J.H. (2016), "Vibration analysis of a shear deformed anti-symmetric angleply conical shells with varying sinusoidal thickness", Struct. Eng. Mech., 58(6), 1001-1020. https://doi.org/10.12989/sem.2016.58.6.1001.   DOI
42 Reddy, J.N. (1998), "Thermomechanical behavior of functionally graded materials", Dept. of Mechanical Engineering, Texas A&M Univ. College Station.
43 Reddy, J.N. (2003), Mechanics of Laminated Composite Plates and Shells, Theory and Application, CRC Press, New York.
44 Heydarpour, Y., Aghdam, M.M. and Malekzadeh, P. (2014), "Free vibration analysis of rotating functionally graded carbon nanotube-reinforced composite truncated conical shells", Compos. Struct., 117, 187-200. https://doi.org/10.1016/j.compstruct.2014.06.023.   DOI
45 Yan, K., Zhang, Y., Cai, H. and Tahouneh, V. (2020), "Vibrational characteristic of FG porous conical shells using Donnell's shell theory", Steel. Compos. Struct., 35(2), 249-260. https://doi.org/10.12989/scs.2020.35.2.249.   DOI
46 Irie, T., Yamada, G. and Tanaka, K. (1984), "Natural frequencies of truncated conical shells", J. Sound, Vib., 92(3), 447-453. https://doi.org/10.1016/0022-460X(84)90391-2.   DOI