Vibration analysis of FG cylindrical shell: Evaluation of Ritz-polynomial mixed with ring terms |
Khadimallah, Mohamed A.
(Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department)
Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad) Naeem, Muhammad Nawaz (Department of Mathematics, Govt. College University Faisalabad) Qazaq, Amjad (Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department) Alqahtani, Abdulaziz (Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department) Tounsi, Abdelouahed (YFL (Yonsei Frontier Lab), Yonsei University) |
1 | Mehar, K. and Panda, S.K. (2016a), "Geometrical nonlinear free vibration analysis of FG-CNT reinforced composite flat panel under uniform thermal field", Compos. Struct., 143, 336-346. https://doi.org/10.1016/j.compstruct.2016.02.038 DOI |
2 | Mehar, K. and Panda, S.K. (2018e), "Nonlinear finite element solutions of thermoelastic flexural strength and stress values of temperature dependent graded CNT-reinforced sandwich shallow shell structure", Struct. Eng. Mech., Int. J., 67(6), 565-578. https://doi.org/10.12989/sem.2018.67.6.565 DOI |
3 | Mehar, K. and Panda, S.K. (2019), "Multiscale modeling approach for thermal buckling analysis of nanocomposite curved structure", Adv. Nano Res., Int. J., 7(3), 181-190. https://doi.org/10.12989/anr.2019.7.3.181 DOI |
4 | Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017a), "Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure", Eur. J. Mech.- A/Solids, 65, 384-396. https://doi.org/10.1016/j.euromechsol.2017.05.005 DOI |
5 | Mehar, K., Panda, S.K., Bui, T.Q. and Mahapatra, T.R. (2017b), "Nonlinear thermoelastic frequency analysis of functionally graded CNT-reinforced single/doubly curved shallow shell panels by FEM", J. Thermal Stress., 40(7), 899-916. https://doi.org/10.1080/01495739.2017.1318689 DOI |
6 | Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017c), "Theoretical and experimental investigation of vibration characteristic of carbon nanotube reinforced polymer composite structure", Int. J. Mech. Sci., 133, 319-329. https://doi.org/10.1016/j.ijmecsci.2017.08.057 DOI |
7 | Mehar, K., Panda, S.K. and Patle, B.K. (2017d), "Thermoelastic vibration and flexural behavior of FG-CNT reinforced composite curved panel", Int. J. Appl. Mech., 9(4), 1750046. https://doi.org/10.1142/S1758825117500466 DOI |
8 | Arnold, R.N. and Warburton, G.B. (1949), "Flexural vibrations of the walls of thin cylindrical shells having freely supported ends", Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 197(1049), 238-256. http://dx.doi.org/10.1098/rspa.1949.0061 DOI |
9 | Mehar, K. and Panda, S.K. (2018d), "Thermoelastic flexural analysis of FG-CNT doubly curved shell panel", Aircr. Eng. Aerosp. Technol., 90(1), 11-23. https://doi.org/10.1108/AEAT-11-2015-0237 DOI |
10 | Asghar, S., Hussain, M. and Naeem, M. (2019), "Non-local effect on the vibration analysis of double walled carbon nanotubes based on Donnell shell theory", Physica E: Low-dimens. Syst. Nanostruct., 116, 113726. https://doi.org/10.1016/j.physe.2019.113726 DOI |
11 | Bisen, H.B., Hirwani, C.K., Satankar, R.K., Panda, S.K., Mehar, K. and Patel, B. (2018), "Numerical study of frequency and deflection responses of natural fiber (Luffa) reinforced polymer composite and experimental validation", J. Natural Fibers, 1-15. https://doi.org/10.1080/15440478.2018.1503129 DOI |
12 | Goncalves, P.B. and Batista, R.C. (1987), "Frequency response of cylindrical shells partially submerged or filled with liquid", J. Sound Vib., 113(1), 59-70. https://doi.org/10.1016/S0022-460X(87)81340-8 DOI |
13 | Mehar, K., Panda, S.K. and Mahapatra, T.R. (2018b), "Thermoelastic deflection responses of CNT reinforced sandwich shell structure using finite element method", Scientia Iranica, 25(5), 2722-2737. https://doi.org/10.24200/SCI.2017.4525 DOI |
14 | Mehar, K., Panda, S.K. and Patle, B.K. (2018c), "Stress, deflection, and frequency analysis of CNT reinforced graded sandwich plate under uniform and linear thermal environment: A finite element approach", Polym. Compos., 39(10), 3792- 3809. https://doi.org/10.1002/pc.24409 DOI |
15 | Mehar, K., Panda, S.K. and Mahapatra, T.R. (2018d), "Nonlinear frequency responses of functionally graded carbon nanotube-reinforced sandwich curved panel under uniform temperature field", Int. J. Appl. Mech., 10(3), 1850028. https://doi.org/10.1142/S175882511850028X DOI |
16 | Gasser, L.F.F. (1987), "Free vibrations on thin cylindrical shells containing liquid", M.S. Thesis, Federal University of Rio de Janerio, peccoppe-ufrj, Rio de Janerio, Portugal. [In Portuguese] |
17 | Ghobaei-Arani, M., Jabbehdari, S. and Pourmina, M.A. (2018), "An autonomic resource provisioning approach for service-based cloud applications: A hybrid approach", Future Gener. Comput. Syst., 78, 191-210. https://doi.org/10.1016/j.future.2017.02.022 DOI |
18 | Goncalves, P.B. and Batista, R.C. (1988), "Non-linear vibration analysis of fluid-filled cylindrical shells", J. Sound Vib., 127(1), 133-143. https://doi.org/10.1006/jsvi.2001.4139 DOI |
19 | Mehar, K., Panda, S.K., Devarajan, Y. and Choubey, G. (2019), "Numerical buckling analysis of graded CNT-reinforced composite sandwich shell structure under thermal loading", Compos. Struct., 216, 406-414. https://doi.org/10.1016/j.compstruct.2019.03.002 DOI |
20 | Mehar, K. and Panda, S.K. (2018b), "Thermal free vibration behavior of FG-CNT reinforced sandwich curved panel using finite element method", Polym. Compos., 39(8), 2751-2764. https://doi.org/10.1002/pc.24266 DOI |
21 | Moazzez, K., Googarchin, H.S. and Sharifi, S.M.H. (2018), "Natural frequency analysis of a cylindrical shell containing a variably oriented surface crack utilizing line-spring model", Thin-Wall. Struct., 125, 63-75. https://doi.org/10.1016/j.tws.2018.01.009 DOI |
22 | Ramteke, P., Mehar, K., Sharma, N. and Panda, S. (2020a), "Numerical Prediction of Deflection and Stress Responses of Functionally Graded Structure for Grading Patterns (Power-Law, Sigmoid and Exponential) and Variable Porosity (Even/Uneven)", Scientia Iranica. |
23 | Shah, A.G., Mahmood, T. and Naeem, M.N. (2009), "Vibrations of FGM thin cylindrical shells with exponential volume fraction law", Appl. Mathe. Mech., 30(5), 607-615. https://doi.org/10.1007/s10483-009-0507-x DOI |
24 | Tohidi, H., Hosseini-Hashemi, S.H. and Maghsoudpour, A. (2018), "Size-dependent forced vibration response of embedded micro cylindrical shells reinforced with agglomerated CNTs using strain gradient theory", Smart Struct. Syst., Int. J., 22(5), 527-546. https://doi.org/10.12989/sss.2018.22.5.527 DOI |
25 | Xuebin, L. (2008), "Study on free vibration analysis of circular cylindrical shells using wave propagation", J. Sound Vib., 311, 667-682. https://doi.org/10.1016/j.jsv.2007.09.023 DOI |
26 | Wuite, J. and Adali, S. (2005), "Deflection and stress behavior of nanocomposite reinforced beams using a multiscale analysis", Compos. Struct., 71(3-4), 388-396. https://doi.org/10.1016/j.compstruct.2005.09.011 DOI |
27 | Wang, C. and Lai, J.C.S. (2000), "Prediction of natural frequencies of finite length circular cylindrical shells", Appl. Acoust., 59(4), 385-400. https://doi.org/10.1016/S0003-682X(99)00039-0 DOI |
28 | Wang, C.M., Swaddiwudhipong, S. and Tian, J. (1997), "Ritz method for vibration analysis of cylindrical shells with ring-stiffeners", J. Eng. Mech., 123, 134-143. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:2(134) DOI |
29 | Warburton, G.B. (1965), "Vibration of thin cylindrical shells", J. Mech. Eng. Sci., 7, 399-407. DOI |
30 | Xiang, Y., Ma, Y.F., Kitipornchai, S. and Lau, C.W.H. (2002), "Exact solutions for vibration of cylindrical shells with intermediate ring supports", Int. J. Mech. Sci., 44(9), 1907-1924. https://doi.org/10.1016/S0020-7403(02)00071-1 DOI |
31 | Zhang, X.M., Liu, G.R. and Lam, K.Y. (2001), "Coupled vibration of fluid-filled cylindrical shells using the wave propagation approach", Appl. Acoust., 62, 229-243. https://doi.org/10.1016/S0003-682X(00)00045-1 DOI |
32 | Yeh, J.Y. (2016), "Vibration characteristic analysis of sandwich cylindrical shells with MR elastomer", Smart Struct. Syst., Int. J., 18(2), 233-247. https://doi.org/10.12989/sss.2016.18.2.233 DOI |
33 | Zahrai, S.M. and Kakouei, S. (2019), "Shaking table tests on a SDOF structure with cylindrical and rectangular TLDs having rotatable baffles", Smart Struct. Syst., Int. J., 24(3), 391-401. https://doi.org/10.12989/sss.2019.24.3.391 DOI |
34 | Zhang, X.M. (2002), "Frequency analysis of submerged cylindrical shells with the wave propagation approach", J. Mech. Sci., 44, 1259-1273. https://doi.org/10.1016/S0020-7403(02)00059-0 DOI |
35 | Kareem, M.G. and Majeed, W.I. (2019), "Transient dynamic analysis of laminated shallow spherical shell under low-velocity impact", J. Mater. Res. Technol., 8(6), 5283-5300. https://doi.org/10.1016/j.jmrt.2019.08.050 DOI |
36 | Galletly, G.D. (1955), "On the in-vacuo vibrations of simply supported, ring-stiffened cylindrical shells", US National Congress of Applied Mechanics. http//www.vacuo-vibrations-supported-ring-stiffened-cylindrical/dp/B0007FTWBQ |
37 | Jweeg, M.J. and Alazzawy, W.I. (2007), "A suggested analytical solution for laminated closed cylindrical shells using General Third Shell Theory (GTT)", Al-Nahrain J. Eng. Sci., 10(1), 11-26. |
38 | Jweeg, M.J. and Majeed, W.I. (2020), "Free vibration Analysis solution for laminated truncated conical shells using high orde theory", Proceedings of the 6th Sc Conference of the College of Engineering, University of Baghdad, Volume 3, pp. 208-225. |
39 | Koizumi, M. (1997), "FGM Activities in Japan", Composites. https://doi.org/10.1016/S1359-8368(96)00016-9 DOI |
40 | Alazzawy, W.I. (2008), "Static and Dynamic Analysis of Stiffened Plate Used in Machine Tool Column", J. Eng., 14(4), 3099-3111. |
41 | Alazzawy, W.I. and Jweeg, M.J. (2010), "A study of free vibration and fatigue for cross-ply closed cylindrical shells using General Third shell Theory (GTT)", J. Eng., 16(2), 5170-5184. |
42 | AlSaleh, R.J. and Fuggini, C. (2020), "Combining GPS and accelerometers' records to capture torsional response of cylindrical tower", Smart Struct. Syst., Int. J., 25(1), 111-122. https://doi.org/10.12989/sss.2020.25.1.111 DOI |
43 | Amabili, M. (1999), "Vibration of circular tubes and shells filled and partially immersed in dense fluids", J. Sound Vib., 221(4), 567-585. https://doi.org/10.1006/jsvi.1998.2050 DOI |
44 | Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., Int. J., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197 DOI |
45 | Chi, S.H. and Chung, Y.L. (2006b), "Mechanical behavior of functionally graded material plates under transverse load-part II: numerical results", Int. J. Solids Struct., 43, 3657-3691. https://doi.org/10.1016/j.ijsolstr.2005.04.010 DOI |
46 | Chung, H., Turula, P., Mulcahy, T.M. and Jendrzejczyk, J.A. (1981), "Analysis of cylindrical shell vibrating in a cylindrical fluid region", Nuclear Eng. Des., 63(1), 109-1012. https://doi.org/10.1016/0029-5493(81)90020-0 DOI |
47 | Mehar, K., Mahapatra, T.R., Panda, S.K., Katariya, P.V. and Tompe, U.K. (2018a), "Finite-element solution to nonlocal elasticity and scale effect on frequency behavior of shear deformable nanoplate structure", J. Eng. Mech., 144(9), 04018094. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001519 DOI |
48 | Sharma, P., Singh, R. and Hussain, M. (2019), "On modal analysis of axially functionally graded material beam under hygrothermal effect", Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci., 234(5), 1085-1101. https://doi.org/10.1177/0954406219888234. DOI |
49 | Sodel, W. (1981), "Vibration of shell and plates", In: Mechanical Engineering Series, New York, USA. |
50 | Sofiyev, A.H. and Avcar, M. (2010), "The stability of cylindrical shells containing an FGM layer subjected to axial load on the Pasternak foundation", Eng., 2, 228-236. https://doi.org/10.4236/eng.2010.24033 DOI |
51 | Jiang, J. and Olson, M.D. (1994), "Vibrational analysis of orthogonally stiffened cylindrical shells using super elements", J. Sound Vib., 173, 73-83. https://doi.org/10.1006/jsvi.1994.1218 DOI |
52 | Naeem, M.N., Ghamkhar, M., Arshad, S.H. and Shah, A.G. (2013), "Vibration analysis of submerged thin FGM cylindrical shells", J. Mech. Sci. Technol., 27(3), 649-656. https://doi.org/10.1007/s12206-013-0119-6 DOI |
53 | Chi, S.H. and Chung, Y.L. (2006a), "Mechanical behavior of functionally graded material plates under transverse load-Part I: Analysis", Int. J. Solids Struct., 43(13), 3657-3674. https://doi.org/10.1016/j.ijsolstr.2005.04.010 DOI |
54 | Suresh, S. and Mortensen, A. (1997), "Functionally graded metals and metal-ceramic composites: Part 2 Thermomechanical behaviour", Int. Mater. Rev., 42, 85-116. https://doi.org/10.1179/imr.1995.40.6.239 DOI |
55 | Swaddiwudhipong, S., Tian, J. and Wang, C.M. (1995), "Vibration of cylindrical shells with ring supports", J. Sound Vib., 187(1), 69-93. https://doi.org/10.1006/jsvi.1995.0503 DOI |
56 | Toulokian, Y.S. (1967), Thermo Physical Properties of High Temperature Solid Materials, New York: Macmillan. https://apps.dtic.mil/dtic/tr/fulltext/u2/649947.pdf |
57 | Dewangan, H.C., Panda, S.K. and Sharma, N. (2020a), "Experimental Validation of Role of Cut-Out Parameters on Modal Responses of Laminated Composite-A Coupled Fe Approach", Int. J. Appl. Mech., 12(6), 2050068. https://doi.org/10.1142/S1758825120500684 DOI |
58 | Lam, K.Y. and Loy, C.T. (1998), "Influence of boundary conditions for a thin laminated rotating cylindrical shell", Compos. Struct., 41(3-4), 215-228. https://doi.org/10.1016/S0263-8223(98)00012-9 DOI |
59 | Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., Int. J., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197 DOI |
60 | Mehar, K., Panda, S.K., Dehengia, A. and Kar, V.R. (2016), "Vibration analysis of functionally graded carbon nanotube reinforced composite plate in thermal environment", J. Sandw. Struct. Mater., 18(2), 151-173. https://doi.org/10.1177/1099636215613324 DOI |
61 | Mehar, K. and Panda, S.K. (2016b), "Free vibration and bending behaviour of CNT reinforced composite plate using different shear deformation theory", Proceedings of IOP Conference Series: Materials Science and Engineering, 115(1), 012014. |
62 | Lee, S.Y., Huynh, T.C., Dang, N.L. and Kim, J.T. (2019), "Vibration characteristics of caisson breakwater for various waves, sea levels, and foundations", Smart Struct. Syst., Int. J., 24(4), 525-539. https://doi.org/10.12989/sss.2019.24.4.525 DOI |
63 | Leissa, A.W. (1973), "Vibration of shells". https://ntrs.nasa.gov/search.jsp?R=19730018197 |
64 | Marcel Dekker, Books: https://www.abebooks.com/book-search/title/vibrations-shells-plates/author/soedel-werner/ |
65 | Mehar, K. and Panda, S.K. (2018a), "Dynamic response of functionally graded carbon nanotube reinforced sandwich plate", Proceedings of IOP Conference Series: Materials Science and Engineering, Vol. 338, No. 1, p. 012017. |
66 | Krommer, M., Vetyukova, Y. and Staudigl, E. (2016), "Nonlinear modelling and analysis of thin piezoelectric plates: buckling and post-buckling behavior", Smart Struct. Syst., Int. J., 18(1), 155-181. https://doi.org/10.12989/sss.2016.18.1.155 DOI |
67 | Ansari, R. and Rouhi, H. (2015), "Nonlocal Flugge shell model for the axial buckling of single-walled Carbon nanotubes: An analytical approach", Int. J. Nano Dimens., 6(5), 453-462. https://doi.org/10.7508/IJND.2015.05.002 DOI |
68 | Najafizadeh, M.M. and Isvandzibaei, M.R. (2007), "Vibration of (FGM) cylindrical shells based on higher order shear deformation plate theory with ring support", Acta Mechanica, 191, 75-91. https://doi.org/10.1007/s00707-006-0438-0 DOI |
69 | Sharma, C.B., Darvizeh, M. and Darvizeh, A. (1998), "Natural frequency response of vertical cantilever composite shells containing fluid", Eng. Struct., 20(8), 732-737. https://doi.org/10.1016/S0141-0296(97)00102-8 DOI |
70 | Amabili, M., Pellicano, F. and Paidoussis, M.P. (1998), "Nonlinear vibrations of simply supported, circular cylindrical shells, coupled to quiescent fluid", 12(7), 883-918. https://doi.org/10.1006/jfls.1998.0173 DOI |
71 | Arani, A.G., Kolahchi, R. and Esmailpour, M. (2016), "Nonlinear vibration analysis of piezoelectric plates reinforced with carbon nanotubes using DQM", Smart Struct. Syst., Int. J., 18(4), 787-800. https://doi.org/10.12989/sss.2016.18.4.787 DOI |
72 | Sharma, C.B. and Johns, D.J. (1971), "Vibration characteristics of a clamped-free and clamped-ring-stiffened circular cylindrical shell", J. Sound Vib., 14(4), 459-474. https://doi.org/10.1016/0022-460X(71)90575-X DOI |
73 | Dewangan, H.C., Sharma, N., Hirwani, C.K. and Panda, S.K. (2020b), "Numerical eigenfrequency and experimental verification of variable cutout (square/rectangular) borne layered glass/epoxy flat/curved panel structure", Mech. Based Des. Struct. Mach., 1-18. https://doi.org/10.1080/15397734.2020.1759432 DOI |
74 | Ramteke, P.M., Mahapatra, B.P., Panda, S.K. and Sharma, N. (2020b), "Static deflection simulation study of 2D Functionally graded porous structure", Materials Today: Proceedings, 33, 5544-5547. https://doi.org/10.1016/j.matpr.2020.03.537 DOI |
75 | Sadoughifar, A., Farhatnia, F., Izadinia, M. and Talaeetaba, S.B. (2020), "Size-dependent buckling behaviour of FG annular/circular thick nanoplates with porosities resting on Kerr foundation based on new hyperbolic shear deformation theory", Struct. Eng. Mech., Int. J., 73(3), 225-238. https://doi.org/10.12989/sem.2020.73.3.225 DOI |
76 | Sewall, J.L. and Naumann, E.C. (1968), "An experimental and analytical vibration study of thin cylindrical shells with and without longitudinal stiffeners", National Aeronautic and Space Administration; for sale by the Clearinghouse for Federal Scientific and Technical Information, Springfield, Va. https://ntrs.nasa.gov/search.jsp?R=19680024266%202020-06-07T18:48:40+00:00Z |
77 | Sharma, C.B. (1974), "Calculation of natural frequencies of fixed-free circular cylindrical shells", J. Sound Vib., 35(1), 55-76. https://doi.org/10.1016/0022-460X(74)90038-8 DOI |
78 | Flugge, W. (1962), Stresses in Shells, (2nd Edition), Springer-Verlag, Berlin, Germany. |
79 | Dong, S.B. (1977), "A block-stodola eigen solution technique for large algebraic systems with non-symmetrical matrices", Int. J. Numer. Methods Eng., 11, 247. https://doi.org/10.1002/nme.1620110204 DOI |
80 | Ergin, A. and Temarel, P. (2002), "Free vibration of a partially liquid-filled and submerged, horizontal cylindrical shell", J. Sound Vib., 254(5), 951-965. https://doi.org/10.1006/jsvi.2001.4139 DOI |
81 | Flugge, W. (1967), Stresses in Shells, (2nd Edition), Springer-Verlag, Berlin, Germany. https://www.springer.com/gp/book/9783662010280 |
82 | Forsberg, K. (1964), "Influence of boundary conditions on modal characteristics of cylindrical shells", J. Am. Inst. Aeronaut. Astronaut., 2, 182-189. https://arc.aiaa.org/doi/abs/10.2514/6.1964-77 DOI |
83 | Arefi, M. and Zenkour, A.M. (2017), "Nonlinear and linear thermo-elastic analyses of a functionally graded spherical shell using the Lagrange strain tensor", Smart Struct. Syst., Int. J., 19(1), 33-38. https://doi.org/10.12989/sss.2017.19.1.033 DOI |
84 | Poplawski, B., Mikulowski, G., Pisarski, D., Wiszowaty, R. and Jankowski, L. (2019), "Optimum actuator placement for damping of vibrations using the Prestress-Accumulation Release control approach", Smart Struct. Syst., Int. J., 24(1), 27-35. https://doi.org/10.12989/sss.2019.24.1.027 DOI |
85 | Love, A.E.H. (1888), "XVI. The small small free vibrations and deformation of thin elastic shell", Phil. Trans. R. Soc. London, A179, 491-549. https://doi.org/10.1098/rsta.1888.0016 DOI |
86 | Loy, C.T. and Lam, K.Y. (1997), "Vibration of cylindrical shells with ring supports", J. Mech. Eng., 39, 455-471. https://doi.org/10.1016/S0020-7403(96)00035-5 DOI |
87 | Loy, C.T., Lam, K.Y. and Reddy, J.N. (1999), "Vibration of functionally graded cylindrical shells", Int. J. Mech. Sci., 41(3), 309-324. https://doi.org/10.1016/S0020-7403(98)00054-X DOI |
88 | Mehar, K. and Panda, S.K. (2018c), "Elastic bending and stress analysis of carbon nanotube-reinforced composite plate: Experimental, numerical, and simulation", Adv. Polym. Technol., 37(6), 1643-1657. https://doi.org/10.1002/adv.21821 DOI |
![]() |