Computers and Concrete

  • 제25권5호
  • /
  • Pages.411-425
  • /
  • 2020
  • /
  • 1598-8198(pISSN)
  • /
  • 1598-818X(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Computer-aided approach for modelling of FG cylindrical shell sandwich with ring supports

  • Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad) ;
  • Naeem, Muhammad Nawaz (Department of Mathematics, Govt. College University Faisalabad) ;
  • Khan, Muhammad Shabaz (Department of Mathematics, Govt. College University Faisalabad) ;
  • Tounsi, Abdelouahed (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Algeria Faculty of Technology, Civil Engineering Department)
  • 투고 : 2020.01.12
  • 심사 : 2020.04.10
  • 발행 : 2020.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, the shell material has been taken as functionally graded material and their material quantity is located by the exponential volume fraction law. Moreover, the impact of ring supports around the shell circumference has been examined for their various positions along the shell axial length. These rings support restraints the radial displacement in the transverse direction. While the axial modal deformation functions have been estimated by characteristic beam functions and nature of materials used for construction of cylindrical shells. The fundamental natural frequency of cylindrical shell of parameter versus ratios of length- and height-to-radius for a wide range has been reported and investigated through the study. In addition, by increasing height-to-radius ratio resulting frequencies also increase and frequencies decrease on ratio of length-to-radius. Though the trends of frequency values of both ratios are converse to each other with three different boundary conditions. Also it is examined the position of ring supports with length-to radius ratio, height-to-radius ratio and varying the exponent of volume fraction. MATLAB software package has been utilized for extracting shell frequency spectra. The obtained results are confirmed by comparing with available literature.

키워드

참고문헌

  1. 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.
  2. Amabili, M., Pellicano, F. and Paidoussis, M.P. (1998), "Nonlinear vibrations of simply Love, A.E.H. (1888), 'On the small free vibrations and deformation of thin elastic shell'", Phil. Tran. R. Soc. London, A179, 491-549.
  3. 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.
  4. Arshad, S.H., Naeem, M.N. and Sultana, N. (2007), "Frequency analysis of functionally graded cylindrical shells with various volume fraction laws", J. Mech. Eng. Sci., 221, 1483-1495. https://doi.org/10.1243/09544062JMES738.
  5. 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.
  6. Ayat, H., Kellouche, Y., Ghrici, M. and Boukhatem, B. (2018), "Compressive strength prediction of limestone filler concrete using artificial neural networks", Adv. Comput. Des., 3(3), 289-302. https://doi.org/10.12989/acd.2018.3.3.289.
  7. Batou, B., Nebab, M., Bennai, R., Atmane, H.A., Tounsi, A. and Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., 33(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699.
  8. Behera, S. and Kumari, P. (2018), "Free vibration of Levy-type rectangular laminated plates using efficient zig-zag theory", Adv. Comput. Des., 3(3), 213-232. https://doi.org/10.12989/acd.2018.3.3.213.
  9. Bilouei, B.S., Kolahchi, R. and Bidgoli, M.R. (2016), "Buckling of concrete columns retrofitted with Nano-Fiber Reinforced Polymer (NFRP)", Comput. Concrete, 18(5), 1053-1063. https://doi.org/10.12989/cac.2016.18.5.1053.
  10. Chi, S.H. and Chung, Y.L. (2006), "Mechanical behavior of functionally graded material plates under transverse load-part II: numerical results", Int. J. Solid. Struct., 43, 3657-3691. https://doi.org/10.1016/j.ijsolstr.2005.04.010.
  11. Chung, H., Turula, P., Mulcahy, T.M. and Jendrzejczyk, J.A. (1981), "Analysis of cylindrical shell vibrating in a cylindrical fluid region", Nucl. Eng. Des., 63(1), 109-1012. https://doi.org/10.1016/0029-5493(81)90020-0.
  12. Dong, S.B. (1977), "A block-stodola eigen solution technique for large algebraic systems with non-symmetrical matrices", Int. J. Numer. Meth. Eng., 11, 247. https://doi.org/10.1002/nme.1620110204.
  13. 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.
  14. Esmaeili, J. and Andalibia, K. (2019), "Development of 3D Meso-Scale finite element model to study the mechanical behavior of steel microfiber-reinforced polymer concrete", Comput. Concrete, 24(5), 413-422. https://doi.org/10.12989/cac.2019.24.5.413.
  15. Fatahi-Vajari, A., Azimzadeh, Z. and Hussain, M. (2019), "Nonlinear coupled axial-torsional vibration of single-walled carbon nanotubes using Galerkin and Homotopy perturbation method", Micro Nano Lett., 14(14), 1366-1371. https://doi.org/10.1049/mnl.2019.0203.
  16. Gasser, T.C. (2007), "Validation of 3D crack propagation in plain concrete. Part II: Computational modeling and predictions of the PCT3D test", Comput. Concrete, 4(1), 67-82. https://doi.org/10.12989/cac.2007.4.1.067.
  17. Ghodrati, B., Yaghootian, A., Ghanbar Zadeh, A. and Mohammad-Sedighi, H. (2018), "Lamb wave extraction of dispersion curves in micro/nano-plates using couple stress theories", Wave. Rand. Complex Media, 28(1), 15-34. https://doi.org/10.1080/17455030.2017.1308582.
  18. Golabchi, H., Kolahchi, R. and Bidgoli, M.R. (2018), "Vibration and instability analysis of pipes reinforced by $SiO_2$ nanoparticles considering agglomeration effects", Comput. Concrete, 21(4), 431-440. https://doi.org/10.12989/cac.2018.21.4.431.
  19. 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/10.1016/0022-460X(88)90354-9.
  20. Greif, R. and Chung, H. (1975), "Vibration of constrained cylindrical shells", Am. Inst. Aeronaut. J., 13, 1190-1198. https://doi.org/10.2514/3.6970.
  21. Hussain, M. and Naeem, M. (2017), "Vibration analysis of single-walled carbon nanotubes using wave propagation approach", Mech. Sci., 8(1), 155-164. https://doi.org/10.5194/ms-8-155-2017.
  22. Hussain, M. and Naeem, M. (2018), "Vibration of single-walled carbon nanotubes based on Donnell shell theory using wave propagation approach", Chapter, Intechopen, Novel Nanomaterials - Synthesis and Applications, ISBN 978-953-51-5896-7. https://doi.org/10.5772 /intechopen.73503.
  23. Hussain, M. and Naeem, M. (2018a), "Vibration of single-walled carbon nanotubes based on Donnell shell theory using wave propagation approach", Chapter, Intechopen, Novel Nanomaterials - Synthesis and Applications, ISBN 978-953-51-5896-7. https://doi.org/10.5772 /intechopen.73503.
  24. Hussain, M. and Naeem, M. (2019a), "Vibration characteristics of single-walled carbon nanotubes based on non-local elasticity theory using wave propagation approach (WPA) including chirality", Perspective of Carbon Nanotubes. IntechOpen. https://doi.org/10.5772/intechopen.85948.
  25. Hussain, M. and Naeem, M. (2019d), "Rotating response on the vibrations of functionally graded zigzag and chiral single walled carbon nanotubes", Appl. Math. Model., 75, 506-520. https://doi.org/10.1016/j.apm.2019.05.039.
  26. Hussain, M. and Naeem, M.N. (2017), "Vibration analysis of single-walled carbon nanotubes using wave propagation approach", Mech. Sci., 8(1), 155-164. https://doi.org/10.5194/ms-8-155-2017.
  27. Hussain, M. and Naeem, M.N. (2018b), "Effect of various edge conditions on free vibration characteristics of rectangular plates", Chapter, Intechopen, Advance Testing and Engineering, ISBN 978-953-51-6706-8, Intechopen.
  28. Hussain, M. and Naeem, M.N. (2019b), "Effects of ring supports on vibration of armchair and zigzag FGM rotating carbon nanotubes using Galerkin's method", Compos. Part B. Eng., 163, 548-561. https://doi.org/10.1016/j.compositesb.2018.12.144.
  29. Hussain, M. and Naeem, M.N. (2019c), "Vibration characteristics of zigzag and chiral FGM rotating carbon nanotubes sandwich with ring supports", J. Mech. Eng. Sci., Part C, 233(16), 5763-5780. https://doi.org/10.1177/0954406219855095.
  30. Hussain, M. and Naeem, M.N. (2020a), "Mass density effect on vibration of zigzag and chiral SWCNTs", J. Sandw. Struct. Mater., 1099636220906257. https://doi.org/10.1177/1099636220906257.
  31. Hussain, M. and Naeem, M.N. (2020b), "Vibration characteristics of zigzag FGM single-walled carbon nanotubes based on Ritz method with ring-stiffeners", Ind. J. Phys., 140, 85-98. https://doi.org/10.1016/j.tws.2019.03.018.
  32. Hussain, M., Naeem, M., Shahzad, A. and He, M. (2017), "Vibrational behavior of single-walled carbon nanotubes based on cylindrical shell model using wave propagation approach", AIP Adv., 7(4), 045114. https://doi.org/10.1063/1.4979112.
  33. Hussain, M., Naeem, M., Shahzad, A. and He, M. (2018a), "Vibration characteristics of fluid-filled functionally graded cylindrical material with ring supports", Chapter, Intechopen, Computational Fluid Dynamics, ISBN 978-953-51-5706-9, https://doi.org/10.5772 /intechopen.72172.
  34. Hussain, M., Naeem, M.N. and Isvandzibaei, M. (2018c), "Effect of Winkler and Pasternak elastic foundation on the vibration of rotating functionally graded material cylindrical shell", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 232(24), 4564-4577. https://doi.org/10.1177/0954406217753459.
  35. Hussain, M., Naeem, M.N. and Taj, M. (2019b), "Effect of length and thickness variations on the vibration of SWCNTs based on Flugge's shell model", Micro Nano Lett., https://doi.org/10.1049/mnl.2019.0309.
  36. Hussain, M., Naeem, M.N. and Tounsi, A. (2020a), "Simulating vibration of single-walled carbon nanotube based on Relagh-Ritz Method".
  37. Hussain, M., Naeem, M.N. and Tounsi, A. (2020b), "On mixing the Rayleigh-Ritz formulation with Hankel's function for vibration of fluid-filled Fluid-filled cylindrical shell", Adv. Comput. Des.. (in Press)
  38. Hussain, M., Naeem, M.N. and Tounsi, A. (2020c), "Numerical Study for nonlocal vibration of orthotropic SWCNTs based on Kelvin's model", Adv. Concrete Constr., 9(3), 301-312. https://doi.org/10.12989/acc.2020.9.3.301.
  39. Hussain, M., Naeem, M.N. and Tounsi, A. (2020d), "Response of orthotropic Kelvin modeling for single-walled carbon nanotubes: Frequency analysis", Adv. Nano Res., 8(3). (in Press)
  40. Hussain, M., Naeem, M.N. and Tounsi, A. (2020e), "Theoretical impact of Kelvin's theory for vibration of double walled carbon nanotubes", Advance Nano Research. (submitted)
  41. Hussain, M., Naeem, M.N., Sehar, A. and Tounsi, A. (2020g), "Eringen's nonlocal model sandwich with Kelvin's theory for vibration of DWCNT", Comput. Concrete, 25(4). (in Press)
  42. Hussain, M., Naeem, M.N., Shahzad, A., He, M. and Habib, S. (2018b), "Vibrations of rotating cylindrical shells with FGM using wave propagation approach", IMechE Part C: J. Mech. Eng. Sci., 232(23), 4342-4356. https://doi.org/10.1177/0954406218802320
  43. Hussain, M., Naeem, M.N., Tounsi, A. and Taj. M. (2019a), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., 7(6), 431-442. https://doi.org/10.12989/anr.2019.7.6.431.
  44. Hussain, M., Naeem., M.N., Shahzad, A. and He, M. (2017), "Vibrational behavior of single-walled carbon nanotubes based on cylindrical shell model using wave propagation approach", AIP Adv., 7(4), 045114. https://doi.org/10.1063/1.4979112.
  45. Jamali, M., Shojaee, T., Mohammadi, B. and Kolahchi, R. (2019), "Cut out effect on nonlinear post-buckling behavior of FG-CNTRC micro plate subjected to magnetic field via FSDT", Adv. Nano Res., 7(6), 405-417. https://doi.org/10.12989/anr.2019.7.6.405.
  46. 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.
  47. 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.
  48. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B: Eng., 28(1-2), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9
  49. Lal, A. and Markad, K. (2018), "Deflection and stress behaviour of multi-walled carbon nanotube reinforced laminated composite beams", Comput. Concrete, 22(6), 501-514. https://doi.org/10.12989/cac.2018.22.6.501.
  50. Lam, K.Y. and Loy, C.T. (1998), "Influence of boundary conditions for a thin laminated rotating cylindrical shell", Compos. Struct., 41, 215-228. https://doi.org/10.1016/S0263-8223(98)00012-9.
  51. Loghman, A., Arani, A.G. and Barzoki, A.A.M. (2017), "Nonlinear stability of non-axisymmetric functionally graded reinforced nano composite microplates", Comput. Concrete, 19(6), 677-687. https://doi.org/10.12989/cac.2017.19.6.677.
  52. 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.
  53. Loy, C.T., Lam, K.Y. and Reddy, J.N. (1999), "Vibration of functionally graded cylindrical shells", Int. J. Mech. Sci., 41, 309-324. https://doi.org/10.1016/S0020-7403(98)00054-X.
  54. Mahapatra, T.R., Kar, V.R., Panda, S.K. and Mehar, K. (2017), "Nonlinear thermoelastic deflection of temperature-dependent FGM curved shallow shell under nonlinear thermal loading", J. Therm. Stress., 40(9), 1184-1199. https://doi.org/10.1080/01495739.2017.1302788.
  55. Meftah, S.A., Tounsi, A. and Adda Bedia, E.A. (2006), "Dynamic behaviour of stiffened and damaged coupled shear walls"Comput. Concrete, 3(5), 1-15. https://doi.org/10.12989/cac.2006.3.5.285.
  56. Mehar, K. and Kumar Panda, S. (2018), "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.
  57. Mehar, K. and Panda, S.K. (2016), "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.
  58. Mehar, K. and Panda, S.K. (2017a), "Numerical investigation of nonlinear thermomechanical deflection of functionally graded CNT reinforced doubly curved composite shell panel under different mechanical loads", Compos. Struct., 161, 287-298. https://doi.org/10.1016/j.compstruct.2016.10.135.
  59. Mehar, K. and Panda, S.K. (2017b), "Thermoelastic analysis of FG-CNT reinforced shear deformable composite plate under various loadings", Int, J. Comput. Meth., 14(2), 1750019. https://doi.org/10.1142/S0219876217500190.
  60. Mehar, K. and Panda, S.K. (2017d), "Nonlinear static behavior of FG-CNT reinforced composite flat panel under thermomechanical load", J. Aerosp. Eng., 30(3), 04016100. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000706.
  61. Mehar, K. and Panda, S.K. (2019), "Multiscale modeling approach for thermal buckling analysis of nanocomposite curved structure", Adv. Nano Res., 7(3), 181. https://doi.org/10.12989/anr.2019.7.3.181.
  62. Mehar, K., Mishra, P.K. and Panda, S.K. (2020b), "Numerical investigation of thermal frequency responses of graded hybrid smart nanocomposite (CNT-SMA-Epoxy) structure", Mech. Adv. Mater. Struct., 1-13. https://doi.org/10.1080/15376494.2020.1725193.
  63. 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/Solid., 65, 384-396. https://doi.org/10.1016/j.euromechsol.2017.05.005.
  64. 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.
  65. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017d), "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.
  66. Mehar, K., Panda, S.K. and Patle, B.K. (2018), "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.
  67. Mehar, K., Panda, S.K. and Sharma, N. (2020a), "Numerical investigation and experimental verification of thermal frequency of carbon nanotube-reinforced sandwich structure", Eng. Struct., 211, 110444. https://doi.org/10.1016/j.engstruct.2020.110444.
  68. 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. Therm. Stress., 40(7), 899-916. https://doi.org/10.1080/01495739.2017.1318689.
  69. 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.
  70. 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.
  71. Mousavi, M., Mohammadimehr, M. and Rostami, R. (2019), "Analytical solution for buckling analysis of micro sandwich hollow circular plate", Comput. Concrete, 24(3), 185-192. https://doi.org/10.12989/cac.2019.24.3.185.
  72. 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.
  73. 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.
  74. Najafizadeh, M.M. and Isvandzibaei, M.R. (2009), "Vibration of functionally graded cylindrical shells based on different shear deformation shell theories with ring support under various boundary conditions", J. Mech. Sci. Technol., 23(8), 2072-2084. https://doi.org/10.1007/s12206-009-0432-2.
  75. Narwariya, M., Choudhury, A. and Sharma, A.K. (2018), "Harmonic analysis of moderately thick symmetric cross-ply laminated composite plate using FEM", Adv. Comput. Des., 3(2), 113-132. https://doi.org/10.12989/acd.2018.3.2.113.
  76. Rezaiee-Pajand, M., Masoodi, A.R. and Mokhtari, M. (2018), "Static analysis of functionally graded non-prismatic sandwich beams", Adv. Comput. Des., 3(2), 165-190. https://doi.org/10.12989/acd.2018.3.2.165.
  77. Salah, F., Boucham, B., Bourada, F., Benzair, A., Bousahla, A.A. and Tounsi, A. (2019), "Investigation of thermal buckling properties of ceramic-metal FGM sandwich plates using 2D integral plate model", Steel Compos. Struct., 32(5), 595-610. https://doi.org/10.12989/scs.2019.33.6.805.
  78. Salamat, D. and Sedighi, H.M. (2017), "The effect of small scale on the vibrational behavior of single-walled carbon nanotubes with a moving nanoparticle", J. Appl. Comput. Mech., 3(3), 208-217. https://doi.org/10.22055/JACM.2017.12740.
  79. Sedighi, H.M. and Sheikhanzadeh, A.S.H.K.A.N. (2017), "Static and dynamic pull-in instability of nano-beams resting on elastic foundation based on the nonlocal elasticity theory", Chin. J. Mech. Eng., 30(2), 385-397. https://doi.org/10.1007/s10033-017-0079-3.
  80. Sedighi, H.M., Reza, A. and Zare, J. (2011), "Study on the frequency-amplitude relation of beam vibration", Int. J. Phys. Sci., 6(36), 8051-8056. https://doi.org/10.5897/IJPS11.1556.
  81. 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, the Clearinghouse for Federal Scientific and Technical Information, Springfield, VA..
  82. Shah, A.G., Mahmood, T. and Naeem, M.N. (2009), "Vibrations of FGM thin cylindrical shells with exponential volume fraction law", Appl. Math. Mech., 30(5), 607-615. https://doi.org/10.1007/s10483-009-0507-x.
  83. 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.
  84. 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.
  85. Sharma, P., Singh, R. and Hussain, M. (2019), "On modal analysis of axially functionally graded material beam under hygrothermal effect", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 234(5), 1085-1101. https://doi.org/10.1177/0954406219888234.
  86. Sharma, P., Singh, R., Hussain, M. (2019), "On modal analysis of axially functionally graded material beam under hygrothermal effect", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 234(5), 1085-1101. https://doi.org/10.1177/0954406219888234.
  87. Sodel, W. (!981), Vibration of Shell and Plates, Mechanical Engineering Series, Marcel Dekker, New York.
  88. 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(4), 228. https://doi.org/10.4236/eng.2010.24033.
  89. Suresh, S. and Mortensen, A. (1997), "Functionally gradient metals and metal ceramic composites, Part 2: Thermo Mechanical Behavior", Int. Mater., 42, 85-116. https://doi.org/10.1179/imr.1997.42.3.85.
  90. Swaddiwudhipong, S., Tian, J. and Wang, C.M. (1995), "Vibrations of cylindrical shells with intermediate supports", J. Sound Vib., 187, 69-93. https://doi.org/10.1006/jsvi.1995.0503.
  91. Taj, M., Hussain, M., Naeem, M.N. and Tounsi, A. (2020c), "Effects of elastic medium on buckling of microtubules due to bending and torsion", Advances in Concrete Construction. (submitted)
  92. Taj, M., Safeer, M., Hussain, M., Naeem, M.N., Ahmad, M., Abbas, K., Khan, A.Q. and Tounsi, A. (2020b), "A effect of external force on cytoskeleton components in viscoelastic media", Computers and Concrete. (submitted)
  93. Taj, M., Safeer, M., Hussain, M., Naeem, M.N., Majeed, A., Ahmad, M., Khan, H.U. and Tounsi, A. (2020a), "Non-local orthotropic elastic shell model for vibration analysis of protein microtubules", Comput. Concrete, 25(3), 245-253. https://doi.org/10.12989/cac.2020.25.3.245
  94. Thomee, B., Schikora, K. and Bletzinger, K.U. (2006), "Material modeling of steel fiber reinforced concrete", Comput. Concrete, 3(4), 197-212. https://doi.org/10.12989/cac.2006.3.4.197.
  95. Toulokian, Y.S. (1967), Thermo Physical Properties of High Ttemperature Solid Materials, Macmillan, New York.
  96. 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.
  97. 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).
  98. Wuite, J. and Adali, S. (2005), "Deflection and stress behaviour 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.
  99. 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.
  100. 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.
  101. Yaman, I.O., Akbay, Z. and Aktan, H. (2006), "Numerical modelling and finite element analysis of stress wave propagation for ultrasonic pulse velocity testing of concrete", Comput. Concrete, 3(6), 423-437. https://doi.org/10.12989/cac.2006.3.6.423.
  102. Yazdani, R. and Mohammadimehr, M. (2019), "Double bonded Cooper-Naghdi micro sandwich cylindrical shells with porous core and CNTRC face sheets: Wave propagation solution", Comput. Concrete, 24(6), 499-511. https://doi.org/10.12989/cac.2019.24.6.499.
  103. Zamani, A., Kolahchi, R. and Bidgoli, M.R. (2017), "Seismic response of smart nanocomposite cylindrical shell conveying fluid flow using HDQ-Newmark methods", Comput. Concrete, 20(6), 671-682. https://doi.org/10.12989/cac.2017.20.6.671.
  104. Zhang, X.M. (2002), "Parametric analysis of frequency of rotating laminated composite cylindrical shells with the wave propagation approach", Comput. Meth. Appl. Mech. Eng., 191, 2057-2071. https://doi.org/10.1016/S0045-7825(01)00368-1.

피인용 문헌

  1. Multiphysical theoretical prediction and experimental verification of vibroacoustic responses of fruit fiber‐reinforced polymeric composite vol.41, pp.11, 2020, https://doi.org/10.1002/pc.25724
  2. A mechanical model to investigate Aedesaegypti mosquito bite using new techniques and its applications vol.11, pp.6, 2020, https://doi.org/10.12989/mwt.2020.11.6.399
  3. Predictions of the maximum plate end stresses of imperfect FRP strengthened RC beams: study and analysis vol.9, pp.4, 2020, https://doi.org/10.12989/amr.2020.9.4.265
  4. Simulation Investigation of the Stowing and Deployment Processes of a Self-Deployable Sunshield vol.2021, 2020, https://doi.org/10.1155/2021/6672177
  5. Size dependent vibration of embedded functionally graded nanoplate in hygrothermal environment by Rayleigh-Ritz method vol.10, pp.1, 2020, https://doi.org/10.12989/anr.2021.10.1.025
  6. Numerical and experimental investigation for monitoring and prediction of performance in the soft actuator vol.77, pp.2, 2021, https://doi.org/10.12989/sem.2021.77.2.167
  7. Vibration analysis of porous FGM plate resting on elastic foundations: Effect of the distribution shape of porosity vol.10, pp.1, 2020, https://doi.org/10.12989/csm.2021.10.1.061
  8. Free vibration of multi-cracked beams vol.79, pp.4, 2020, https://doi.org/10.12989/sem.2021.79.4.441