Advances in nano research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Monitoring and control of multiple fraction laws with ring based composite structure

  • 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) ;
  • Taj, Muhammad (Department of Mathematics, University of Azad Jammu and Kashmir) ;
  • Tounsi, Abdelouahed (YFL (Yonsei Frontier Lab), Yonsei University)
  • Received : 2020.07.15
  • Accepted : 2020.11.29
  • Published : 2021.02.25
⟨ Previous Next ⟩

Abstract

In present article, utilizing the Love shell theory with volume fraction laws for the cylindrical shells vibrations provides a governing equation for the distribution of material composition of material. Isotopic materials are the constituents of these rings. The position of a ring support has been taken along the radial direction. The Rayleigh-Ritz method with three different fraction laws gives birth to the shell frequency equation. Moreover, the effect of height- and length-to-radius ratio and angular speed is investigated. The results are depicted for circumferential wave number, length- and height-radius ratios with three laws. It is found that the backward and forward frequencies of exponential fraction law are sandwich between polynomial and trigonometric laws. It is examined that the backward and forward frequencies increase and decrease on increasing the ratio of height- and length-to-radius ratio. As the position of ring is enhanced for clamped simply supported and simply supported-simply supported boundary conditions, the frequencies go up. At mid-point, all the frequencies are higher and after that the frequencies decreases. The frequencies are same at initial and final stage and rust itself a bell shape. The shell is stabilized by ring supports to increase the stiffness and strength. Comparison is made for non-rotating and rotating cylindrical shell for the efficiency of the model. The results generated by computer software MATLAB.

Keywords

Acknowledgement

This project was supported by the Deanship of Scientific Research at Prince Sattam Bin Abdulaziz University under research project no. 2020/01/16794.

References

  1. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., Int. J., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421.
  2. Akbas, S.D. (2017), "Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory", Int. J. Struct. Stab. Dyn., 17(3), 1750033. https://doi.org/10.1142/S021945541750033X.
  3. Akbas, S.D. (2018a), "Investigation on free and forced vibration of a bi-material composite beam", J. Politech. Dergisi, 21(1), 65-73.
  4. Akbas, S.D. (2018b), "Post-buckling responses of a laminated composite beam", Steel Compos. Struct., Int. J., 26(6), 733-743. http://dx.doi.org/10.12989/scs.2018.26.6.733.
  5. Akbas, S.D. (2018c), "Nonlinear thermal displacements of laminated composite beams", Coupled Syst. Mech., Int. J., 7(6), 691-705. https://doi.org/10.12989/csm.2018.7.6.691.
  6. Akbas, S.D. (2018d), "Geometrically nonlinear analysis of a laminated composite beam", Struct. Eng. Mech., Int. J., 66(1), 27-36. http://dx.doi.org/10.12989/sem.2018.66.1.027.
  7. Akbas, S.D. (2018e), "Thermal post-buckling analysis of a laminated composite beam", Struct. Eng. Mech., Int. J., 67(4), 337-346. http://dx.doi.org/10.12989/sem.2018.67.4.337.
  8. Akbas, S.D. (2018f), "Large deflection analysis of a fiber reinforced composite beam", Steel Compos. Struct., Int. J., 27(5), 567-576. https://doi.org/10.12989/scs.2018.27.5.567.
  9. Akbas, S.D. (2019a), "Hygrothermal post-buckling analysis of laminated composite beams", Int. J. Appl. Mech., 11(1), 1950009. https://doi.org/10.1142/S1758825119500091.
  10. Akbas, S.D. (2019b), "Forced vibration analysis of functionally graded sandwich deep beams", Coupled Syst. Mech., Int. J., 8(3), 259-271. https://doi.org/10.12989/csm.2019.8.3.259.
  11. Akbas, S.D. (2019c), "Post-buckling analysis of a fiber reinforced composite beam with crack", Eng. Fract. Mech., 212, 70-80. https://doi.org/10.1016/j.engfracmech.2019.03.007.
  12. Akbas, S.D. (2019d), "Nonlinear static analysis of laminated composite beams under hygro-thermal effect", Struct. Eng. Mech., Int. J., 72(4), 433-441. https://doi.org/10.12989/sem.2019.72.4.433.
  13. Akbas, S.D. (2019e), "Nonlinear behavior of fiber reinforced cracked composite beams", Steel Compos. Struct., Int. J., 30(4), 327-336. http://dx.doi.org/10.12989/scs.2019.30.4.327.
  14. Akbas, S.D. and Kocaturk, T. (2013), "Post-buckling analysis of functionally graded three-dimensional beams under the influence of temperature", J. Therm. Stresses, 36(12), 1233-1254. https://doi.org/10.1080/01495739.2013.788397.
  15. Amabili, M., Pellicano, F. and Paidoussis M.P. (1998), "The small free vibrations and deformation of thin elastic shell", Phil. Trans. R Soc. London, 179, 491-549. https://doi.org/10.1098/rsta.1888.0016.
  16. 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.
  17. Arnold, R.N. and Warburton, G.B. (1953), "The flexural vibrations of thin cylinders", Proc. Inst. Mech. Eng., 167(1), 62-80. https://doi.org/10.1243/PIMEPROC195316701402.
  18. Benmansour, D.L., Kaci, A., Bousahla, A.A., Heireche, H., Tounsi, A., Alwabli, A.S., Alhebshi, A.M., Al-Ghmady, K. and Mahmoud, S.R. (2019), "The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory", Adv. Nano Res., Int. J., 7(6), 443-457. https://doi.org/10.12989/anr.2019.7.6.443.
  19. Bryan, G.H. (1890), "On the beats in the vibration of revolving cylinder", Proc. Cambridge Philos. Soc., 7,101-111.
  20. Chen, Y., Zhao, H.B. and Shin, Z.P. (1993), "Vibration of high speed rotating shells with calculation for cylindrical shells", J. Sound Vib., 160, 137. https://doi.org/10.1006/jsvi.1993.1010.
  21. 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.
  22. Civalek, O. (2020), "Vibration of functionally graded carbon nanotube reinforced quadrilateral plates using geometric transformation discrete singular convolution method", Int. J. Num. Methods Eng., 121(5), 990-1019. https://doi.org/10.1002/nme.6254.
  23. Shah, A. G., Mahmood, T., and Naeem, M. N. (2009), "Vibrations of FGM thin cylindrical shells with exponential volume fraction law", Applied Mathematics and Mechanics, 30(5), 607-615. http/10.1007/s10483-009-0507-x
  24. Di Taranto, R.A. and Lessen, M. (1964), "Coriolis acceleration effect on the vibration of rotating thin walled circular cylinder", J. Appl. Mech. T. ASME, 31, 700-701. https://doi.org/10.1115/1.3629733.
  25. Ebrahimi, F., Dabbagh, A., Rabczuk, T. and Tornabene, F. (2019), "Analysis of propagation characteristics of elastic waves in heterogeneous nanobeams employing a new two-step porosity-dependent homogenization scheme", Adv. Nano Res., Int. J., 7(2), 135-143. https://doi.org/10.12989/anr.2019.7.2.135.
  26. 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.
  27. Eltaher, M.A., Almalki, T.A., Ahmed, K.I. and Almitani, K.H. (2019), "Characterization and behaviors of single walled carbon nanotube by equivalent-continuum mechanics approach", Adv. Nano Res., Int. J., 7(1), 39-49. https://doi.org/10.12989/anr.2019.7.1.039.
  28. Galletly, G.D. (1955), "On the in-vacuo vibrations of simply supported, ring-stiffened cylindrical shells", US National Congress of Applied Mechanics, USA.
  29. 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.
  30. 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.
  31. Kar, V.R. and Panda, S.K. (2017), "Large-amplitude vibration of functionally graded doubly-curved panels under heat conduction", AIAA J., 55(12), 4376-4386. https://doi.org/10.2514/1.J055878.
  32. Love, A.E.H. (1888), "On the small free vibrations and deformation of thin elastic shell", Phil. Trans. R. Soc. London, 179, 491-549. https://doi.org/10.1098/rsta.1888.0016
  33. 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.
  34. 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.
  35. 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.
  36. 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.
  37. 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., 2020, 1-13. https://doi.org/10.1080/15376494.2020.1725193.
  38. 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.
  39. Naeem, M.N. and Sharma, C.B. (2000), "Prediction of natural frequencies for thin circular cylindrical shells", Proc. Inst. Mech. Eng., 214(10), 1313-1328. https://doi.org/10.1243/0954406001523290
  40. 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://10.1007/s12206-013-0119-6.
  41. 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 Mech., 191, 75-91. http/10.1007/s00707-006-0438-0.
  42. Penzes, R.L.E. and Kraus, H. (1972), "Free vibrations of prestresses cylindrical shells having arbitrary homogeneous boundary conditions", AIAA J., 10, 1309. https://doi.org/10.2514/3.6605.
  43. Ramteke, P.M., 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)", Sci. Iranica., In Press.
  44. Ramteke, P.M., Mahapatra, B.P., Panda, S.K. and Sharma, N. (2020b), "Static deflection simulation study of 2D Functionally graded porous structure", Mater. Today Proc., 33(8), 5544-5547. https://doi.org/10.1016/j.matpr.2020.03.537.
  45. Ramteke, P.M., Panda, S.K. and Sharma, N. (2019a), "Effect of grading pattern and porosity on the eigen characteristics of porous functionally graded structure", Steel Compos. Struct., Int. J., 33(6), 865-875. https://doi.org/10.12989/scs.2019.33.6.865.
  46. Rayliegh, J.W.S. (1884), Theory of Sound, Macmillan, London, UK.
  47. 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.
  48. Safaei, B., Khoda, F.H. and Fattahi, A.M. (2019), "Non-classical plate model for single-layered graphene sheet for axial buckling", Adv. Nano Res., Int. J., 7(4), 265-275. https://doi.org/10.12989/anr.2019.7.4.265.
  49. 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, Springfield, USA.
  50. 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. http/10.1007/s10483-009-0507-x.
  51. Shahsavari, D., Karami, B. and Janghorban, M. (2019), "Size-dependent vibration analysis of laminated composite plates", Adv. Nano Res., Int. J., 7(5), 337-349. https://doi.org/10.12989/anr.2019.7.5.337.
  52. 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.
  53. Sharma, P., Singh, R. and Hussain, M. (2019), "On modal analysis of axially functionally graded material beam under hygrothermal effect", Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci., 234(5), 1085-1101. https://doi.org/10.1177/0954406219888234.
  54. Sofiyev, A.H. and Avcar, M. (2010), "The stability of cylindrical shells containing an FGM layer subjected to axial load on the Pasternak foundation", Engineering, 2, 228-236. https://10.4236/eng.2010.24033.
  55. Srinivasan, A.V. and Luaterbach, G.F. (1971), "Travelling waves in rotating cylindrical shells", Trans. ASME J. Eng. Ind., 93, 1229-1232. https://doi.org/10.1115/1.3428067.
  56. 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.
  57. 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).
  58. 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.
  59. 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.