Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Free vibration of conical shell frusta of variable thickness with fluid interaction

  • M.D. Nurul Izyan (Faculty of Entrepreneurship and Business, Universiti Malaysia Kelantan) ;
  • K.K. Viswanathan (Department of Mathematical Modeling, Faculty of Mathematics, Samarkand State University) ;
  • D.S. Sankar (School of Applied Sciences and Mathematics, Universiti Teknologi Brunei) ;
  • A.K. Nor Hafizah (Kolej Genius Insan, Universiti Sains Islam Malaysia)
  • Received : 2023.11.04
  • Accepted : 2024.06.20
  • Published : 2024.06.25
⟨ Previous Next ⟩

Abstract

Free vibration of layered conical shell frusta of thickness filled with fluid is investigated. The shell is made up of isotropic or specially orthotropic materials. Three types of thickness variations are considered, namely linear, exponential and sinusoidal along the radial direction of the conical shell structure. The equations of motion of the conical shell frusta are formulated using Love's first approximation theory along with the fluid interaction. Velocity potential and Bernoulli's equations have been applied for the expression of the pressure of the fluid. The fluid is assumed to be incompressible, inviscid and quiescent. The governing equations are modified by applying the separable form to the displacement functions and then it is obtained a system of coupled differential equations in terms of displacement functions. The displacement functions are approximated by cubic and quintics splines along with the boundary conditions to get generalized eigenvalue problem. The generalized eigenvalue problem is solved numerically for frequency parameters and then associated eigenvectors are calculated which are spline coefficients. The vibration of the shells with the effect of fluid is analyzed for finding the frequency parameters against the cone angle, length ratio, relative layer thickness, number of layers, stacking sequence, boundary conditions, linear, exponential and sinusoidal thickness variations and then results are presented in terms of tables and graphs.

Keywords

References

  1. Ahlberg, J.H., Nilson, E.N. and Walsh, J.L. (1967), The Theory of Spline and their Application, Academic Press, New York, USA.
  2. Amabili, M. and Balasubramanian, P. (2020), "Nonlinear vibrations of truncated conical shells considering multiple internal resonances", Nonlin. Dyn., 100(1), 77-93. https://doi.org/10.1007/s11071-020-05507-8.
  3. Ansari, E., Hemmatnezhad, M. and Taherkhani, A. (2023), "Free vibration analysis of grid-stiffened composite truncated spherical shells", Thin Wall. Struct., 182, 110237. https://doi.org/10.1016/j.tws.2022.110237.
  4. Ansari, R., Hasrati, E. and Torabi, J. (2019), "Nonlinear vibration response of higher-order shear deformable FG-CNTRC conical shells", Compos. Struct., 222, 110906. https://doi.org/10.1016/j.compstruct.2019.110906.
  5. Bickley, W.G. (1968), "Piecewise cubic interpolation and two-point boundary problems", Comput. J., 11, 206-208.
  6. Gao, C., Miao, X., Lu, L., Huo, R., Hu, Q. and Shan, Y. (2019), "Free vibration analysis of functionally graded spherical torus structure with uniform variable thickness along axial direction", Shock Vib., 2019(1), 2803841. https://doi.org/10.1155/2019/2803841.
  7. Greville, T.N.E. (1969), Theory and Applications of Spline Functions, Academic Press, New York, USA.
  8. Guo, Z., Niu, W., Cui, J., Chai G.B., Li, Y. and Wu, X. (2023), "Numerical analysis of stress wave of projectile impact composite laminate", Struct. Eng. Mech., 87(2), 107-116. http://doi.org/10.12989/sem.2023.87.2.107.
  9. Irie, T., Yamada, G. and Kaneko, Y. (1982), "Free vibration of a conical shell with variable thickness", J. Sound Vib., 82(1), 83-94. https://doi.org/10.1016/0022-460X(82)90544-2.
  10. Javed, S., Viswanathan, K.K., Aziz, Z.A. and Lee, J.H. (2016), "Vibration analysis of a shear deformed antisymmetric angleply conical shells with varying sinusoidal thickness", Struct. Eng. Mech., 58(6), 1001-1020. http://doi.org/10.12989/sem.2016.58.6.1001.
  11. Javed, S., Viswanathan, K.K., Nurul Izyan, M.D., Aziz, Z.A. and Lee, J.H. (2018), "Free vibration of cross-ply laminated plates based on higher-order shear deformation theory", Steel Compos. Struct., 26(4), 473-484. https://doi.org/10.12989/scs.2018.26.4.473.
  12. Jin, G., Ma, X., Shi, S., Ye, T. and Liu, Z. (2014), "A modified Fourier series solution for vibration analysis of truncated conical shells with general boundary conditions", Appl. Acoust., 85, 82-96. https://doi.org/10.1016/j.apacoust.2014.04.007.
  13. Leissa, A.W. (1973), Vibration of Shells, NASA SP-288, Washington.
  14. Liu, M., Liu, J. and Cheng, Y. (2014), "Free vibration of a fluid loaded ring-stiffened conical shell with variable thickness", J. Vib. Acoust., 136(5), 051003. https://doi.org/10.1115/1.4027804.
  15. Love, A.E.H. (1994), A Treatise on the Mathematical Theory of Elasticity, 6th Edition, Dover Publications, New York, USA.
  16. Meskini, M. and Ghasemi, A.R. (2023), "Free vibration analysis of laminated cylindrical adhesive joints with conical composite shell adherends", J. Vib. Control, 29(15-16), 3475-3491. https://doi.org/10.1177/10775463221097466.
  17. Nor Hafizah, A.K., Viswanathan, K.K., Aziz, Z.A. and Lee, J.H. (2018), "Vibration of antisymmetric angle-ply composite annular plates of variable thickness", J. Mech. Sci. Technol., 32(5), 2155-216. https://doi.org/10.1007/s12206-018-0424-1.
  18. Nurul Izyan, M.D. and Viswanathan, K.K. (2019), "Vibration of symmetrically layered angle-ply cylindrical shells filled with fluid", Plos One, 14(7), e0219089. https://doi.org/10.1371/journal.pone.0219089.
  19. Nurul Izyan, M.D., Aziz, Z.A., Ghostine, R., Lee, J.H. and Viswanathan, K.K. (2019), "Free vibration of cross-ply layered circular cylindrical shells filled with quiescent fluid under first order shear deformation theory", Int. J. Press. Ves. Pip., 170, 73-81. https://doi.org/10.1016/j.ijpvp.2019.01.019.
  20. Nurul Izyan, M.D., Sabri, N.A.A., Hafizah, A.N., Sankar, D.S. and Viswanathan, K.K. (2021), "Axisymmetric free vibration of layered cylindrical shell filled with fluid", Int. J. Appl. Mech. Eng., 26(4), 63-76. https://doi.org/10.2478/ijame-2021-0050.
  21. Nurul Izyan, M.D., Viswanathan, K.K., Aziz, Z.A., Lee, J.H. and Prabakar, K. (2017), "Free vibration of layered truncated conical shells filled with quiescent fluid using spline method", Compos. Struct., 163, 385-398. https://doi.org/10.1016/j.compstruct.2016.12.011.
  22. Paidoussis. M.P. (2004), Fluid-Structure Interactions; Slender Structures and Axial Flow, Vol. 2, Elsevier, Academic Press, London.
  23. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells; Theory and Analysis, 2nd Edition, CRC Press, London.
  24. Sankaranarayanan, N., Chandrasekaran, K. and Ramaiyan, G. (1987), "Axisymmetric vibrations of laminated conical shells of variable thickness", J. Sound Vib., 118(1), 151-161. https://doi.org/10.1016/0022-460X(87)90260-4.
  25. Schoenberg, I.J. (1946), "Contributions to the problems of approximation of equidistant data by analytic functions", Quart. J. Appl. Math., 4, 45-99.
  26. Schoenberg, I.J. and Whitney, A. (1953), "On polya frequency functions 111. The positivity of translation determinants with an application to the interpolation problem by spline curves", Trans. Am. Math. Soc., 74(2), 246-259. https://doi.org/10.1007/978-1-4899-0433-1_16.
  27. Sofiyev, A.H. (2014), "Large-amplitude vibration of nonhomogeneous orthotropic composite truncated conical shell", Compos. Part B: Eng., 61, 365-374. https://doi.org/10.1016/j.compositesb.2013.06.040.
  28. Song, X., Wang, C., Wang, S. and Zhang, Y. (2023), "Vibration evolution of laminated composite conical shell with arbitrary foundation in hygrothermal environment: Experimental and theoretical investigation", Mech. Syst. Signal Pr., 200, 110565. https://doi.org/10.1016/j.ymssp.2023.110565.
  29. Viswanathan, K.K. and Navaneethakrishnan, P.V. (2005), "Free vibration of layered truncated conical shell frusta of differently varying thickness by the method of collocation with cubic and quintic splines", Int. J. Solid. Struct., 42, 1129-1150. https://doi.org/10.1016/j.ijsolstr.2004.06.065.
  30. Viswanathan, K.K., Hafizah, A.K. and Aziz, Z.A. (2018), "Free vibration of angle-ply laminated conical shell frusta with linear and exponential thickness variations", Int. J. Acoust. Vib., 23(2), 264-276. https://doi.org/10.20855/ijav.2018.23.21164.
  31. Viswanathan, K.K., Javed, S. and Aziz, Z.A. (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. http://doi.org/10.12989/sem.2013.45.2.259.
  32. Viswanathan, K.K., Kim, K.S., Lee, K.H. and Lee, J. H. (2010), "Free vibration of layered circular cylindrical shells of variable thickness using spline function approximation", Math. Prob. Eng., 28(6), 749-765. https://doi.org/10.1155/2010/547956.
  33. Viswanathan, K.K., Lee, J.H., Aziz, Z.A. and Hossain, I. (2011), "Free vibration of symmetric angle ply laminated cylindrical shells of variable thickness", Acta Mechanica, 221, 309-319. https://doi.org/10.1007/s00707-011-0505-z.
  34. Yousefi, A.H., Memarzadeh, P., Afshari, H. and Hosseini, S.J. (2020), "Agglomeration effects on free vibration characteristics of three-phase CNT/polymer/fiber laminated truncated conical shells", Thin Wall. Struct., 157, 107077. https://doi.org/10.1016/j.tws.2020.107077.