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Numerical Determination of Natural Frequencies and Modes of Closed Corrugated Cylindrical Shells

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The natural frequencies and modes of cantilever isotropic thin closed corrugated circular cylindrical shells with arbitrary number of corrugations are determined using the finite-element method. Two test problems for longitudinally corrugated open circular cylindrical shells are solved. The frequencies determined with our method and with the spline-collocation method in combination with the method of discrete orthogonalization are in good agreement (the difference is no greater than 5.5%). The natural frequencies of corrugated shells with different number of corrugations are compared. The dependence of the natural frequency of corrugated shells on the number of corrugations and vibration modes is established. The symmetric and antisymmetric modes of vibrations including those of tensile, shear, flexural, and torsional vibrations for all the corrugated shells considered are found.

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References

  1. V. D. Budak, O. Ya. Grigorenko, M. Yu. Borisenko, O. P. Prigoda, and O. V. Boichuk, “Determining the natural frequencies of a thin-walled shell with noncircular cross-section by the stroboholographic interferometry method,” Probl. Obchysl. Mekh. Prochn. Konstr., No. 24, 18–25 (2015).

  2. V. D. Budak, O. Ya. Grigorenko, M. Yu. Borisenko, and O. V. Boichuk, “Influence of the eccentricity of an elliptic shell on the distribution of its dynamic characteristics,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauki, No. 1, 23–28 (2015).

  3. S. V. Puzyrev, “On the free vibrations of corrugated elliptical cylindrical shells with section,” Zb. Nauk. Prats’ NUK, No. 1, 47–53 (2013).

  4. R. N. Arnold and G. B. Warburton, “The flexural vibration of thin cylinders,” Proc. Inst. Mech. Engs., 167 A, No. 1, 62–80 (1953).

  5. M. L. Baron and H. H. Bleich, “Tables for frequencies and modes of free vibration of infinitely long thin cylindrical shells,” J. Appl. Mech., 21, No. 2, 178–188 (1954).

    Article  MATH  Google Scholar 

  6. V. D. Budak, A. Ya. Grigorenko, M. Yu. Borisenko, and E. V. Boichuk, “Natural frequencies and modes of noncircular cylindrical shells with variable thickness,” Int. Appl. Mech., 53, No. 2, 164–172 (2017).

    Article  Google Scholar 

  7. V. D. Budak, A. Ya. Grigorenko, M. Yu. Borisenko, and E. V. Boychuk, “Determination of eigenfrequencies of an elliptic shell with constant thickness by the finite-element method,” J. Math. Sci., 212, No. 2, 182–192 (2016).

    Article  Google Scholar 

  8. V. D. Budak, A. Ya. Grigorenko, V. V. Khorishko, and M. Yu. Borisenko, “Holographic interferometry study of the free vibrations of cylindrical shells of constant and variable thickness,” Int. Appl. Mech., 50, No. 1, 68–74 (2014).

    Article  Google Scholar 

  9. H. Du et al., “High-frequency vibrations of corrugated cylindrical piezoelectric shells,” Acta Mechanica Solida Sinica, 21, No. 6, 564–572 (2008).

    Article  Google Scholar 

  10. J. F. Greenspon, “Vibration of thick cylindrical shells,” J. Acoust. Soc. Amer., 31, No. 12, 1682–1683 (1959).

    Article  Google Scholar 

  11. A. Grigorenko, Yu. Zolotoi, A. Prigoda, I. Zhuk, V. Khorishko, and A. Ovcharenko, “Experimental investigation of natural vibrations of a thick-walled cylindrical shell by the method of holographic interferometry,” J. Math. Sci., 194, No. 3, 239–244 (2013).

    Article  MATH  Google Scholar 

  12. A. Ya. Grigorenko, M. Yu. Borisenko, O. V. Boychuk, and L. Y, Vasil’eva, “Free vibrations of an open non-circular cylindrical shell of variable thickness,” in: H. Altenbach, N. Chinchaladze, R. Kienzler, and W. Muller (eds.), Analysis of Shells, Plates, and Beams. Advanced Structured Materials, 134, Springer, Cham (2020), pp. 141–154.

  13. A. Ya. Grigorenko, M. Yu. Borisenko, and E. V. Boichuk, “Free vibrations of an open elliptical cylindrical shell,” Int. Appl. Mech., 56, No. 4, 389–401 (2020).

    Article  MathSciNet  Google Scholar 

  14. A. Ya. Grigorenko, M. Yu. Borisenko, E. V. Boichuk, and A. P. Prigoda, “Numerical determination of natural frequencies and modes of the vibrations of a thick-walled cylindrical shell,” Int. Appl. Mech., 54, No. 1, 75–84 (2018).

    Article  Google Scholar 

  15. A. Ya. Grigorenko, O. Yu. Parkhomenko, L. Ya. Vasil’eva, and M. Yu. Borisenko, “Solution of the problem of free vibrations of a nonthin orthotropic shallow shell of variable thickness in the refined statement,” J. Math. Sci., 229, No. 3, 253–268 (2017).

  16. Ya. M. Grigorenko and L. S. Rozhok, “Solving the stress problem for hollow cylinders with corrugated elliptical cross section,” Int. Appl. Mech., 40, No. 2, 169–175 (2004).

    Article  Google Scholar 

  17. A. Ya. Grigorenko and T. L. Efimova, “Using spline-approximation to solve problems of axisymmetric free vibration of thick-walled orthotropic cylinders,” Int. Appl. Mech., 44, No. 10, 1137–1147 (2008).

    Article  MathSciNet  Google Scholar 

  18. A. M. Khalifa, “Solving the vibration problem of inhomogeneous orthotropic cylindrical shells with hoop-corrugated oval cross section,” Comptes Rendus Mecanique, 343, No. 9, 482–494 (2015).

    Article  Google Scholar 

  19. Y. W. Kim, “Vibration analysis of longitudinally corrugated cylindrical shells,” Trans. of the Korean Society for Noise and Vibration Eng., 26, No. 7, 851–856 (2016).

  20. T. P. Nguen et al., “Nonlinear vibration of full-filled fluid corrugated sandwich functionally graded cylindrical shells,” J. of Vibration and Control, 1077546320936537 (2020).

  21. N. P. Semenyuk, I. Yu. Babich, and N. B. Zhukova, “Natural vibrations of corrugated cylindrical shells,” Int. Appl. Mech., 41, No. 5, 512–519 (2005).

    Article  MATH  Google Scholar 

  22. L. Xu et al., “Study on the vibration characteristics of a finite-width corrugated cylindrical shell piezoelectric transducer,” IEEE Trans. on Ultrasonics, Ferroelectrics, and Frequency Control, 57, No. 6, 1460–1469 (2010).

  23. L. Xu et al., “Vibration characteristics of a corrugated cylindrical shell piezoelectric transducer,” IEEE Trans. on Ultrasonics, Ferroelectrics, and Frequency Control, 55, No. 11, 2502–2508 (2008).

  24. J. S. Yang et al., “Modal response of all-composite corrugated sandwich cylindrical shells,” Compos. Sci. Technol., 115, 9–20 (2015).

    Article  Google Scholar 

  25. H. Juan and Rh. Liu, “Nonlinear vibration of corrugated shallow shells under uniform load,” Appl. Math. Mech., 28, 573–580 (2007).

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova St, Kyiv, 03057, Ukraine

    O. Ya. Grigorenko & M. Yu. Borisenko

  2. Mykolayiv State Agrarian University, 9 Georgiya Gongadze St, Mykolayiv, 54020, Ukraine

    O. V. Boychuk

  3. Igor Sikorsky Kyiv Polytechnic Institute, 37 Peremogy Av, Kyiv, 03056, Ukraine

    A. A. Shums’ka

Authors
  1. O. Ya. Grigorenko
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  2. M. Yu. Borisenko
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  3. O. V. Boychuk
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  4. A. A. Shums’ka
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Correspondence to O. Ya. Grigorenko.

Additional information

Translated from Prykladna Mekhanika, Vol. 58, No. 5, pp. 27–38, September–October 2022.

This study was sponsored by the budgetary program Support of Priority Areas of Research (KPKVK 6541230).

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Grigorenko, O.Y., Borisenko, M.Y., Boychuk, O.V. et al. Numerical Determination of Natural Frequencies and Modes of Closed Corrugated Cylindrical Shells. Int Appl Mech 58, 520–532 (2022). https://doi.org/10.1007/s10778-023-01177-2

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  • DOI: https://doi.org/10.1007/s10778-023-01177-2

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