Free vibrations of thin elastic orthotropic cylindrical panel with hinge-mounted edge generator

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Abstract

Using the system of equations corresponding to the classical theory of orthotropic cylindrical shells, the free vibrations of a thin elastic orthotropic cylindrical panel with hinge-mounted edge generator are investigated. To calculate the natural frequencies and to identify the respective natural modes, the generalized Kantorovich–Vlasov method of reduction to ordinary differential equations is used. Dispersion equations for finding the natural frequencies of possible types of vibrations are derived. An asymptotic relation between the dispersion equations of the problems at hand and the analogous problem for a rectangular plate is established. A mechanism is given by which possible types of edge oscillations are distinguished. As examples, the values of dimensionless characteristics of natural frequencies are derived for an orthotropic cylindrical panels.

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About the authors

G. R. Ghulghazaryan

Armenian State Pedagogical University

Author for correspondence.
Email: ghulghazaryangurgen08@aspu.am
Armenia, Yerevan

L. G. Ghulghazaryan

Armenian State Pedagogical University; Institute of Mechanics of NAS Armenia

Email: ghulghazaryanlusine08@aspu.am
Armenia, Yerevan; Yerevan

References

  1. Norris A.N. Flexural edge waves // J. of Sound&Vibr., 1994, vol. 171(4), pp. 571–573.
  2. Thompson I., Abrahams I.D. On the existence of flexural edge waves on thin orthotropic plates // J. Acoust. Soc. Amer., 1994, vol. 112(5), pp. 1756–1765.
  3. Grinchenko V.T. Wave motion localization effects in elastic waveguides // Int. Appl. Mech., 2005, vol. 41(9), pp. 988–994.
  4. Vilde M.V., Kaplunov Yu.D., Kassovich L.Yu. Boundary and Interface Resonant Phenomena in Elastic Bodies. Moscow: Fizmatlit, 2010. 280 p. (in Russian)
  5. Mikhasev G.I., Tovstik P.E. Localized Vibrations and Waves in Thin Shells. Asymptotic Methods. Moscow: Fizmatlit, 2009. 292 p. (in Russian)
  6. Gol’denveizer A.L., Lidskii V.B., Tovstik P.E. Free Vibrations of Thin Elastic Shells. Moscow: Nauka, 1979. 383 p. (in Russian)
  7. Ghulghazaryan G.R., Ghulghazaryan R.G., Srapionyan D.L. Localized vibrations of a thin-walled structure consisted of orthotropic elastic non-closed cylindrical shells with free and rigid-clamped edge generators // ZAMM. Z. Math. Mech., 2013, vol. 93, no. 4, pp. 269–283.
  8. Gulgazaryan G.R., Gulgazaryan L.G., Saakyan R.D. The vibrations of a thin elastic orthotropic circular cylindrical shell with free and hinged edges // JAMM, 2008, vol. 72, pp. 312–322.
  9. Vlasov V.Z. A new practical method to design folded-plate structures and shells // Stroit. Promyshl., 1932, no. 11, pp. 33–38; no. 12, pp. 21–26. (in Russian)
  10. Kantorovich L.V. A direct method for approximate solution of a problem on the minimum of a double integral // Izv. AN SSSR, Separ. Math.&Nat. Sci., 1933, no. 5, pp. 647–653. (in Russian)
  11. Prokopov V.G., Bespalov E.I., Sherenkovskii Yu.V., Kontorovich L.V. Method of reduction to ordinary differential equations and a general method for solving multidimensional problems of heat transfer // Inzh. Fiz. zh., 1982, vol. 42(6), pp. 1007–1013. (in Russian)
  12. Bespalova E.I. Solving stationary problems for shallow shells by a generalized Kantorovich–Vlasov method // Int. Appl. Mech., 2008, vol. 44, pp. 1283–1293. https://doi.org/10.1007/s10778-009-0138-2
  13. Mikhlin S.G. Variational Methods in Mathematical Physics. Moscow: Nauka, 1970. 510 p. (in Russian)
  14. Ambartsumyan S.A. General Theory of Anisotropic Shells. Moscow: Nauka, 1974. 446 p. (in Russian)
  15. Ghulghazaryan G.R., Lidskii V.B. Density of free vibrations frequencies of a thin anisotropic shell with anisotropic layers // Izv. AN.SSSR. MTT, 1982, no. 3, pp. 171–174.
  16. Gulgazaryan G.R. Vibrations of semi-infinite, orthotropic cylindrical shells of open profile // Int. Appl. Mech., 2004, vol. 40(2), pp. 199–212.
  17. Ghulghazaryan G.R., Ghulghazaryan L.G., Kudish I.I. Free vibrations of a thin elastic orthotropic cylindrical panel with free edges // Mech. of Compos. Mater., 2019, vol. 55(5), pp. 557–574. https://doi.org/10.1007/s11029-019-09834-9
  18. Ghulghazaryan G.R., Ghulghazaryan L.G. Free vibrations of thin elastic orthotropic cantilever cylindrical panel // in: Advanced Problem in Mechanics II. APM 2020. Lecture Notes in Mechanical Engineering / ed. by Indeitsev D.A., Krivtsov A.M. Cham: Springer, 2022. pp. 441–462. https://doi.org/10.1007/978-3-030-92144-6_34
  19. Ghulghazaryan G.R., Ghulghazaryan L.G. Free localized vibrations of a thin elastic composite panel // in: Mechanics of High-Contrast Elastic Solids. Advanced Structured Materials. Vol. 187 / Altenbach H., Prikazchikov D., Nobili A. Cham: Springer, 2023. pp. 91–118. https://doi.org/10.1007/978-3-031-24141-3_7
  20. Ghulghazaryan G.R., Ghulghazaryan L.G. Free vibrations of thin elastic orthotropic cylindrical panel with rigid-clamped edge generator // ASPU after Kh. Abovyan. Sci. Bull., 2023, vol. 2, no. 45, pp. 46–72. https://doi.org/10.24234/scientific.v2i45.93

Supplementary files

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2. Fig. 1. Cylindrical panel with generatrices orthogonal to the ends of the panel

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3. Fig. 2. Rectangular plate with a hinged side

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4. Application
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