Numerical analysis of free vibration frequencies of pentagonal plates




pentagonal plate, frequency and mode of free vibrations, finite element method, Rayleigh—Ritz method, FEMAP


Free vibrations of the isotropic pentagonal plates of the different thicknesses with the free edges are considered based on two different approaches. The approach Rayleigh—Ritz method has been extended to the calculation of the frequencies of free vibrations of pentagonal plates. Frequencies and forms of free vibrations of the plates of this class are calculated by the finite element method (FEM). The frequencies calculated were compared and the accuracy of the calculations by the two methods was established. The modes of the vibrations obtained based on the FEM are compared with the modes of vibrations obtained numerically and experimentally by other authors.


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Grigorenko, A. Ya. & Efimova, T. L. (2005). Spline-Approximation Method Applied to Solve Natural Vibration Problems for Rectangular Plates of Varying Thickness. Int. Appl. Mech., 41, No. 10, pp. 1161-1169.

Lam, K. Y., Liew, K. M. & Chow, S. T. (1990). Free vibration analysis of isotropic and orthotropic triangular plate. Int. J. Mech. Sci., 32, No. 5, pp. 455-464.

Leissa, A. W. & Jaber, N. A. (1992). Vibrations of completely free triangular plate. Int. J. Mech. Sci., 34, No. 8, pp. 605-616.

Liew K. M., Xiang Y. & Kitipornchai S. (1995). Research on thick plate vibration: a literature survey. J. Sound Vib., 180, No. 1, pp. 163-176.

Meleshko, V. V. & Papkov, S. O. (2009). Bending vibration of the rectangular elastic plates with free edges: from Chladni (1809) and Ritz (1909) to the present day. Acoust. Bullet., 12, No. 4, pp. 34-51 (in Russian).

Wang, C. Y. (2015). Vibrations of Completely Free Rounded Regular Polygonal Plates. Int. J. Acoust. Vib., 20, No. 2, pp. 107-112.

Grigorenko, O. Y., Borisenko, M. Y., Boichuk, O. V. & Vasil’eva, L. Y. (2021). Free Vibrations of Triangular Plates with a Hole. Int. Appl. Mech., 57, No. 5, pp. 534-542.

Grigorenko, O. Ya., Borisenko, M. Yu., Boichuk, O. V. & Novitskii, V. S. (2019). Numerical analysis of the free vibrations of rectangular plates using various approaches. Visn. Zaporizhzhya Nat. Univ. Phys. -Mat. Sci., No. 1, pp. 33-41. (in Ukrainian).

Borysenko, M., Zavhorodnii, A. & Skupskyi, R. (2019). Numerical analysis of frequencies and forms of own collars of different forms with free zone. J. Appl. Math. Comput. Mech., 18, No. 1, pp. 5-13. 2019. 1. 01

Grigorenko, O. Ya., Borisenko, M. Yu., Boichuk, O. V. & Novitskii, V. S. (2019). Usage of experimental and numerical methods to study the free vibrations of rectangular plates. Probl. Comp. Mech. Streng. Struct., 29, pp. 103-112. (in Ukrainian).

Ma, C. C. & Huang, C. H. (2004). Experimental whole-field interferometry for transverse vibration of plate. J. Sound Vib., 271, No. 3-5, pp. 493-506.

Karlash, V. L. (2005). Resonant electromechanical vibrations of piezoelectric plates. Int. Appl. Mech., 41, No. 7, pp. 709-747.

Byrger, I. A. & Panovko, Y. G. (1968). Strength. Sustainability. Oscillations. Moscow: Mashinostroenie (in Russian).

Grigorenko, O. Ya., Borysenko, M. Yu. & Boychuk, O. V. (2020). Numerical evaluation of frequencies and modes of free vibrations of isosceles triangular plates with free edges. Mat. Metody ta Fiz. -Mekh. Polya, 63, No. 3, pp. 28-39. (in Ukrainian). 63. 3. 28-39

Waller, M. D. (1952). Vibrations of free plates: line symmetry; corresponding modes. Proc. Roy. Soc. Lond. A Math. Phys. Sci., 211, No. 1105, pp. 265-276. 0038



How to Cite

Grigorenko О. ., Borysenko М. ., Sperkach С., Bezuglaya А. ., & Mikhrin Е. . (2022). Numerical analysis of free vibration frequencies of pentagonal plates. Reports of the National Academy of Sciences of Ukraine, (6), 36–45.