Determination of the frequencies and forms of free vibrations of pentagonal plates by the finite-element method-Reference-Cited by-同舟云学术

Determination of the frequencies and forms of free vibrations of pentagonal plates by the finite-element method

Published:2020 Issue:1-2 Volume: Page:61-66
ISSN:2218-2055
Container-title:Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics
language:uk
Short-container-title:BKNUPhM

Author:

Grigorenko A.¹,Borysenko M.¹,Boychuk O.²

Affiliation:

1. Institute of Mechanics after S.P. Tymoshenko NAS of Ukraine

2. Nikolaev National Agrarian University

Abstract

Frequencies and modes of free vibrations of an isotropic thin pentagonal plate of regular shape with various configurations of rigid attachment at the edges are determined using the finite element method (FEM). The results obtained for some pentagonal plates are compared with the results obtained for square plates of an equivalent mass with corresponding boundary conditions. We present the vibration modes of the studied plates and the topology of the vibration modes for some of the considered plates corresponding to the square plates with free edges and rigidly fixed edges. The reliability of the obtained results is ensured by the use of a substantiated mathematical model, the correct formulation of the problem and the practical convergence of the calculated frequencies when using the FEM.

Publisher

Taras Shevchenko National University of Kyiv

Subject

Medical Assisting and Transcription,Medical Terminology

Reference12 articles.

1. BORYSENKO M.Y., BOYCHUK O.V., BORYSENKO I.A., ROGOVTSOV Y.O. (2016) Computer modeling of free vibration of thin plates with different materials. Science Journal of Geometric modeling and information technologies. – No. 2. – P. 29-33.

2. GPIGORENKO O.Y., BORYSENKO M.Y., BOYCHUK O.V., NOVYTSKYI V.S. (2019) Application of experimental and numerical methods to the study of the free vibrations or rectangular plates. Problems of computational mechanics and strength of structures: col. of sci. art. – No. 29. – P. 103-112.

3. GPIGORENKO O.Y., BORYSENKO M.Y., BOYCHUK O.V., NOVYTSKYI V.S. (2019) Numerical analysis of free vibrations for rectangular plates based different approaches. Bulletin of Zaporizhzhia National University. Physical and Mathematical Sciences. – No. 1. – P. 33-41.

4. MELESHKO V.V., PAPKOV S.O. (2009) Flexural vibration of elastic rectangular plates with free edges: from Chladni (1809) and Ritz (1990) to the present day. Akustychnyi visnyk. – Vol. 12, No. 4. – P. 34-51.

5. RUDAKOV K.N. (2005) FEMAP. The Geometric and finite element modeling of structures in MSC. visual Nastran for Windows. Kyiv: NTUU «KPI».