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The natural vibrations of thin (Kirchhoff-Love) plates with constant and variable thickness are considered in the paper. Isotropic and orthotropic rectangular plates with different boundary conditions are analysed. The Finite Element Method and the Finite Difference Method are used to describe structural deformation. The elements of stiffness matrix are derived numerically using author’s approaches of localization of integration points. The plate inertia forces are expressed by diagonal, lumped mass matrix or consistent mass matrix. The presence of the external medium, which can be a fluid, is described by the fluid velocity potential of double layer and the fundamental solution of Laplace equation which leads to the fully-populated mass matrix. The influence of external additional liquid mass on natural frequencies of plate is analysed, too.
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art. no. 2020216
Opis fizyczny
Bibliogr. 12 poz., rys., wykr.
Twórcy
autor
- Doctoral School of Poznan University of Technology, Piotrowo 3 Street, 60-965 Poznan
autor
- Institute of Structural Analysis of Poznan University of Technology, Piotrowo 5 Street, 60-965 Poznan
Bibliografia
- 1. W. Nowacki, Structural dynamics, Arkady Publishing House, 1961 (in Polish).
- 2. M.S. Nerantzaki, J.T. Katsikadelis, An Analog Equation Solution to dynamic analysis of plates with variable thickness, Engng. Analysis Bound. Elem. 17, 2 (1996) 145 - 152.
- 3. W.P. Jones, J.A. Moore, Simplified aerodynamic theory of oscillating thin surfaces in subsonic flow, J. Am. Inst. Aeronaut. Assoc. 11, 9 (1973) 1305 - 1307.
- 4. R. Sygulski, Drgania własne siatek cięgnowych z uwzględnieniem masy otaczającego powietrza (Natural vibrations of the string meshes, taking into account the mass of the surrounding air), Arch. Civil Engng. XXIX, 4 (1983).
- 5. J.S. Lee, S.W. Lee, Fluid-structure interaction analysis on a flexible plate normal to a free stream at low Reynolds number, J. Fluids Struct. 29 (2012) 18 -34.
- 6. J. Rakowski, M. Guminiak, Non-linear vibration of Timoshenko beams by Finite Element Method, J. Theoret. and Appl. Mech.53, 3(2015) 731 - 743.
- 7. M. Kamiński, The Stochastic Perturbation Method for Computational Mechanics, Wiley, 2013.
- 8. M. Guminiak, The Boundary Element Method in plate analysis, Poznan University of Technology Publishing House, Poznań 2016, ISBN 978-83-7775-407-8 (in Polish).
- 9. M. Kuczma, Foundations of structural mechanics with shape memory. Numerical modeling, University of Zielona Góra Publishing House, Zielona Góra, 2010, ISBN 978--83-7481-411-9 (in Polish).
- 10. J. Pietrzak, G. Rakowski, K. Wrześniowski, Macierzowa analiza konstrukcji, PWN Publishing House, Warszawa-Poznań, 1979 (in Polish).
- 11. C-C. Liang, C-C. Liao, Y-S. Tai, W-H. Lai, The free vibration analysis of submerged cantilever plates, Ocean Engng. 28 (2001) 1225 - 1245.
- 12. J. Ma, Y. Ren, Free vibration and chatter stability of a rotating thin-walled composite bar, Advances in Mech. Engng. 10, 9 (2018) 1 - 10.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-47c5e2ac-4644-4a0c-81a1-3d01ac8a2fe9