Abstract
The linear study of free vibrations of structures coupled to incompressible and inviscid fluids are studied by using the Rayleigh-Ritz method. The system is modelled by using different components. The artificial spring method is used to synthesise these components. The advantage is that admissible functions are defined in each component and the continuity condition of translational and rotational displacements between the rigid joints of the structure is no longer required. The fluid-structure interaction can be accurately described by using this method, including the effect of the free surface waves and the dynamic interaction among structural components via the fluid medium. An application of the method to a vertical circular tank partially filled with water is also presented in order to show the potential of the method.
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References
Meirovitch, L., Computational Methods in Structural Dynamics. Sijthoff and Noordhoff, Alphen aan den Rijn, The Nederlands (1980) 439 pp.
Soedel, W., Vibrations of Shells and Plates, 2nd edition. Marcel Dekker, New York (1993).
Yamada, G., Irie, T. and Tamiya, T., Free vibration of a circular cylindrical double-shell system closed by end plates. Journal of Sound and Vibration 108 (1986) 297–304.
Yuan, J. and Dickinson, S.M., On the use of artificial springs in the study of the free vibrations of systems comprised of straight and curved beams. Journal of Sound and Vibration 152 (1992) 203–216.
Cheng, L. and Nicolas, J., Free vibration analysis of a cylindrical shell-circular plate system with general coupling and various boundary conditions. Journal of Sound and Vibration 155 (1992) 231–247.
Yuan, J. and Dickinson, S.M., The flexural vibration of rectangular plate systems approached by using artificial springs in the Rayleigh—Ritz method. Journal of Sound and Vibration 159 (1992) 39–55.
Yuan, J. and Dickinson, S.M., The free vibration of circularly cylindrical shell and plate systems. Journal of Sound and Vibration 175 (1994) 241–263.
Missaoui, J., Cheng, L. and Richard, M.J., Free and forced vibration of a cylindrical shell with a floor partition. Journal of Sound and Vibration 190 (1996) 21–40.
Cheng, L., Fluid-structural coupling of a plate-ended cylindrical shell: Vibration and internal sound field. Journal of Sound and Vibration 174 (1994) 641–654.
Cheng, L., Vibroacustic modelling of mechanically coupled structures: Artificial spring technique applied to light and heavy mediums. Shock and Vibration 3 (1996) 193–200.
Amabili, M., Free vibration of a fluid-filled circular cylindrical shell with lumped masses attached, using the receptance method. Shock and Vibration 3 (1996) 159–167.
Amabili, M., Shell-plate interaction in the free vibrations of circular cylindrical tanks partially filled with a liquid: The artificial spring method. Journal of Sound and Vibration 199 (1997) 431–452.
Amabili, M., Ritz method and substructuring in the study of vibration with strong fluidstructure interaction. Journal of Fluids and Structures 11 (1997) 507–523.
Petyt, M., Vibrations of curved plates. Journal of Sound and Vibration 15 (1971) 381–395.
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Amabili, M. Rayleigh Quotient, Ritz Method and Substructuring to Study Vibrations of Structures Coupled to Heavy Fluids: Potential of the Artificial Spring Method. Flow, Turbulence and Combustion 61, 21–30 (1998). https://doi.org/10.1023/A:1026432717204
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DOI: https://doi.org/10.1023/A:1026432717204