Fluid-structure Interaction Vibration Analysis of Vertical Cylindrical Containers with Elastic Bottom Plate Made of Functionally Graded Materials
الموضوعات : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیک
علی اکبر شفیعی
1
(
کارشناسی ارشد، دانشکده مهندسی مکانیک، دانشگاه شیراز، شیراز، ایران
)
مجتبی محزون
2
(
دانشیار، دانشکده مهندسی مکانیک، دانشگاه شیراز، شیراز، ایران.
)
احسان عسکری
3
(
دانشجوی دکتری، دانشکده مهندسی پزشکی، دانشگاه مک کووری، سیدنی، استرالیا
)
الکلمات المفتاحية: Free vibration, Functionally Graded Materials, Liquid–structure interaction, Rayleigh–Ritz method, Eigen function expansion,
ملخص المقالة :
In the present paper a method is proposed to investigate the free vibration of a partially liquid-filled cylindrical tank. The mechanical properties of the container are assumed to change continuously along the thickness according to volume fraction Power-law, Sigmoid or Exponential distribution. The liquid is supposed to be incompressible and in viscid and its velocity potential is formulated by using Eigen function expansions. The interaction between the liquid and the plate was considered and the dynamic characteristics of the plate are extracted by using the Rayleigh–Ritz method. The results from the proposed method are in good agreement with experimental and numerical solutions available in the literature. A finite element analysis is also applied to check the validity of the results. Furthermore, the influence of various variables such as the number of nodal circles and diameters, volume fractions of functionally graded materials and liquid level on the dynamic behavior of the coupled system is investigated.
[1] Kwak M.K., Kim K.C., Axisymmetric vibration of circular plates in contact with fluid, Journal of Sound and Vibration, 146, 1991, pp. 381–389.
[2] Kwak M.K. , Vibration of circular plates in contact with water, Transactions of the American Society of Mechanical Engineers, Journal of Applied Mechanics, 58, 1991, pp.480–483.
[3] Chiba M., Nonlinear hydroelastic vibration of a cylindrical tank with an elastic bottom, containing liquid. Part II: linear axisymmetric vibration analysis, Journal of Fluids and Structures, 7, 1993, pp. 57–73.
[4] Bauer H.F., Coupled frequencies of a liquid in a circular cylindrical container with elastic liquid surface cover, Journal of Sound and Vibration, 180, 1995, pp. 689–704.
[5] Amabili M., Bulging modes of circular bottom plates in rigid cylindrical containers filled with a liquid, Shock and Vibration, 4, 1997, pp. 51–68.
[6] Kwak M.K., Han S.B., , Effect of fluid depth on the hydroelastic vibration of free-edge circular plate, Journal of Sound and Vibration, 230, 2000, pp. 171–185.
[7] Amabili M., Kwak, M.K., ,Vibration of circular plates on a free fluid surface; effect of surface waves, Journal of Sound and Vibration, 226, 1999, pp. 407–424.
[8] Cheung Y.K., Zhou D., Hydroelastic vibration of a circular container bottom plate using the Galerkin method, Journal of Fluids and Structures, 16, 2002, pp. 561–580.
[9]Liang C. C., Liao C. C., Tai Y. S., The free vibration analysis of submerged cantilever plates, Ocean Engineering, 28, 2001, pp.1225–1245.
[10] Jeong K.H., Kim K.J., Hydroelastic vibration of a circular plate submerged in a bounded compressible fluid, Journal of Sound and Vibration, 283, 2005, pp. 153–172.
[11] Jeong K.H., Hydroelastic vibration of two annular plates coupled with a bounded compressible fluid, Journal of Fluids and Structures, 22, 2006, pp. 1079–1096.
[12] Askari E., Daneshmand F., Free vibration of an elastic bottom plate of a partially fluid-filled cylindrical container with an internal body, European Journal of Mechanics A/Solids, 29, 2010, pp. 68–80.
[13]Kutlu A., Ugurlu B., Omurtag M.H., Ergin A., Dynamic response of Mindlin plates resting on arbitrarily orthotropic Pasternak foundation and partially in contact with fluid, Ocean Engineering, 42, 2012, pp. 112–125.
[14] Yamanouchi M., Koizumi M., Hirai T., Shiota, Resonances of an air-filled elastic cylindrical shell immersed in a fluid, Proceedings of the First International Symposium on Functionally Gradient Materials, Japan ,1990.
[15] Koizumi M., The concept of FGM, Ceramic Transactions, Functionally Gradient Materials, 1993, pp. 34, 3–10.
[16] Anon, FGM components: PM meets the challenge, Metal Powder Report, 51, 1996, pp. 28–32.
[17] Reddy J. N., , Analysis of functionally graded plates, International journal for numerical method in engineering- International Journal for Numerical Methods in Engineering, 47, 2000, pp. 663–684.
[18] Nie G.J., Zhong Z., Semi-analytical solution for three-dimensional vibration of functionally graded circular plates, Computer Methods in Applied Mechanics and Engineering, 196, 2007, pp. 4901–4910.
[19] Allahverdizadeh A., Naei M. H., Nikkhah Bahrami M., Nonlinear free and forced vibration analysis of thin circular functionally graded plates, Journal of Sound and Vibration, 310, 2008, pp. 966–984.
[20] Dong C. Y., Three-dimensional free vibration analysis of functionally graded annular plates using the Chebyshev–Ritz method, Materials and Design, 29, 1995, pp.1518–1525.
[21] Chen W.Q., Bian Z.G., Ding H.J., 3D free vibration analysis of a functionally graded piezoelectric hollow cylinder filled with compressible fluid, International Journal of Solids and Structures, Vol. 41, 2004, pp. 947–964.
[22] Morand H.J.P., Ohayon, R., Fluid–Structure Interaction: Applied Numerical Methods, Wiley, New York, 1995.
[23] Delale F., Erdogan, F., The crack problem for a nonhomogeneous plane, ASME Journal of Applied Mechanics, 50, 1983, pp.609–614.
[24] Shyang-Ho Chi., Yen-Ling Chung., Mechanical behavior of functionally graded material plates under transverse load—Part I: Analysis, International Journal of Solids and Structures, 43, 2006, pp. 3657–3674.
[25] Leissa A.W., , Vibration of Plates, NASA SP-160. U.S Government Printing Office, Washington, DC., 1969.
[26] Askari E., Daneshmand, F., ,Coupled vibration of a partially fluid-filled cylindrical container with a cylindrical internal body, Journal of Fluids and Structures, 25, 2009, pp. 389–405.
[27] 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, pp.431–452.
[28] Zhu F., Rayleigh quotients for coupled free vibrations, Journal of Sound and Vibration, 171, 1994, pp. 641–649.
[29] Virella J., Godoy L., Su´arez, L., Fundamental modes of tank-liquid systems under horizontal motions, Engineering Structures, 28, 2006, pp. 1450–1461.
[30] Ergin A., Ugurlu B., Hydroelastic analysis of fluid storage tanks by using a boundary integral equation method, Journal of Sound and Vibration, 17, 2004, pp. 927–939.
[31] Koval’chuk, Kruk P. S., On the spectrum of natural frequencies of circular cylindrical shells completely filled with a fluid, International Applied Mechanics, 42, 2006, pp. 529-535.
