Browse > Article
http://dx.doi.org/10.12989/sem.2014.50.1.053

Dynamic behavior of a functionally graded plate resting on Winkler elastic foundation and in contact with fluid  

Shafiee, Ali A. (Faculty of Mechanical Engineering, Shiraz University)
Daneshmand, Farhang (Department of Mechanical Engineering, McGill University)
Askari, Ehsan (Australian School of Advanced Medicine, Macquarie University)
Mahzoon, Mojtaba (Faculty of Mechanical Engineering, Shiraz University)
Publication Information
Structural Engineering and Mechanics / v.50, no.1, 2014 , pp. 53-71 More about this Journal
Abstract
A semi-analytical method is developed to consider free vibrations of a functionally graded elastic plate resting on Winkler elastic foundation and in contact with a quiescent fluid. Material properties are assumed to be graded distribution along the thickness direction according to a power-law in terms of the volume fractions of the constituents. The fluid is considered to be incompressible and inviscid. In the analysis, the effect of an in-plane force in the plate due to the weight of the fluid is taken into account. By satisfying the compatibility conditions along the interface of fluid and plate, the fluid-structure interaction is taken into account and natural frequencies and mode shapes of the coupled system are acquired by employing energy methods. The results obtained from the present approach are verified by those from a finite element analysis. Besides, the effects of volume fractions of functionally graded materials, Winkler foundation stiffness and in-plane forces on the dynamic of plate are elucidated.
Keywords
dynamic behavior; fluid-structure interaction; functionally graded material; Winkler elastic foundation; in-plane forces;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 Aliaga, J.W. and Reddy, J.N. (2004), "Nonlinear thermoelastic analysis of functionally graded plates using the third-order shear deformation theory", Int. J. Comput. Eng. Sci., 5, 753-779.   DOI
2 Allahverdizadeh, A., Naei, M.H. and Nikkhah Bahrami, M. (2008), "Nonlinear free and forced vibration analysis of thin circular functionally graded plates", J. Sound. Vib., 310(4-5), 966-984.   DOI   ScienceOn
3 Amabili, M. (1997), "Shell-plate interaction in the free surface vibration of circular cylindrical tanks partially filled with a liquid: the artificial spring method", J. Sound. Vib., 199(3), 431-452.   DOI
4 Amabili, M. and Dalpiaz, G. (1998), "Vibrations of base plates in annular cylindrical tanks: theory and experiments", J. Sound. Vib., 210(3), 329-350.   DOI
5 Askari, E. and Daneshmand, F. (2010), "Free vibration of an elastic bottom plate of a partially fluid-filled cylindrical container with an internal body", Eur. J. Mech. A-Solid., 29(1), 68-80.   DOI
6 Chan Il, P. (1992), "Hydroelastic vibration of a cylindrical tank with an elastic bottom, containing liquid. Part I: experiment", J. Fluid. Struct., 313(1-2), 325-333.
7 Chen, W.R., Chen, C.S. and Yu, S.Y. (2011), "Nonlinear vibration of hybrid composite plates on elastic foundations", Struct. Eng. Mech., 37(4), 367-383.   DOI   ScienceOn
8 Chiba, M. (1992), "Nonlinear hydroelastic vibration of a cylindrical tank with an elastic bottom, containing liquid. Part I: Experiment", J. Fluid. Struct., 6(2), 181-206.   DOI
9 Chun-Sheng, C. (2005), "Nonlinear vibration of a shear deformable functionally graded plate", Compos. Struct., 68(3), 295-302.   DOI
10 Ebrahimi, F., Sepiani, H. and Ghorbanpour Arani , A. (2011), Progress in Analysis of Functionally Graded Structures, Nova Science, United States.
11 Ergin, A. and Uğurlu, B. (2004), "Hydroelastic analysis of fluid storage tanks by using a boundary integral equation method", J. Sound. Vib., 275(3-5), 489-513.   DOI
12 Gunaratnam, D.J. and Bhattacharya, A.P. (1985), "Transverse vibration of circular plates having mixed elastic rotational edge restraints and subjected to in-plane forces", J. Sound. Vib., 102(3), 431-439.   DOI
13 Hosseini-Hashemi, S., Rokni Damavandi Taher, H., Akhavan, H. and Omidi, M. (2010), "Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory", Appl. Math. Model., 34(5), 1276-1291.   DOI   ScienceOn
14 Leissa, A.W. (1969), Vibration of Plates, NASA SP 160U.S. Government Printing Office, Washington, DC.
15 Jain, R.K. (1972), "Vibrations of circular plates of variable thickness under an inplane force", J. Sound. Vib., 23(4), 407-414.   DOI
16 Rad, A.B. (2012), "Static response of 2-D functionally graded circular plate with gradient thickness and elastic foundations to compound loads", Struct. Eng. Mech., 44(2), 139-161.   DOI   ScienceOn
17 Jeong, K.H. (2003), "Free vibration of two identical circular plates coupled with bounded fluid", J. Sound. Vib., 260(4), 653-670.   DOI   ScienceOn
18 Kutlu, A., Ugurlu, B., Omurtag, M.H. and Ergin, A. (2012), "Dynamic response of Mindlin plates resting on arbitrarily orthotropic Pasternak foundation and partially in contact with fluid", Ocean Eng., 42, 112-125.   DOI
19 Nie, G.J. and Zhong, Z. (2007), "Semi-analytical solution for three-dimensional vibration of functionally graded circular plates", Comput. Method. Appl. M., 196(49-52), 4901-4910.   DOI   ScienceOn
20 Shen, H.S. (2009), Functionally Graded Materials: Nonlinear Analysis of Plates and Shells, CRC Press, Boca Raton.
21 Yang, J. and Shen, H.S. (2001), "Dynamic response of initially stressed functionally graded rectangular thin plates", Compos. Struct., 54(4), 497-508.   DOI   ScienceOn
22 Zhu, F. (1994), "Rayleigh quotients for coupled free vibrations", J. Sound. Vib., 171(5), 641-649.   DOI   ScienceOn
23 Bouderba., B., Houari., M.S.A. and Tounsi., A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., 14(1), 85-104.   DOI   ScienceOn
24 Ergin, A. and Ugurlu, B. (2003), "Linear vibration analysis of cantilever plates partially submerged in fluid", J. Fluid. Struct., 17(7), 927-939.   DOI   ScienceOn