Browse > Article
http://dx.doi.org/10.12989/sem.2006.23.2.115

Exact solutions of axisymmetric free vibration of transversely isotropic magnetoelectroelastic laminated circular plates  

Chen, Jiangying (Faculty of Engineering, Ningbo University, Ningbo Institute of Technology, Zhejiang University)
Xu, Rongqiao (Department of Civil Engineering, Zhejiang University)
Huang, Xusheng (Faculty of Engineering, Ningbo University)
Ding, Haojiang (Department of Civil Engineering, Zhejiang University)
Publication Information
Structural Engineering and Mechanics / v.23, no.2, 2006 , pp. 115-127 More about this Journal
Abstract
The axisymmetric free vibrations of transversely isotropic magnetoelectroelastic laminated circular plates are studied. Based on the three-dimensional governing equations of magnetoelectroelastic medium, the state space equations of laminated circular plates are obtained. By using the finite Hankel transform and rendering the free terms left by the transform in terms of the boundary quantities, the solutions of the state space equations are given for two kinds of boundary conditions. The frequency equations of the free vibration are derived using the propagator matrix method and the boundary conditions at top and bottom surfaces. By virtue of the inverse Hankel transform, the mode shapes are also determined. Since the solutions strictly satisfy the governing equations in the region and the boundary conditions at the edges, they are the three-dimensionally exact. Finally, the natural frequencies of such plates are tabulated and compared with those of the piezoelectric and elastic plates in the numerical example.
Keywords
magnetoelectroelastic medium; laminated circular plates; free vibration; state space method;
Citations & Related Records

Times Cited By Web Of Science : 9  (Related Records In Web of Science)
Times Cited By SCOPUS : 3
연도 인용수 순위
1 Celep, Z. (1978), ' On the axially symmetric vibration of thick circular plate ', Ingenieus-Archive, 47(6), 411-420   DOI
2 Celep, Z. (1980),' Free vibration of some circular plates of arbitrary thickness ', J. Sound Vib., 70(3), 379-388   DOI   ScienceOn
3 Chen, J.Y., Ding, H.J. and Hou, P.F. (2003a), ' Analytical solutions of simply supported magnetoelectroelastic circular plate under uniform loads' , J. of Zhejiang University Science, 4(5), 560-564   DOI
4 Chen, J.Y., Ding, H.J. and Hou, P.F. (2003b), ' Three-dimensional analysis of magnetoelectroelastic rotating annualr plate' , J. of Zhejiang University (Engineering Science), 37(4),440-444
5 Chen, W.Q. and Lee, K.Y. (2003), ' Alternative state space formulations for magnetoelectric thermoelasticity with transverse isotropy and the application to bending analysis of nonhomogeneous plates ', Int. J. Solids Struct., 40, 5689-5705   DOI   ScienceOn
6 Deresiewicz, H. (1956), ' Symmetric flexural vibrations of a clamped circular disk' , J. Appl. Mech., 23(2), 319
7 Deresiewicz, H. and Mindlin, R.D. (1955),' Axially symmetric flexural vibrations of a circular disk ', J. Appl. Mech., 22(1), 86-88
8 Iyengar, K.T.S.R. and Raman, P.Y. (1977), ' Free vibration of rectangular plates of arbitrary thickness ', J .Sound Vib., 54(2), 229-236   DOI   ScienceOn
9 Iyengar, K.T.S.R. and Raman, P.Y. (1978), ' Free vibration of circular plates of arbitrary thickness ', The J. of the Acoustical Society of America, 64(4), 1088-1092   DOI   ScienceOn
10 Kane, T.R. and Mindlin, D. (1956), ' High-frequency extensional vibration of plates ', J. Appl. Mech., 23(2), 277-283
11 Li, J.Y. (2000), ' Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials ', Int. J. Eng. Sci., 38(18),1993-2011   DOI   ScienceOn
12 Mindlin, R.D. (1951a), ' Influence of rotatory inertia and shear on flexural motions of isotropic, elasticplate ', J. Appl. Mech., 18(1), 31-38
13 Mindlin, R.D. and Deresiewicz, H. (1954), ' Thickness-shear and flexural vibration of a circular disk ', J. Appl.Phy., 25(10), 1329-1332   DOI
14 Pan, E. and Heyliger, P.R. (2002),' Free vibrations of simply supported and multilayered magneto-electro-elastic plates ', J .Sound Vib., 252(3), 429-442   DOI   ScienceOn
15 Wang, J.G, Chen, L.F. and Fang, S.S. (2003),' State vector approach to analysis of multilayered magnetoelectro- elastic plates ', Int. J .Solids Struct., 40, 1669-1680   DOI   ScienceOn
16 Rao, N.S.Y.K. and Das, Y.C. (1977),' A mixed method in elasticity ', J. Appl. Mech., 44(1), 51-56   DOI
17 Sneddon, I.N. (1970), Fourier Transform. McGraw-HilI, NewYork. 3rd Edition
18 Timoshenko, S. and Goodier, J.N. (1951), Theory of Elasticity, McGraw-Hill, NewYork. 3rd Edition.
19 Chen, W.Q., Lee, K.Y. and Ding, H.J. (2005), ' On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates' , J. Sound Vib., 279(1-2), 237-251   DOI   ScienceOn
20 Ding, H.J., Xu, R.Q., Chi, Y.W and Chen, W.Q. (1999), ' Free axisymmetric vibration of transversely isotropic piezoelectric circular plates' , Int. J. Solids Struct., 36(30), 4629-4652   DOI   ScienceOn
21 Mindlin, R.D. (1951 b), ' Thickness-shear and flexural vibrations of crystal plates ', J .Appl. Phy., 22(3), 316-323   DOI
22 Pan, E. (2001), ' Exact solution for simply supported and multilayered magneto-electro-elastic plates ', J .Appl.Mech., ASME, 68, 608-618   DOI   ScienceOn
23 Pan, E. and Heyliger, P.R. (2003), ' Exact solutions for magneto-electro-elastic laminates in cylindrical bending ', Int. J. Solids Struct., 40(24), 6859-6876   DOI   ScienceOn