An exact analytical approach for in-plane and out-of-plane free vibration analysis of thick laminated transversely isotropic plates

Archive of Applied Mechanics

Volumn 82, Issue 5, 2012, Pages 677-698

  Hashemi, Sh Hosseini ^a   Atashipour, S R ^a   Fadaee, M ^a  

^a IRAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Iran)

Author keywords

Exact analytical procedure; Free vibration; In plane and out of plane modes; Thick laminated plates; Third order shear deformation theory

Indexed keywords

ANALYTICAL PROCEDURE; FREE VIBRATION; LAMINATED PLATE; OUT-OF-PLANE MODES; THIRD-ORDER SHEAR DEFORMATION THEORY;

APPROXIMATION THEORY; BOUNDARY CONDITIONS; EQUATIONS OF MOTION; SHEAR DEFORMATION; VIBRATION ANALYSIS;

LAMINATING;

EID: 84861823332     PISSN: 09391533     EISSN: 14320681     Source Type: Journal    
DOI: 10.1007/s00419-011-0583-3     Document Type: Article

References (45)

1. Yu, Y.Y.: A new theory of elastic sandwich plates-one dimensional case. J. Appl. Mech. 26, 415-421 (1959)
2. Boal, J.L., Reissner, E.: Three-dimensional theory of elastic plates with transverse inextensibility. J. Math. Phys. 39, 161-181 (1961)
3. Srinivas, S.: A refined analysis of laminated composites. J. Sound Vib. 30, 495-507 (1973)
4. Mindlin, R.D.: Influence rotatory inertia and shear in flexural motion of isotropic, elastic plates. ASME J. Appl. Mech. 18, 31-38 (1951)
5. Mindlin, R.D., Schaknow, A., Deresiewicz, H.: Flexural vibration of rectangular plates. ASME J. Appl. Mech. 23, 430-436 (1956)
6. Selezov, I.T.: Studies of transverse vibrationof plates. Prikl. Mech. 6, 319-327 (1960)
7. Reddy, J.N.: A simple higher-order theory for laminated composite plates. Trans. ASME J. Appl.Mech. 51, 745-752 (1984)
8. Reddy, J.N., Phan, N.D.: Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory. J. Sound Vib. 98, 157-170 (1985)
9. Selezov, I.T.: Some degenerate and generalized wave models in elasto- and hydrodynamics. J. Appl. Maths. Mech. 67, 871-877 (2003)
10. Reddy, J.N.: Free vibration of antisymmetric, angle-ply laminated plates including transverse shear deformation by the finite element method. J. Sound Vib. 66, 565-576 (1979)
11. Reddy, J.N., Kuppusamy, Z.: Natural vibrations of laminated anisotropic plates. J. Sound Vib. 94, 63-69 (1984)
12. Khdeir, A.A.: Free vibration and buckling of unsymmetric cross-ply laminated plates using a refined theory. J. Sound Vib. 128, 377-395 (1989)
13. Kabir, H.R.H., Chaudhuri, R.A.: Free vibration of clamped, moderately thick, arbitrary laminated plates using a generalized Navier's approach. J. Sound Vib. 171, 397-410 (1994)
14. Nosier, A., Reddy, J.N.: On vibration and buckling of symmetric laminated plates according to shear deformation theories Part I. Acta Mech. 94, 123-144 (1992)
15. Nosier, A., Reddy, J.N.: On vibration and buckling of symmetric laminated plates according to shear deformation theories Part II. Acta Mech. 94, 145-169 (1992)
16. Liew, K.M., Huang, Y.Q., Reddy, J.N.: Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method. Comput. Method. Appl. Mech. Eng. 192, 2203-2222 (2003)
17. Kabir, H.R.H.: On free vibration response and mode shapes of arbitrarily laminated rectangular plates. Compos. Struct. 65, 13-27 (2004)
18. Ferreira, A.J.M., Batra, R.C.: Natural frequencies of orthotropic, monoclinic and hexagonal plates by a meshless method. J. Sound Vib. 285, 734-742 (2005)
19. Ferreira, A.J.M., Roque, C.M.C., Jorge, R.M.N., Kansa, E.J.: Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and multiquadrics discretizations. Eng. Anal. Bound. Elem. 29, 1104-1114 (2005)
20. Ferreira, A.J.M., Roque, C.M.C., Jorge, R.M.N.: Free vibration analysis of symmetric laminated composite plates by FSDT and radial basis functions. Comput. Method Appl. Mech. Eng. 194, 4265-4278 (2005)
21. Ferreira, A.J.M., Fasshauer, G.E.: Analysis of natural frequencies of composite plates by an RBF-pseudospectral method. Compos. Struct. 79, 202-210 (2007)
22. Karami, G., Malekzadeh, P., Mohebpour, S.R.: DQM free vibration analysis of moderately thick symmetric laminated plates with elastically restrained edges. Compos. Struct. 74, 115-125 (2006)
23. Viswanathan, K.K., Lee, S.K.: Free vibration of laminated cross-ply plates including shear deformation by spline method. Int. J. Mech. Sci. 49, 352-363 (2007)
24. Viswanathan, K.K., Kim, K.S.: Free vibration of antisymmetric angle-ply-laminated plates including transverse shear deformation: spline method. Int. J. Mech. Sci. 50, 1476-1485 (2008)
25. Van, H.N.,Duy, N.M., Cong, T.T.: Free vibration analysis of laminated plate/shell structures based on FSDTwith a stabilized nodal-integrated quadrilateral element. J. Sound Vib. 313, 205-223 (2008)
26. Malekzadeh, P.: Differential quadrature large amplitude free vibration analysis of laminated skew plates based on FSDT. Compos. Struct. 83, 189-200 (2008)
27. Ferreira, A.J.M., Fasshauer, G.E., Batra, R.C., Rodrigues, J.D.: Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter. Compos. Struct. 86, 328-343 (2008)
28. Liu, G.R., Zhao, X., Dai, K.Y., Zhong, Z.H., Li, G.Y., Han, X.: Static and free vibration analysis of laminated composite plates using the conforming radial point interpolation method. Compos. Sci. Technol. 68, 354-366 (2008)
29. Ferreira, A.J.M., Fasshauer, G.E., Batra, R.C.: Natural frequencies of thick plates made of orthotropic, monoclinic, and hexagonal materials by a meshless method. J. Sound Vib. 319, 984-992 (2009)
30. Moleiro, F., Soares, C.M.M., Soares, C.A.M., Reddy, J.N.: Mixed least-squares finite element models for static and free vibration analysis of laminated composite plates. Comput. Method Appl. Mech. Eng. 198, 1848-1856 (2009)
31. Ferreira, A.J.M., Castro, L.M.S., Bertoluzza, S.: A high order collocation method for the static and vibration analysis of composite plates using a first-order theory. Compos. Struct. 89, 424-432 (2009)
32. Putcha, N.S., Reddy, J.N.: Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory. J. Sound Vib. 104, 285-300 (1986)
33. Shiau, L.C., Wu, T.Y.: A high precision higher order triangular element for free vibration of general laminated plates. J. Sound Vib. 161, 265-279 (1993)
34. Hadian, J., Nayfeh, H.: Free vibration and buckling of shear-deformable cross-ply laminated plates using the state-space concept. Comput. Struct. 48, 677-693 (1993)
35. Wang, W.J., Lin, K.: Free vibration of laminated plates using a finite strip method based on a higher-order plate theory. Comput. Struct. 53, 1281-1289 (1994)
36. Chen, C.C., Kitipornchai, S., Lim, C.W., Liew, K.M.: Free vibration of cantilevered symmetrically laminated thick trapezoidal plates. Int. J. Mech. Sci. 41, 685-702 (1999)
37. Kant, T., Swaminathan, K.: Analytical solutions for free vibration of laminated composite sandwich plates based on a higher-order refined theory. Compos. Struct. 53, 73-85 (2001)
38. Dai, K.Y., Liu, G.R., Lim, K.M., Chen, X.L.: A mesh-free method for static and free vibration analysis of shear deformable laminated composite plates. J. Sound Vib. 269, 633-652 (2004)
39. Matsunaga, H.: Free vibration and stability of angle-ply laminated composite and sandwich plates under thermal loading. Compos. Struct. 77, 249-262 (2007)
40. Alibeigloo, A., Shakeri, M., Kari, M.R.: Free vibration analysis of antisymmetric laminated rectangular plates with distributed patch mass using third-order shear deformation theory. Ocean Eng. 35, 183-190 (2008)
41. Moleiro, F., Soares, C.M.M., Soares, C.A.M., Reddy, J.N.: Mixed least-squares finite element models for static and free vibration analysis of laminated composite plates. Comput. Method Appl. Mech. Eng. 198, 1848-1856 (2009)
42. Thai, H.T., Kim, S.E.: Free vibration of laminated composite plates using two variable refined plate theory. Int. J. Mech. Sci. 52, 626-633 (2010)
43. Srinivas, S., Rao, C.V.J., Rao, A.K.: An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates. J. Sound Vib. 12, 187-199 (1970)
44. Reismann, H., Lee, Y.: Forced motions of rectangular plates. In: Fredrick, D. Developments Theoretical and Applied Mechanics, vol. 4, pp. 3-18. Pergamon Press, New York (1969)
45. Xing,Y.F., Liu, B.: Exact solutions for the free in-plane vibrations of rectangular plates. Int. J. Mech. Sci. 51, 246-255 (2009)