Nonlinear vibration analysis of composite laminated trapezoidal plates

- Journal title : Steel and Composite Structures
- Volume 21, Issue 2, 2016, pp.395-409
- Publisher : Techno-Press
- DOI : 10.12989/scs.2016.21.2.395

Title & Authors

Nonlinear vibration analysis of composite laminated trapezoidal plates

Jiang, Guoqing; Li, Fengming; Li, Xinwu;

Jiang, Guoqing; Li, Fengming; Li, Xinwu;

Abstract

Nonlinear vibration characteristics of composite laminated trapezoidal plates are studied. The geometric nonlinearity of the plate based on the von Karman`s large deformation theory is considered, and the finite element method (FEM) is proposed for the present nonlinear modeling. Hamilton`s principle is used to establish the equation of motion of every element, and through assembling entire elements of the trapezoidal plate, the equation of motion of the composite laminated trapezoidal plate is established. The nonlinear static property and nonlinear vibration frequency ratios of the composite laminated rectangular plate are analyzed to verify the validity and correctness of the present methodology by comparing with the results published in the open literatures. Moreover, the effects of the ply angle and the length-high ratio on the nonlinear vibration frequency ratios of the composite laminated trapezoidal plates are discussed, and the frequency-response curves are analyzed for the different ply angles and harmonic excitation forces.

Keywords

composite laminated trapezoidal plates;nonlinear vibration;finite element method;frequency ratios;frequency-response curves;

Language

English

Cited by

References

1.

Alear, R.S. and Rao, N.S. (1973), "Nonlinear analysis of orthotropic skew plates", AIAA Journal, 11(4), 495-498.

2.

Amabili, M. (2004), "Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments", Comput. Struct., 82(31-32), 2587-2605.

3.

Ashour, A.S. (2009), "The free vibration of symmetrically angle-ply laminated fully clamped skew plates", J. Sound Vib., 323(1-2), 444-450.

4.

Bhimaraddi, A. (1993), "Large amplitude vibrations of imperfect antisymmetric angle-ply laminated plates", J. Sound Vib., 162(3), 457-470.

5.

Catania, G. and Sorrentino, S. (2011), "Spectral modeling of vibrating plates with general shape and general boundary conditions", J. Vib. Control, 18(11), 1607-1623.

6.

Civalek, O. (2008), "Free vibration analysis of symmetrically laminated composite plates with first-order shear deformation theory (FSDT) by discrete singular convolution method", Finite Elem. Anal. Des., 44(12-13), 725-731.

7.

Civalek, O. (2009), "A four-node discrete singular convolution for geometric transformation and its application to numerical solution of vibration problem of arbitrary straight-sided quadrilateral plates", Appl. Math. Model., 33(1), 300-314.

8.

Gupta, A.K. and Sharma, S. (2010), "Thermally induced vibration of orthotropic trapezoidal plate of linearly varying thickness", J. Vib. Control, 17(10), 1591-1598.

9.

Gupta, A.K. and Sharma, S. (2013), "Effect of thermal gradient on vibration of non-homogeneous orthotropic trapezoidal plate of linearly varying thickness", Ain Shams Eng. J., 4(3), 523-530.

10.

Gurses, M., Civalek, O., Ersoy, H. and Kiracioglu, O. (2009), "Analysis of shear deformable laminated composite trapezoidal plates", Mater. Des., 30(8), 3030-3035.

11.

Houmat, A. (2015), "Nonlinear free vibration analysis of variable stiffness symmetric skew laminates", Euro. J. Mech. A/Solids, 50, 70-75.

12.

Jaberzadeh, E., Azhari, M. and Boroomand, B. (2013), "Thermal buckling of functionally graded skew and trapezoidal plates with different boundary conditions using the element-free Galerkin method", Euro. J. Mech. A/Solids, 42, 18-26.

13.

Karami, G., Shahpari, S.A. and Malekzadeh, P. (2003), "DQM analysis of skewed and trapezoidal laminated plates", Compos. Struct., 59(3), 393-402.

14.

Li, F.M. and Song, Z.G. (2013), "Flutter and thermal buckling control for composite laminated panels in supersonic flow", J. Sound Vib., 332(22), 5678-5695.

15.

Malekzadeh, P. (2007), "A differential quadrature nonlinear free vibration analysis of laminated composite skew thin plates", Thin-Wall. Struct., 45(2), 237-250.

16.

Malekzadeh, P. (2008), "Differential quadrature large amplitude free vibration analysis of laminated skew plates based on FSDT", Compos. Struct., 83(2), 189-200.

17.

Mei, C. and Decha-Umphai, K. (1985), "A finite element method for nonlinear forced vibrations of rectangular plates", AIAA Journal, 23(7), 1104-1110.

18.

Quintana, M.V. and Nallim, L.G. (2013), "A general Ritz formulation for the free vibration analysis of thick trapezoidal and triangular laminated plates resting on elastic supports", Int. J. Mech. Sci., 69, 1-9.

19.

Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells-Theory and Analysis, CRC Press.

20.

Reddy, J.N. and Kuppusamy, T. (1984), "Natural vibrations of laminated anisotropic plates", J. Sound Vib., 94(1), 63-69.

21.

Saha, K.N., Misra, D., Ghosal, S. and Pohit, G. (2005), "Nonlinear free vibration analysis of square plates with various boundary conditions", J. Sound Vib., 287(4-5), 1031-1044.

22.

Shufrin, I., Rabinovitch, O. and Eisenberger, E. (2010), "A semi-analytical approach for the geometrically nonlinear analysis of trapezoidal plates", Int. J. Mech. Sci., 52(12), 1588-1596.

23.

Singha, M.K. and Daripa, R. (2007), "Nonlinear vibration of symmetrically laminated composite skew plates by finite element method", Int. J. Non-Linear Mech., 42(9), 1144-1152.

24.

Singha, N.K. and Ganapathi, M. (2004), "Large amplitude free flexural vibrations of laminated composite skew plates", Int. J. Non-Linear Mech., 39(10), 1709-1720.

25.

Taj, G. and Chakrabarti, A. (2013), "Static and dynamic analysis of functionally graded skew plates", J. Eng. Mech., 139(7), 848-857.

26.

Tubaldi, E., Alijani, F. and Amabili, M. (2014), "Non-linear vibrations and stability of a periodically supported rectangular plate in axial flow", Int. J. Non-Linear Mech., 66, 54-65.

27.

Wang, X., Wang, Y.L. and Yuan, Z.X. (2014), "Accurate vibration analysis of skew plates by the new version of the differential quadrature method", Appl. Math. Model., 38(3), 926-937.

28.

Yao, G. and Li, F.M. (2013), "Chaotic motion of a composite laminated plate with geometric nonlinearity in subsonic flow", Int. J. Non-Linear Mech., 50, 81-90.

29.

Zamani, M., Fallah, A. and Aghdam, M.M. (2012), "Free vibration analysis of moderately thick trapezoidal symmetrically laminated plates with various combinations of boundary conditions", Euro. J. Mech. A/Solids, 36, 204-212.

30.

Zhang, L.W., Lei, Z.X. and Liew, K.M. (2015), "Buckling analysis of FG-CNT reinforced composite thick skew plates using an element-free approach", Compos. Part B, 75, 36-46.