Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear vibration analysis of composite laminated trapezoidal plates

  • Jiang, Guoqing (Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology) ;
  • Li, Fengming (Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology) ;
  • Li, Xinwu (Hong Du Aviation Industry Group)
  • Received : 2015.07.05
  • Accepted : 2016.04.07
  • Published : 2016.06.10
⟨ Previous Next ⟩

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

Acknowledgement

Supported by : National Natural Science Foundation of China

References

  1. Alear, R.S. and Rao, N.S. (1973), "Nonlinear analysis of orthotropic skew plates", AIAA Journal, 11(4), 495-498. https://doi.org/10.2514/3.6777
  2. Amabili, M. (2004), "Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments", Comput. Struct., 82(31-32), 2587-2605. https://doi.org/10.1016/j.compstruc.2004.03.077
  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. https://doi.org/10.1016/j.jsv.2008.12.027
  4. Bhimaraddi, A. (1993), "Large amplitude vibrations of imperfect antisymmetric angle-ply laminated plates", J. Sound Vib., 162(3), 457-470. https://doi.org/10.1006/jsvi.1993.1133
  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. https://doi.org/10.1177/1077546311426593
  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. https://doi.org/10.1016/j.finel.2008.04.001
  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. https://doi.org/10.1016/j.apm.2007.11.003
  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. https://doi.org/10.1177/1077546310384641
  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. https://doi.org/10.1016/j.asej.2012.10.012
  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. https://doi.org/10.1016/j.matdes.2008.12.016
  11. Houmat, A. (2015), "Nonlinear free vibration analysis of variable stiffness symmetric skew laminates", Euro. J. Mech. A/Solids, 50, 70-75. https://doi.org/10.1016/j.euromechsol.2014.10.008
  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. https://doi.org/10.1016/j.euromechsol.2013.03.006
  13. Karami, G., Shahpari, S.A. and Malekzadeh, P. (2003), "DQM analysis of skewed and trapezoidal laminated plates", Compos. Struct., 59(3), 393-402. https://doi.org/10.1016/S0263-8223(02)00188-5
  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. https://doi.org/10.1016/j.jsv.2013.05.032
  15. Malekzadeh, P. (2007), "A differential quadrature nonlinear free vibration analysis of laminated composite skew thin plates", Thin-Wall. Struct., 45(2), 237-250. https://doi.org/10.1016/j.tws.2007.01.011
  16. Malekzadeh, P. (2008), "Differential quadrature large amplitude free vibration analysis of laminated skew plates based on FSDT", Compos. Struct., 83(2), 189-200. https://doi.org/10.1016/j.compstruct.2007.04.007
  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. https://doi.org/10.2514/3.9044
  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. https://doi.org/10.1016/j.ijmecsci.2012.12.016
  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. https://doi.org/10.1016/S0022-460X(84)80005-X
  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. https://doi.org/10.1016/j.jsv.2005.03.003
  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. https://doi.org/10.1016/j.ijmecsci.2010.07.008
  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. https://doi.org/10.1016/j.ijnonlinmec.2007.08.001
  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. https://doi.org/10.1016/j.ijnonlinmec.2004.04.003
  25. Taj, G. and Chakrabarti, A. (2013), "Static and dynamic analysis of functionally graded skew plates", J. Eng. Mech., 139(7), 848-857. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000523
  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. https://doi.org/10.1016/j.ijnonlinmec.2013.12.004
  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. https://doi.org/10.1016/j.apm.2013.07.021
  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. https://doi.org/10.1016/j.ijnonlinmec.2012.11.010
  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. https://doi.org/10.1016/j.euromechsol.2012.03.004
  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.

Cited by

  1. Large amplitude free flexural vibration of arbitrary thin plates using superparametric element vol.5, pp.4, 2017, https://doi.org/10.1007/s40435-016-0275-5
  2. An Optimized Approach for Tracing Pre- and Post-Buckling Equilibrium Paths of Space Trusses pp.1793-6764, 2018, https://doi.org/10.1142/S0219455419500408
  3. Nonlinear vibration study of fiber-reinforced composite thin plate with strain-dependent property based on strain energy density function method pp.1537-6532, 2019, https://doi.org/10.1080/15376494.2018.1495792
  4. Geometrically nonlinear bending of functionally graded nanocomposite trapezoidal plates reinforced with graphene platelets (GPLs) pp.1573-8841, 2019, https://doi.org/10.1007/s10999-019-09442-4
  5. Nonlinear vibration of laminated composite plates subjected to subsonic flow and external loads vol.22, pp.6, 2016, https://doi.org/10.12989/scs.2016.22.6.1261
  6. A dual approach to perform geometrically nonlinear analysis of plane truss structures vol.27, pp.1, 2018, https://doi.org/10.12989/scs.2018.27.1.013
  7. Combined effects of end-shortening strain, lateral pressure load and initial imperfection on ultimate strength of laminates: nonlinear plate theory vol.33, pp.2, 2016, https://doi.org/10.12989/scs.2019.33.2.245
  8. Bending analysis of the multi-phase nanocomposite reinforced circular plate via 3D-elasticity theory vol.40, pp.4, 2021, https://doi.org/10.12989/scs.2021.40.4.601