Structural Engineering and Mechanics

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Dynamic instability of functionally graded material plates subjected to aero-thermo-mechanical loads

  • Prakash, T. (Department of Applied Mechanics, Indian Institute of Technology Delhi) ;
  • Ganapathi, M. (FEA Group, Institute of Armament Technology)
  • Received : 2004.10.21
  • Accepted : 2005.04.15
  • Published : 2005.07.10
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Abstract

Here, the dynamic instability characteristics of aero-thermo-mechanically stressed functionally graded plates are investigated using finite element procedure. Temperature field is assumed to be a uniform distribution over the plate surface and varied in thickness direction only. Material properties are assumed to be temperature dependent and graded in the thickness direction according to simple power law distribution. For the numerical illustrations, silicon nitride/stainless steel is considered as functionally graded material. The aerodynamic pressure is evaluated based on first-order high Mach number approximation to the linear potential flow theory. The boundaries of the instability region are obtained using the principle of Bolotin's method and are conveniently represented in the non-dimensional excitation frequency-load amplitude plane. The variation dynamic instability width is highlighted considering various parameters such as gradient index, temperature, aerodynamic and mechanical loads, thickness and aspect ratios, and boundary condition.

Keywords

References

  1. Ashley, H. and Zartarian, G. (1956), 'Piston theory - a new aerodynamic tool for the aeroelastician', J. Aeronaut Sci., 12, 11 09-1118
  2. Birman, V. and Librescu, L. (1990), 'Supersonic flutter of sheardeformation laminated flat panel', J. Sound Vib., 139, 265-275 https://doi.org/10.1016/0022-460X(90)90887-6
  3. Bolotin, V.V. (1964), The Dynamic Stability of Elastic Systems, Holden-Day, San Francisco
  4. Cheng, Z.Q. and Batra, R.C. (2000), 'Three dimensional thermoelastic deformations of a functionally graded elliptic plate', Compos. Part B: Engg., 31,97-106 https://doi.org/10.1016/S1359-8368(99)00069-4
  5. Dixon, S.C. (1966), 'Comparison of panel flutter results from approximate aerodynamic theory with results from exact theory and experiment', NASA TN D-3649
  6. Evan-Iwanowski, R.M. (1965), 'On the parametric response of structures', Appl. Mech. Rev., 18, 699-702
  7. Feldman, E. and Aboudi, J. (1997), 'Buckling analysis of functionally graded plates subjected to thermal loading', Compos. Struct., 38, 29-36 https://doi.org/10.1016/S0263-8223(97)00038-X
  8. Ganapathi, M., Varadan, T.K and Sarma, B.S. (1991), 'Nonlinear flexural vibrations of laminated orthotropic plates', Comput. Struct., 39, 685-688 https://doi.org/10.1016/0045-7949(91)90211-4
  9. He, X.Q., Ng, T.Y, Sivashankar, S. and Liew, K.M. (2001), 'Active control of FGM plates with integrated piezoelectric sensors and actuators', Int. J. Solids Struct., 38, 1641-1655 https://doi.org/10.1016/S0020-7683(00)00050-0
  10. Huang, X.L. and Shen, H.S. (2004), 'Nonlinear vibration and dynamic response of functionally graded plates in thermal environments', Int. J. Solids Struct., 41, 2403-2427 https://doi.org/10.1016/j.ijsolstr.2003.11.012
  11. Koizumi, M. (1993), 'The concept of FGM', Ceram. Trans Functionally Graded Material, 34, 3-10
  12. Koizumi, M. (1997), 'FGM activities in Japan', Composites, 28, 1-4
  13. Liew, K.M., He, X.Q., Ng, T.Y and Sivashankar, S. (2001), 'Active control of FGM plates subjected to a temperature gradient: Modeling via finite element method based on FSDT', Int. J. Numer. Methods Engg., 52,1253-1271 https://doi.org/10.1002/nme.252
  14. Ma, L.S. and Wang, T.J (2003), 'Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings', Int. J. Solids Struct., 40, 3311-3330 https://doi.org/10.1016/S0020-7683(03)00118-5
  15. Najafizadeh, M.M. and Eslami, M.R (2002), 'First order theory based thermoelastic stability of functionally graded materials circular plates', AIAA J, 40, 1444-1450 https://doi.org/10.2514/2.1807
  16. Ng, T.Y, Lam, K.Y and Liew, K.M. (2000), 'Effect of FGM materials on parametric response of plate structures', Comput. Methods Appl. Mech. Engg., 190, 953-962 https://doi.org/10.1016/S0045-7825(99)00455-7
  17. Patel, B.P., Ganapathi, M., Prasad, K.R and Balamurugan, V. (1999), 'Dynamic instability of layered anisotropic composite plates on elastic foundations', Engg. Struct., 21, 988-995 https://doi.org/10.1016/S0141-0296(98)00063-7
  18. Pindera, M.J., Arnold, S.M., Aboudi, J. and Hui, D. (1994), 'Use of composites in functionally graded materials', Compos. Engng., 4, 1-145 https://doi.org/10.1016/0961-9526(94)90003-5
  19. Prathap, G, Naganarayana, B.P. and Somashekar, B.R (1988), 'A field consistency analysis of the isoparametric eight-noded plate bending elements', Comput. Struct., 29, 857-874 https://doi.org/10.1016/0045-7949(88)90354-9
  20. Praveen, G.N. and Reddy, J.N. (1998), 'Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates', Int. J. Solids Struct., 35, 4457-4476 https://doi.org/10.1016/S0020-7683(97)00253-9
  21. Reddy, J.N. and Chin, C.D. (1998), 'Thermomechanical analysis of functionally graded cylinders and plates', J. Therm. Stresses, 21, 593-629 https://doi.org/10.1080/01495739808956165
  22. Senthil, S. Vel and Batra, R.C. (2003), 'Three-dimensional analysis of transient thermal stresses in functionally graded plates', Int. J. Solids Struct., 40, 7181-7196 https://doi.org/10.1016/S0020-7683(03)00361-5
  23. Sills, L.B., Eliaso, R. and Berlin, Y (2002), 'Modeling of functionally graded materials in dynamic analyses', Compos. Part B: Engg., 33, 7-15 https://doi.org/10.1016/S1359-8368(01)00057-9
  24. Suresh, S. and Mortensen, A. (1997), 'Functionally graded metals and metal-ceramic Composites - Part 2. Thermomechanical behavior', Int. Mater. Rev., 42, 85-1I6 https://doi.org/10.1179/095066097790093217
  25. Tangiawa, Y, Akai, T., Kawamura, R and aka, N. (1996), 'Transient heat conduction and thermal stress problems of a nonhomogeneous plate with temperature-dependent material properties', J. Therm. Stresses, 19, 77-102 https://doi.org/10.1080/01495739608946161
  26. Wu, L. (2004), 'Thermal buckling of a simply supported moderately thick rectangular FGM plate', Compos. Struct., 64, 211-218 https://doi.org/10.1016/j.compstruct.2003.08.004
  27. Yang, J. and Shen, H.S. (2001), 'Dynamic response of initially stressed functionally graded rectangular thin plates', Compos. Struct., 54, 497-508 https://doi.org/10.1016/S0263-8223(01)00122-2
  28. Yang, J. and Shen, H.S. (2002), 'Vibration characteristic and transient response of shear-deformable functionally graded plates in thermal environments', J. Sound Vib., 255, 579-602 https://doi.org/10.1006/jsvi.2001.4161

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