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Submitted
August 9, 2023
Published
August 9, 2023
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Abstract

The nonlinear formulation developed based on von Karman’s assumptions is employed to study the large free flexural vibration characteristics of functionally graded material (FGM) plates subjected to thermal environment. Temperature distribution is uniform 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. The nonlinear governing equations obtained using Lagrange’s equations of motion are solved using finite element procedure coupled with the direct iteration technique. The variation of nonlinear frequency ratio with amplitude is highlighted considering various parameters such as gradient index, temperature, thickness and aspect ratios, skew angle and boundary condition. For the numerical illustrations, silicon nitride/stainless steel is considered as functionally graded material. The results obtained here reveal that the temperature field and gradient index have significant effect on the large amplitude free flexural vibration of the functionally graded plate.

Keywords

Functionally Graded Plate, Large Amplitude Free Flexural Vibration, Aspect Ratio, Temperature, Gradient Index.

Article Details

How to Cite
Ganapathi, M., Prakash, T., Sundararajan, N., & Singha, M. K. (2023). Large Amplitude Free Flexural Vibrations of Functionally Graded Plates. Journal of Aerospace Sciences and Technologies, 58(1), 50–64. https://doi.org/10.61653/joast.v58i1.2006.669
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References

  1. Koizumi, M., "FGM Activities in Japan", Composites, 28 (1-2), 1997, pp.1-4.
  2. Koizumi, M., "The Concept of FGM", Ceram. Trans., Functionally Graded Material, 34, 1993, pp.3-10.
  3. Suresh, S. and Mortensen, A., "Functionally Graded Metals and Metal-ceramic Composites - Part 2. Thermomechanical Behavior", Int Mater Rev, 42, 1997, pp.85-116.
  4. Pindera, M.J., Arnold, S.M., Aboudi, J. and Hui, D., "Use of Composites in Functionally Graded Materials", Composites Engg, 4 (1), 1994, pp.1-145.
  5. Tangiawa, Y., Akai, T., Kawamura, R. and Oka, N., "Transient Heat Conduction and Thermal Stress Problems of a Nonhomogeneous Plate with Temperaturedependent Material Properties", J. Thermal Stresses, 19, 1996, pp.77-102.
  6. Reddy, J.N. and Chin, C.D., "Thermomechanical Analysis of Functionally Graded Cylinders and Plates", J. Thermal Stresses, 21, 1998, pp.593-629.
  7. Senthil S. Vel and Batra, R.C., "Three-dimensional Analysis of Transient Thermal Stresses in Functionally Graded Plates", IJSS, 40, 2003, pp.7181-7196.
  8. He, X.Q., Ng, T.Y., Sivashankar, S. and Liew, K.M., "Active Control of FGM Plates with Integrated Piezoelectric Sensors and Actuators", IJSS, 38, 2001, pp.1641-1655.
  9. Liew, K.M., He, X.Q., Ng, T.Y. and Sivashankar, S., "Active Control of FGM Plates Subjected to a Temperature Gradient : Modeling via Finite Element Method Based on FSDT", IJNME, 52, 2001, pp.1253-1271.
  10. Ng, T.Y., Lam, K.Y. and Liew, K.M., "Effect of FGM Materials on Parametric Response of Plate Structures", Comput. Methods Appl. Mech. Engg, 190, 2000, pp.953-962.
  11. Yang, J. and Hui-Shen Shen, "Dynamic Response of Initially Stressed Functionally Graded Rectangular Thin Plates", Composite Structures, 54, 2001, pp.497-508.
  12. Yang, J. and Shen, H.-S., "Vibration Characteristic and Transient Response of Shear-deformable Functionally Graded Plates in Thermal Environments", Journal of Sound and Vibration, 255, 2002, pp.579602.
  13. Cheng, Z.-Q. and Batra, R.C., "Three Dimensional Thermoelastic Deformations of a Functionally Graded Elliptic Plate", Composites Part B: Engineering, 31 (2), 2000, pp.97-106.
  14. Leslie Banks Sills., Rami Eliaso. and Yuri Berlin., "Modeling of Functionally Graded Materials in Dynamic Analyses", Composites: Part-B, 33, 2002, pp.7-15.
  15. Leissa, A.W., "Plate Vibration Research 1976-1980: Complicating Factors", Shock Vib. Digest, 13, 1981, pp.19-36.
  16. Sathyamoorthy, M., "Nonlinear Vibration Analysis of Plates: a Review and Survey of Current Development", ASME Appl. Mech. Rev., 40, 1987, pp.15531561.
  17. Kapania, R.K. and Racita, S., "Recent Advances in Analysis of Laminated Beams and Plates - Part II: Vibration and Wave Propagation", AIAA, 27, 1989, pp.935-946.
  18. Chia, C.Y., "Geometric Nonlinear Behavior of Composite Plates: A Review", ASME Applied Mech. Rev., 41, 1988, pp.439-451.
  19. Sathyamoorthy, M., "Nonlinear Analysis of Structures", CRC Press, Boca Raton, 1997.
  20. Praveen, G.N. and Reddy, J.N., "Nonlinear Transient Thermoelstic Analysis of Functionally Graded Ceramicmetal Plates", Int. J. Solids Struct, 35, 1998, pp.4457-4476.
  21. Kitipornchai, S., Liew, K.M. and Yang, J., "Large Amplitude Vibration of Thermo-electro-Mechanically Stresses FGM Laminated Plates", Comput. Methods Appl. Mech and Engg, 192, 2003, pp.38613885.
  22. Xiao-Lin Huang and Hui-Shen Shen, "Nonlinear Vibration and Dynamic Response of Functionally Graded Plates in Thermal Environments", Int. J. Solids Struct, 41, 2004, pp.2403-2427.
  23. Prathap, G., Naganarayana, B.P. and Somashekar, B.R., "A Field Consistency Analysis of the Isoparametric Eight-noded Plate Bending Elements", Comput. Struct., 29, 1988, pp.857-874.
  24. Ganapathi, M., Varadan, T.K. and Sarma, B.S., "Nonlinear Flexural Vibrations of Laminated Orthotropic plates", Comput. Struct. , 39, 1991, pp.685-688.
  25. Lanhe Wu., "Thermal Buckling of a Simply Supported Moderately Thick Rectangular FGM Plate", Composite Struct, 64, 2004, pp.211-218.
  26. Rajasekaran, S. and Murray, D. W., "Incremental Finite Element Matrices", ASCE Journal of Structures Division, 99, 1973, pp.2423-2438.
  27. Makhecha, D.P., Patel, B.P. and Ganapathi, M., "Transient Dynamics of Thick Skew Sandwich Laminates under Thermal/Mechanical Loads", J. Reinforces Plastics and Composites, 20, 2001, pp.1524-1545.
  28. Bergan, P.G. and Clough, R.W., "Convergence Criteria of Iteration Process", J. AIAA, 10, 1972, pp.1107-1108.
  29. Prakash, T. and Ganapathi, M., "Supersonic Flutter Characteristics of Functionally Graded Flat Panels including Thermal Effects", Composite Structures (In communication).
  30. Chu, H.N. and Herrmann, G., "Influence of Large Amplitudes on Free Flexural Vibrations of Rectangular Plates", J. Appl. Mech., 23, 1956, pp.532-540.

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