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August 8, 2023
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August 8, 2023
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Abstract

Here, the axisymmetric free flexural vibrations and thermal buckling characteristics of functionally graded spherical caps are investigated employing a three-noded axisymmetric curved shell element based on field consistency approach. The formulation is based on first-order shear deformation theory and it includes the in-plane and rotary inertia effects. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. The effective material properties are evaluated using homogenization method. A detailed numerical study is carried out to bring out the effects of shell geometries, power law index of functional graded material and base radius-to-thickness on the vibrations and buckling characteristics of spherical shells.

Keywords

Functionally graded, Vibration, Spherical shell, Thermal buckling, Power law index

Article Details

How to Cite
Sundararajan, N., & Ganapathi, M. (2023). On the Vibrations and Thermal Buckling of Functionally Graded Spherical Caps. Journal of Aerospace Sciences and Technologies, 59(2), 136–147. https://doi.org/10.61653/joast.v59i2.2007.569
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References

  1. Koizumi, M., "FGM Activities in Japan", Composites Part B, Engineering, 28, 1997, pp.1-4.
  2. Suresh, S. and Mortensen, A., "Fundamentals of Functionally Graded Materials", Institute of Materials, London, 1998.
  3. Fukui, F., "Fundamental Investigation of Function- ally Gradient Material Manufacturing System Using Centrifugal Force", JSME International Journal Series III, 34, 1991, pp.144-48.
  4. Koizumi, M., "The Concept of FGM", Ceramic Transactions Functionally Graded Material, 34, 1993, pp. 3-10.
  5. Yamaoka, H., Yuki, M., Tahara, K., Irisawa, T., Watanabe, R. and Kawasaki, A., "Fabrication of Functionally Gradient Material by Slurry Stacking and Sintering Process", Ceramic Transactions Functionally Gradient Material, 34, 1993, pp.165-72.
  6. Wetherhold, R.C., Seelman, S. and Wang, J.Z., "Use of Functionally Graded Materials to Eliminate or Control Thermal Deformation", Composites Science and Technology, 56, 1996, pp.1099-44.
  7. "Survey for Application of FGM", FGM Forum, Japan Society of Non-Traditional Technology, Dept. of Material Science and Engineering, Tsinghua Uni- versity, Tokyo, 1991.
  8. Praveen, G.N. and Reddy, J.N., "Nonlinear Transient Thermoelastic Analysis of Functionally Graded Ceramic-metal Plates", International Journal of Solids and Structures, 35(33), 1998, pp. 4457-4476.
  9. Wu Lanhe., "Thermal Buckling of a Simply Sup- ported Moderately Thick Rectangular FGM Plate", Composite Structures, 64, 2004, pp. 211-218.
  10. Tauchert, T.R., "Thermally Induced Flexure, Buck- ling and Vibration of Plates", Applied Mechanics Reviews, 44 (8), 1991, pp.347-360.
  11. Ma, L.S. and Wang, T.J., "Nonlinear Bending and Post-buckling of a Functionally Graded Circular Plate Under Mechanical and Thermal Loadings", International Journal of Solids and Structures, 40, 2003, pp.3311-3330.
  12. Yang, J., Kitipornchai, S. and Liew, K.M., "Large Amplitude Vibration of Thermo-electro-mechanically Stressed FGM Laminated Plates", Computer Methods in Applied Mechanics and Engineering, 192, 2003, pp. 3861-3885.
  13. Makino, A., Araki, N., Kitajima, H. and Ohashi. K., "Transient Temperature Response of Functionally Gradient Material Subjected to Partial, Stepwise Heating", Transactions JSME, Part B, 60, 1994, pp.4200-4206.
  14. Obata, Y. and Noda, N., "Steady tHermal Stresses in a Hollow Circular Cylinder and a Hollow Sphere of a Functionally Gradient Material", Journal of Thermal Stresses, 17, 1994, pp.471-487.
  15. Takezono, S., Tao, K., Inamura, E. and Inoue, M., "Thermal Stress and Deformation in Functionally Graded Material Shells of Revolution Under Thermal Loading Due to Fluid", JSME International Series A: Mechanics and Material Engineering, 39, 1994, pp.573-581.
  16. Durodola, J.F. and Adlington, J.E., "Functionally Graded Material Properties for Disks and Rotors", Proc. 1st International Conference on Ceramic and Metal Matrix Composites, San Sebastian, Spain, 1996.
  17. Sang-Yong Oh., Liviu Librescu. and Ohseop Song., "Thin-walled Rotating Blades made of Functionally Graded Materials : Modelling and Vibration Analy- sis", AIAA-2003-1541, 44th AIAA /ASME/ ASCE/AHS/ ASC Structures Structural Dynamics and Ma- terials Conference, Norfolk, Virginia, 2003.
  18. Dao, M., Gu, P., Maeqal, A. and Asaro, R., "A Micro Mechanical Study of a Residual Stress in Function- ally Graded Materials", Acta Materialia, 45, 1997, pp. 3265-3276.
  19. Weisenbek, E., Pettermann, H.E. and Suresh, S., "Elasto-plastic Deformation of Compositionally Graded Metal-ceramic Composites", Acta Materi- alia, 45, 1997, pp.3401-3417.
  20. Li, C., Weng, Z. and Duan, Z., "Dynamic Behavior of a Cylindrical Crack in a Functionally Graded Interlayer under Torsional Loading", International Journal of Solids and Structures, 38, 2001, pp.7473- 7485.
  21. Li, C., Weng, Z. and Duan, Z., "Dynamic Stress Intensity Factor of a Functionally Graded Material with a Finite Crack under Anti-plane Shear Load- ing", Acta Mechanica, 149, 2001, pp.1-10.
  22. Zhang, C., Savaids, A., Savaids, G. and Zhu, H., "Transient Dynamic Analysis of a Cracked Function- ally Graded Material by BIEM", Computational Materials Science, 26, 2003, pp.167-174.
  23. Loy, C.T., Lam, K.Y. and Reddy, J.N., "Vibration of Functionally Graded Cylindrical Shells", International Journal of Mechanical Sciences, 1, 1999, pp.309-324.
  24. Ng, T.Y., Lam, K.Y., Liew, K.M. and Reddy, J.N., "Dynamic Stability Analysis of Functionally Graded Cylindrical Shells Under Periodic Axial Loading", International Journal of Solids and Structures, 38, 2001, pp.1295-1309.
  25. Gangan Prathap. and Ramesh Babu, C., "A Field- Consistent Three-Noded Quadratic Curved Axisym- metric Shell Element", International Journal for Numerical Methods in Engineering, 23, 1986, pp.711-723.
  26. Ganapathi, M., Gupta, S.S. and Patel, B.P., "Non- linear Axisymmetric Dynamic Buckling of Laminated Angle-ply Composite Spherical Caps, Composite Structures, 59, 2003, pp. 89-97.
  27. Mori, T. and Tanaka, K., "Average Stress in Matrix and Average Elastic Energy of Materials with Mis- fitting Inclusions", Acta Metallurgica, 21, 1973, pp.571-574.
  28. Benveniste, Y., "A New Approach to the Application of Mori-Tanaka’s Theory in Composite Materials", Mechanics of Materials, 6, 1987, pp.147-157.
  29. Qian, L.F., Batra, R.C. and Chen, L.M., "Static and Dynamic Deformations of Thick Functionally Graded Elastic Plates by Using Higher-order Shear and Normal Deformable Plate Theory and Meshless local PetrovGalerkin Method", Composites Part B: Engineering, 35, 2004, pp.685-697.
  30. Hatta, H. and Taya, M., "Effective Thermal Conductivity of a Misoriented Short Fiber Composite", Journal of Applied Physics, 58, 1985, pp.2478-2486.
  31. Rosen, B.W. and Hashin, Z., "Effective Thermal Expansion Coefficients and Specific Heats of Composite Materials", International Journal of Engineer- ing Science, 8, 1970, pp.157-173.
  32. Senthil S. Vel. and Batra, R.C., "Three-dimensional Exact Solution for the Vibration of Functionally Graded Rectangular Plates", Journal of Sound and Vibration, 272, 2004, pp.703-730.
  33. Cheng, Z.Q. and Batra, R.C., "Three-dimensional Thermoelastic Deformations of a Functionally Graded Elliptic Plate", Composites Part B : Engineering, 31, 2000, pp.97-106.
  34. Kraus, H., "Thin Elastic Shells", John Wiley New York, 1967.
  35. Zienkiewicz, O.C. and Taylor, R.L., "The Finite Element Method", McGraw-Hill, Singapore, 1989.
  36. Wu Lanhe., "Thermal Buckling of a Simply Sup- ported Moderately Thick Rectangular FGM Plate", Composite Structures, 64, 2004, pp.211-218.
  37. Sathyamoorthy, M., "Vibrations of Moderately Thick Shallow Spherical Shells at Large Amplitudes", Journal of Sound and Vibration, 172, 1994, pp.63-70.
  38. Ganesan, N. and Ravikiran Kadoli., "A Theoretical Analysis of Linear Thermoelastic Buckling of Composite Hemispherical Shells with a Cut-out at the Apex", Composite Structures, 68, 2005, pp.87-101.