Free vibration analysis of four parameter functionally graded plates accounting transverse shear mode


  • Gulshan Taj M. N. A. Indian Institute of Technology Roorkee, India
  • Anupam Chakrabarti Indian Institute of Technology Roorkee, India
  • Mohammad Talha International Institute for Aerospace Engineering and Management, Jain University, India



Functionally graded plate, four parameter law, higher order shear deformation theory, free vibration analysis


In the present investigation, free vibration analysis of functionally graded material (FGM) plate is performed incorporating higher order shear deformation theory in conjunction with C0 based finite element formulation. The cubic component of thickness term is incorporated in in-plane fields and constant variation of thickness is assumed for transverse component. The theory incorporates the realistic parabolic variation of transverse shear stresses thus eliminates the use of shear correction factor. Aluminium/Zirconia plate is considered for the analysis and the effective properties are assumed to have smooth and gradual variation in the thickness direction and remain constant in in-plane direction. The spatial variation of properties pertaining to homogeneous and FGM plate is estimated by means of power law, which is described by the four parameters. With respect to dynamic analysis, it is vital for an analyst to know whether the top of the plate is ceramic or metal rich, and inversely bottom of the plate is ceramic or metal rich. This phenomenon can be described by choosing the appropriate values of the parameters appears in the power law. In the study, prominence has been given to study the influence of power law parameters on frequency response of FGM plates so as to accomplish different combination of FGM profiles. Thin and moderately thick FGM plates are analyzed to generate the frequency values of the FGM plate. The imperative conclusions presented regarding the choice of parameter in the power law could be useful for designer to arrive for particular material profile of FGM plate.


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How to Cite

Taj M. N. A., G., Chakrabarti, A., & Talha, M. (2014). Free vibration analysis of four parameter functionally graded plates accounting transverse shear mode. Vietnam Journal of Mechanics, 36(2), 145–160.



Research Article