Non-linear vibration of functionally graded shallow spherical shells

Dao Huy Bich, Le Kha Hoa
Author affiliations


  • Dao Huy Bich Vietnam National University, Hanoi
  • Le Kha Hoa Military Logistic Academy



The present paper deals with the non-linear vibration of functionally graded shallow spherical shells. The properties of shell material are graded in the thickness direction according to the power law distribution in terms of volume fractions of the material constituents. In the derived governing equations geometric non-linearity in all strain-displacement relations of the shell is considered. From the deformation compatibility equation and the motion equation a system of partial differential equations for stress function and deflection of shell is obtained. The Galerkin method and Runge-Kutta method are used for dynamical analysis of shells to give expressions of natural frequencies and non-linear dynamic responses. Numerical results show the essential influence of characteristics of functionally graded materials and dimension ratios on the dynamical behaviors of shells.


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How to Cite

D. H. Bich and L. K. Hoa, Non-linear vibration of functionally graded shallow spherical shells, Vietnam J. Mech. 32 (2010) 199–210. DOI:



Research Article

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