Free vibration analysis of FGM spherical and elliptical shells under nonlinear thermal environments

Abstract

The thermo-mechanical effects of the free vibration of functionally graded (FG) spherical and elliptical shells under nonlinear temperature distributions (NTD) are investigated. The geometries of the FG spherical and elliptical shells are expressed in terms of the surface fundamental form, and the displacement function is derived based on higher-order shear deformation theory (HSDT). Temperature-dependent (TD) material and heat conduction are investigated based on Voigt's micromechanical model. The equation of motion of the thermo-elastic FG shells is formulated using the classical Hamilton's principle. Numerical results are obtained using the finite element method with quadrilateral Lagrangian isoparametric elements. A comparison of the results for the free vibration of FG shells based on the FSDT and HSDT approaches is presented. The first fundamental mode is the axisymmetric mode for the circular plate and oblate shell, but the results are otherwise for spherical and prolate shells. The torsional mode occurs in the seventh mode within the first ten vibrational modes for the prolate shell. In addition, the frequency parameter in the torsional mode is independent of the different support conditions. Parametric studies show that the non-dimensional frequency parameters of the FG shells decrease quickly, then slowly, as the volume fraction index increases. Finally, the frequency parameters decrease when the temperature at the top of the FG shell surface increases.