Geometrically nonlinear vibrations of FGM shallow shells of an arbitrary planform subjected to thermal environment are investigated with the use of R-functions theory and variational methods. Nonlinear firstorder shear deformation shallow shells are employed. Material properties are assumed to be temperaturedependent and varying along the thickness direction accordingly to Voigt’s law. The developed method is based on the combined applications of R-functions theory, variational Ritz’s method, procedure by Bubnov-Galerkin, and Runge-Kutta’s approach. The effect of the temperature rise, geometry of the shell, and constituent volume fraction index is examined. A comparison of the obtained results with available ones is also carried out for rectangular plates and shallow shells.
