Application of the R-functions in free vibration analysis of FGM plates and shallow shells with temperature dependent properties

The free vibration of plates and shallow shells with/without cutouts made of functionally graded materials (FGM) is investigated using variational FG shallow shells with temperature dependent mechanical characteristics of the constituent materials. First-order shear deformation theory of shallow shells is employed. It is supposed that material properties vary through thickness according to a power-law distribution of the constituent's volume fraction. They depend on both the temperature and the thickness. Temperature field is modeled by one-dimensional heat transfer equation, since the temperature is varied only in thickness direction. Solution of this equation is determined by a polynomial power series expansion. Corresponding software was developed to implement the proposed approach. The vibration analysis was carried out for FG plates and shallow shells with cutout and various boundary conditions.