Thermo-elastic vibration analysis of third-order shear deformable functionally graded plates with distributed patch mass under thermal environment

Thermo-elastic vibration response of functionally graded (FG) plates carrying distributed patch mass is investigated in this paper based on third order shear deformation theory. The solutions are obtained by energy method. It is assumed that the volume fraction of material constituents varies across the plate thickness according to the power law distribution. Three different types of temperature rise throughout the plate thickness; namely, uniform, linear and nonlinear temperature rises; are used to derive the frequency results. The characteristics of free vibration as influenced by plate thickness ratios, plate aspect ratios, the power law index, material properties and shear deformation are discussed. Some available frequency results associated with FG plates without the patch mass are used to validate the present results. The new frequency results of the functionally graded plates with distributed patch mass are also presented in this paper. The effects of magnitude, size and location of the patch mass on free vibratory frequencies are investigated. In addition, forced vibration analysis with external dynamic load acting on the sub-domain of the patch mass is also presented and discussed.