Dynamic response of a heat conducting solid bar of polygonal cross sections subjected to moving heat source

The dynamic response of a heat conducting solid bar of polygonal cross section subjected to moving heat source is discussed using the Fourier expansion collocation method (FECM). The equations of motion are formulated using the three dimensional constitutive equation of elasticity and generalized thermo elastic equation composed of linear homogeneous isotropic material. Three displacement potential functions are introduced to uncouple the equations of motion and the heat conduction. The frequency equations are obtained by satisfying the boundary conditions along the surface of the polygonal solid bar using Fourier expansion collocation method. The numerical calculations are carried out for triangular, square, pentagonal and hexagonal cross sectional bars with different moving heat source speeds. Dispersion curves are plotted for longitudinal and flexural (antisymmetric) modes of non dimensional frequency.