Host: The Japan Society of Mechanical Engineers
Name : [in Japanese]
Date : October 07, 2017 - October 09, 2017
In the present study, a theoretical analysis of the one dimensional unsteady thermal stress problem is dealt with. The beam has the inhomogeneity in the material properties which are expressed in the form of power of the coordinate variable in the height direction. It is assumed that the inhomogeneous beam is subjected to cyclic heat supply at the upper surface, and the lower one is insulated thermally. Analytical solution of temperature change is derived from the unsteady heat conduction equation for the inhomogeneous beam by means of the Laplace transform and inverse one using the residue theorem. The solution is able to express the temperature change in the beam whose specific heat capacity has inhomogeneity in the form of power with arbitrary real index. Analytical solutions of axial displacement, deflection, and thermal stress resulted from the temperature change are derived from the equations of equilibrium for the inhomogeneous beam under the condition of simple supports. Performing numerical calculation, the effect of the inhomogeneity in the specific heat capacity on the temperature change, axial displacement, deflection, and thermal stress is discussed briefly. As the inhomogeneity parameter in the specific heat capacity increases, the phase lag in the temperature change of the inhomogeneous beam increases, and the temperature amplitude decreases.
