The dynamic characteristics of heated cylinders and plates having temperature gradient across the thickness are investigated here.

In the case of the cylinder the frequency equation is derived taking into account the variation of the modulus of elasticity and Poisson's ratio with temperature. The possibility of existence of a similarity law between the vibration of heated and unheated cylinders is examined. It is shown that similarity between the two cases can be established in a particular case of the unpressurized cylinders with Poisson's ratio assumed constant. For a numerical example a thin Inconel- X cylinder with the outside maintained at room temperature and the inside heated to 1800°F is considered. Frequency spectra and vibration modes are plotted for this particular case for both pressurized and unpressurized cylinders. Reductions in frequencies at this high temperature for various combinations of circumferential nodes and axial wavelengths are also presented.

In Part II the vibration and buckling of heated plates with various boundary conditions is considered. It is shown that the frequency of vibration and buckling loads are related when the plate is subjected, at its edges, to a uniform moment the magnitude of which depends upon the temperature gradient.