Dynamic Response of Rapidly Heated Cylindrical Rods: Longitudinal and Flexural Behavior

A very fast temperature increase, produced by a nonuniform heat generation, induces in a simply supported, isotropic, cylindrical rod both longitudinal and flexural vibrations. This paper presents an analytical method to study these vibrations and determine the stresses they provoke. The proposed procedure relies on three main steps: an exact solution for the temperature field is first obtained, by means of Fourier–Bessel expansions; quasistatic thermal stresses are then computed as a function of the calculated temperature distribution, making use of the thermoelastic displacement potential and of the solution to the equivalent isothermal two-dimensional stress problem; finally, longitudinal and flexural vibrations excited by an equivalent thermal force and thermal bending moment are determined using the mode-summation method. The influence of thermal shock duration on the maximum value of the longitudinal dynamic stress and of the ratio between the characteristic thermal time and structural response time on the dynamic bending deflection is analyzed and discussed. Finally, a comparison between the analytical model and experimental measurements is presented. The analytical model described in this paper allows the complete evaluation, within the linear elastic domain, of quasistatic and dynamic thermal stresses induced in an isotropic cylindrical rod by rapid internal heating.