Oscillations of beams in tension under creep conditions
The paper is devoted to the approach and analytical methods of predicting changes in the eigen oscillations of beams under the conditions of longitudinal tension during creep. On the basis of the classical equation of oscillations of beams under tension, a method for estimating eigen frequencies that can vary during creep is obtained. Expressions for the longitudinal force, which depends on the physical and mechanical parameters of the material, were obtained. A relationship was found for determining the time of significant influence of creep on the eigen frequencies. With the help of the obtained expression for the value of the time to fracture of the beam using the Kachanov continuity parameter, an approach to determining the influence on the frequency of the hidden damage accumulation process is proposed. The case of large deflections of the beam is considered in a geometrically nonlinear statement using the method of many scales with the expansion of the solution by a small parameter. The processes of dynamic creep are considered, in which the acceleration of the rate of creep strains in the material is provided by the contribution of amplitude stresses. The resulting equation is solved by the method of weighted residuals in the Galerkin form. Dependencies for determining the rate of stress relaxation in the beam during creep were obtained. The limiting values of the compressive force in terms of the loss of stability of the beam under the given conditions of creep and oscillations are estimated. Computational modeling was performed and results were obtained that allow determining the sensitivity of the eigen oscillation frequencies of beams made of different structural materials to tensile creep. Heat-resistant alloys, alloyed steels, titanium, aluminum alloys and tin-lead solder at temperatures inherent in the typical operating conditions of structural elements made from them are considered. It is shown that the smallest effect of creep on eigen frequencies is found for light alloys. With the help of the obtained ratios, the frequencies of nonlinear oscillations that can occur in the beams were analyzed, and a skeletal curve was built.
Key words: Oscillations, eigen frequencies, creep, beam, tension, bending.