Influence of the residual elastic-plastic state of a tube on the dynamic characteristics

Abstract

The problem of radial vibrations of the isotropic tube in the presence of a nonuniform field of preliminary stresses (PSs) is considered in this article. It is admitted that the nonzero components of the PS tensor are only the radial and tangential components, which depend only on the radial coordinate. The laws of varying these components, which characterize the residual deformation mode of the tube after active action of the internal pressure, are found. The direct problem on finding the radial component of the field of motion at specified variation laws of components of the PS tensor is solved numerically using the false position method. The influence of the internal pressure level on the first two resonant frequencies for tubes with various thicknesses of the walls made of elastic-plastic and reinforcing material is investigated based on the numerical scheme constructed. When considering the inverse problem on the reconstruction of the internal pressure level and the corresponding radius of the plastic deformation zone, a formula is derived that allows one to evaluate the variation in the resonant frequency depending on various types of the structure and PS level. The exactness of this formula is evaluated by the example of numerical experiments.