Vibration of a prestressed tube in the presence of plastic zone

Abstract

The paper is devoted to a problem of radial steady state vibrations for a tube taking into account the inhomogeneous residual stress (RS) field. According to the theory of ideal plasticity the RS field is caused by elastoplastic deformation due to the internal pressure and the further unloading process. Various RS distributions inside both elastic and plastic zones are described. A finding of displacement function is reduced to the numerical solving of the first-order differential equations. Within the framework of the acoustical method, the inverse problem for RS field identification is stated. On the basis of the free radial vibration problem for tube, we derived the formula for a dependency of eigenfrequency on RS distribution by using the linearization method. By using this formula for two different values of eigenfrequencies, we state the system of two equations to identify the plasticity zone radius and RS level. Examples of numerical solution of this system for different values of parameters (RS level and tube thickness) are demonstrated. The estimation accuracy of eigenfrequencies measurement for successful implementation of the proposed approach is given.