On identification of prestress level in elastic bodies

The paper presents a brief overview of the problem of prestress research. Based on the general statement of the problem within the framework of linearized model of a prestressed object, the problem of free planar vibrations of a rectangular elastic region in the presence of an inhomogeneous prestressing field is formulated. To consider the general case of preloads, the numerical solution of the problem is obtained using the finite element method. The FlexPDE package is chosen as the software environment in which this method is implemented. Its main advantages are noted, which makes it possible to carry out the numerical simulation of various types of preloads. Four types of prestressed state are considered as concrete examples. The results of calculations of the first four natural oscillation frequencies are presented. Using the capabilities of the package, the example of one of the types of preloads shows the difference in displacement fields corresponding to the free vibrations of an object in the presence and absence of prestresses. On the basis of the general formulation of the problem, taking into account the assumption of the smallness of the influence of residual stresses on the displacement fields of the object, a generalized relation is formulated. Using the relation, an approximate formula is obtained for calculating the level of prestresses from the data on the natural frequencies of the object in the presence and absence of prestresses and a displacement field corresponding to the natural form of oscillations of a body free from preloads. Also, on the basis of this relation, an approximate formula is derived to determine the frequency of free vibrations of a prestressed body according to the data on the natural frequency and vibration mode of a body in which there are no residual stresses. For the first natural frequency and vibration mode, a series of computational experiments demonstrating the accuracy of the obtained formulas for the rectangular area under consideration was carried out at several types of preloads. An assessment of the possibility of using the results in practice is given.