Some aspects of modeling and identification of inhomogeneous residual stress

Investigations of problems on mechanics of deformable solid body under residual (or initial, or pre-) stress state play a very important part in strength-and-stability assessment and in reconstruction of inhomogeneous properties. The present paper describes different theoretical aspects of modeling of residual stresses (RS). We compare several RS models for the vibrational problems for beams and plates and estimate numerically RS effect on their dynamical characteristics: frequency-response functions and eigenfrequency spectrum. We formulate and investigate the inverse problem on an identification of inhomogeneous plane RS state in a thin plate on the basis of the acoustic method. To solve the inverse problem, we propose two different approaches. We discuss the results of computational experiments on RS identification in detail and provide some practical recommendations on a selection of frequency range in order to obtain the highest reconstruction accuracy.