Inverse problem of non-homogeneous residual stress identification in thin plates

Abstract

Vibration of solid bodies with residual stresses has been attracting attention of researchers from different countries for a long time. Problems of residual stress analysis have its applications in fields of building, mechanical engineering, aircraft construction, biomechanics, manufacturing of composite and functionally-gradient materials. The most common model of residual stresses (or prestresses) is the homogeneous prestress state model; however, in fact the prestress state is often non-homogeneous under natural conditions. One of the most powerful nondestructive methods of reconstruction of non-homogeneous prestress state is the acoustical method.In the present paper the direct problem formulations for 3D bodies and thin plates with non-homogeneous prestress fields are described. A formulation of the inverse problem on a reconstruction of non-homogeneous prestress state is given on the basis of acoustical method. The problem is reduced to the iterative process; at each step of the latter the direct problem and the integral Fredholm equation of the first kind are solved. Two ways of obtaining operator equations of the inverse problem are presented for two oscillation regimes – in-plane and out-of-plane plate vibration modes. Numerical results of solving the inverse problem on a reconstruction of the uniaxial prestress function in case of out-of-plane vibration for a thin rectangular plate are presented. Features and characteristics of the solutions obtained are revealed; the most auspicious conditions for a better quality of the identification procedure are pointed out.