On the residual stress definition in the round plate

Abstract

The inverse coefficient problem of the initial stress definition in the oscillating round elastic plate is considered. The plate vibration is axisymmetric and it's forced by the homogeneous oscillating load. The information about plate deflection on some fixed frequency serves as input data. Two methods for the direct problem solving are introduced. The first method is based on the shooting method. The second is based on Ritz method and reduces the problem to the linear equations system. Results of the direct problem solution are presented for different distribution laws of the initial stresses. Boundary problems both for simply supported and for the clamped edge are considered. Results are compared with well-known analytical results for the plate without initial stresses. Results obtained using different methods show good coincidence. Eigen frequencies are also evaluated using two different methods. The inverse problem is solved by the Galerkin method. Initial stress definition results are presented for different frequencies and boundary conditions.