MODELLING AND ANALYSIS OF INITIAL STRESS STATE IN A THIN-WALL CYLINDER WITH VARIABLE CHARACTERISTICS

A linearized model of prestressed elastic body vibrations is described in terms the nonsymmetric Piola stress tensor, and a weak statement original problem given. With help Lagrange variational principle, we construct steady axisymmetric oscillations thin-walled (shell-like) cylinder with variable material properties presence an inhomogeneous prestress field. The motion equations, essential natural boundary conditions are formulated. Integral characteristics introduced that average change prestresses over shell thickness. On basis presented, on steady-state functionally graded cylindrical numerically investigated via shooting method; influence laws modules components dynamic (e.g., amplitude-frequency characteristics, vibration frequencies) analyzed, comparative analysis solutions carried out depending parameter. For considered axial inhomogeneity, based acoustic sounding data, study inverse restoring two inhomogeneity characterizing nonuniform initial stress-strain state tension or inflation. As additional information, consider measurement data displacement cylinder's surface, given set points at certain frequency oscillations; such case, to be known may depend coordinate, which makes it possible arbitrary functional gradient along axis cylinder. mode probing loading determined by specifying traction type oscillation frequency. Explicit formulas for desired obtained, computational experiments restore them. high accuracy reconstruction revealed far from ends when vicinity first resonance.