Anpilogov D. Bending vibration and the deformation of cylindrical shells with damages.

Object of research is bending vibrations and dynamic processes in cylindrical shells with damage. The subject of research is identifying of damage of a cylindrical shells on the basis of their non-linear oscillations. Purpose of the work is to develop approaches to the damage identification of the shell-type constructions by vibration diagnostics methods. Research methods: a harmonic balance, conformal mappings (complex potentials), the least squares, the direct method of boundary elements. The analytical solutions of the free and forced vibration equations of a bilinear oscillator, modeling the damaged shell, are obtained, and their harmonic analysis is made. The most effective vibrating indicators of damage are founded. It was established that they are determined by the relative decrease of stiffness. Formulated and solved first basic boundary value problem of elasticity theory for a circular sector, which is a cross section of the cylindrical shell. The analysis of the displacement field is made. In the presence of the cutout in the sector a violation of the Kirchhoff-Love hypothesis at points around the cutout is established. The rate of accumulation of the rotation angles of radial cuts is investigated. The angular size of the perturbation zone of the displacement field, induced by damage, was estimate with restore of this speed. The dependence of the relative decrease of stiffness of the ring sector in the case, when the cut is appears, on his depth is determined. The direct boundary element method for the validation of the results is used. Results have been implemented on JSC "Motor Sich". Area of application is aeroenginebuilding, civil building.