Mathematical models for inverse problems of deficient constructions dynamics

The article presents the solution for residual stiffnesses determination in various structural elements, which is based on the results of instrumental measurements of the parameters of natural vibrations carried out using high-precision instruments. Our research is extremely relevant to determine the degree of deficiencies in buildings, supporting structures of aircraft, ship and other systems with a certain operational cycle or structures that have been subjected to intense impacts. The use of dynamic methods for analyzing the state of load-bearing structures has undeniable advantages, since they exclude the need for a detailed surveying, often associated with the opening of enclosure structures. The advantages of using this approach are especially evident when surveying a large area of residential structures located in heterogeneous operating conditions. The article considers the problems of determining the stiffness properties of structural elements with the predominance of shearing strain in continuity and discreteness of inertial parameters distribution. There is a need to determine the level of defects accumulation, so we have calculated the ratio of real stiffness parameters, defined in the process of dynamic tests, to some initial ones, inherent to the constructions without defects. The article shows the invariance of such relations with account of discreteness and continuity properties of the mathematical models for structural elements. These methods have been tested in survey of 1-335 series high-rise residential buildings in Irkutsk.