Issue 46

I. Shardakov et alii, Frattura ed Integrità Strutturale, 46 (2018) 383-390; DOI: 10.3221/IGF-ESIS.46.35 384 front of shock waves as they pass through the structure. When the propagating wave front runs across defects, its frequency composition and propagation time change. By comparing the signals from the structure with and without defects, we can detect any faults, their location and size. The effectiveness of the solution of these problems depend on the selection of the place where the elastic wave is initiated, the spectral composition of the impulse and the place of recording the signal passing through the structure. A well-grounded choice of these parameters is possible in the framework of an appropriate mathematical model, which adequately describes the dynamic processes occurring in the structure. Figure 1 : Testing stand with installed model RC structure. In this study, the mathematical model describing the free vibrations of the structure caused by impact loading is verified. In the experiments, elastic waves in different elements of the model structure (columns, slabs) were excited by an impact of a 460g striker. The resulting vibrograms were recorded by accelerometers mounted at different points of the structure. Registration of vibration processes in the model structure involved a synchronous recording of data from two accelerometers, one of which was located on the striker, and the other – at a certain point of the structure. The registration of the acceleration at the impact point made it possible to obtain the value of the impact force (as the product of the acceleration by the striker mass) as a function of time. These data were used to determine the force boundary condition at the point of impact necessary for solving the initial-boundary problem of propagation of a shock wave in a structure. This allowed us to compare the vibrograms obtained in the experiment and calculated on the basis of the proposed model. This model was used as a framework for performing a series of numerical experiments, in which vibrograms obtained for the structure with crack formation at typical sites were compared with vibrograms for defect-free structure. Based on the results of these solutions we identified an informative diagnostic parameter, which reflects the processes of initiation and growth of cracks in reinforced concrete. This approach makes it possible to create an effective system for vibration control of the process of crack formation in RC structures. C ONCEPTUAL DESCRIPTION OF THE MATHEMATICAL MODEL he object under study is a monolithic reinforced concrete building (Fig. 1), whose columns are mounted on metal supports. The dynamic behavior of the building is described in the framework of the linear theory of viscoelasticity. The concrete is assumed to be viscoelastic and isotropic, and steel reinforcement is modeled within the framework of the linear theory of elasticity. The mathematical model is represented by the following relations. Equations of motion: 2 2 div , V t       U x (1) T Testing stand Model RC structure