Extended phase trajectories in direct and inverse problems of non-linear elastic system dynamics

Project author: National Mining University, Department of Construction, Geotechnics And Geomechanics, Dnepropetrovsk (Ukraine).

Project objective: The goal of the project is to establish methods for solving direct and inverse problems of dynamics of elastic elements of civil and mechanical structures based on a new approach using phase trajectories and their mappings on planes “acceleration – displacement” and �acceleration � velocity�.

Project background: The construction of mathematical model satisfactorily describing or predicting operation of object, process or system is an integral part of any problem of prediction of dynamic behaviour of mechanical systems. There are many types of damage that can cause an initially linear structural system to respond to its operational and environmental loads in a non-linear manner. One of the most common types of damage is cracks that subsequently open and close under analysis of dynamic properties in construction elements.

Most of the methods of structural identification are based on the use of special types of outer excitation for a wide range of frequencies, such as symmetric monoharmonic excitation and rectangular impulse. These types of excitation are often unrealizable in mechanical systems. The methods based on the Fourier transformation do not allow classifying and localizing non-linearity and are inapplicable to investigating stochastic processes. It should be also noted that the application of Winer series and Hilbert transformation for identification of non-smooth non-linear dynamic characteristics is unjustified. This type of damage may include fatigue cracks and cracks that result from excessive deformation. Vibration-based structural health monitoring consists in detecting damages in structures from changes in vibration features obtained from periodically fullfilled measurements.�