Volkova V. Phase trajectories in direct and inverse problems of non-linear elastic system dynamics

Dynamic models of forced and free oscillations in structural elements, structures and mechanisms. The prime objective of this study was to develop alternative methods for solving direct and inverse problems of dynamics by using a novel approach that is based on the application of phase trajectories and their mappings on the planes "acceleration - displacement" and "acceleration- velocity". While carrying out the research, the following methods were used: the analytical methods of the non-linear oscillation theory and the methods of numerical, hybrid and physical experiments. In the course of investigations, the effects of different kinds of non-linearities in the elastic and dissipative characteristics as well as those of outer excitation to a framework of phase trajectories were analyzed. A methodology suggested for solving inverse problems is characterized as highly sensitive to the presence of non-linearity; it ensures the best accuracy in definition of a class of non-linear models of dynamic systems, and it can be realized not only for monoharmonic but also for polyharmonic and chaotic processes. The results obtained have already found their application in the experimental determination of dynamic characteristics of road-transport bridges, in studying dynamic properties of pneumatic dampers in railroad carriages, and also in scientific investigations and teaching. The sphere of application these results includes, as well, prediction of dynamic behaviour structural elements in construction, edifices and machinery.