Semi-analytical modelling of multilayer continuous systems nonlinear dynamics

Problems concerning structures dynamics are being one of most important subjects in recent investigations associated with railways constructions. The need of modelling of such structures and their behaviour prediction leads to necessity of seeking new approaches, mainly due to highly increasing speeds of vehicles and traffic intensity. Comparative studies carried out on experimental data, measurements and theoretical research show that models based on multi-layered approach supported by semi-analytical approximations of solutions can give new insight into undertaken analyses. More detailed consideration of roads components and their physical properties, along with application of effective estimations allowing to avoid numerical instabilities linked with extremal dynamic variations, can be important tools in obtaining new solutions both, theoretical and engineering. This paper briefly presents a number of multilayer railway track models, with special emphasis on nonlinear track properties. Existing analytical and semi-analytical solution methods are presented with main advantages of new approaches. The theoretical double-beam system with two nonlinear layers is solved and computational examples are presented along with possibility of their transition to other multilayer structures analysis.