Beam elements as approximate models of vibrating mechanical subsystems of freight wagons

The complex mechanical system which is a subsystem of mechatronic system composed with many continuous mechanical elements having the same length and variable cross section, loaded by the harmonic force is analyzed. The main subject of deliberation was to determine the flexibility of the mechanical subsystem with constant cross section using algorithms of exact and approximate methods. Next, the comparison of methods and the correction of the approximate method has been made. The model of subsystem of complex transverse vibrating mechanical system of freight wagon was considered and after deliberation the approximate method has been chosen. The presented research of subsystems establishes the foundation to complex systems analysis with cascade structure. By analyzing the diagrams of characteristics of confirmed system it has been determined that in case of approximate method the resonance frequencies cover with those which have been determined with the exact method. However, the values of the characteristic in other areas are different. Therefore, there is the mistake within the approximate method, which while of studying the single system does not have any influence because in resonance areas the characteristic values of the system approach to the infinity. However, the difference between values of flexibility within two methods has the great influence on the result of complex systems. That is why it was necessary to correct the results of the approximate method.