Use of active synthesis in vibration reduction using an example of a four-storey building

The article presents a method of active vibration reduction of vibrating mechanical systems. This method is based on the properties of positive rational functions, which in the case of discrete dynamical systems correspond to the characteristic function describing such systems. The method formalized uses methods for decomposing positive rational functions. The advantage of this approach is taking into account the analytical form of a characteristic function of the system being tested and the vibration-reducing force, as well as the conditions that the system should meet in the event of an active vibration-reducing force. In addition, in the proposed method, the desired dynamic properties of the system and the vibration-reducing force can be defined in such a way that the determined parameters of the active force affect all forms of the natural vibrations of the examined system. Based on the formalized methodology, the force reducing the vibrations of a four-storey frame to the desired displacement amplitude was determined. The impact of the place of application of the specific active force on the reduction of vibration of the tested object was also taken into account. The vibrations of the tested structure’s model were caused by kinematic excitation with a harmonic course and an amplitude corresponding to an earthquake of a magnitude of 5 on the Richter scale. To verify the determined force reducing the vibrations of the object and to create a visualisation of the analysed phenomenon, a dynamic analysis of the building structure was carried out using PLM Siemens NX 12 software.