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

Abstract

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.

Designing of Drive Systems in the Aspect of the Desired Spectrum of Operation

“…The optimization may concern geometric parameters such as module, the number of teeth, or clearances [5][6][7][8], but also dynamic parameters-mass moments of inertia of wheels and elastic components of the designed gearbox, meeting the predetermined properties, e.g., in the form of required frequency spectrum [9][10][11]. Therefore, dynamic properties of the structure, described in the form of frequency transition functions are one of the basic criteria used at the designing stage of the state-of-the-art mechanical structures [12][13][14][15][16][17][18]. Their knowledge enables the avoidance of operating the system in resonance zones, which affects the durability and proper operation of the device.…”

“…Their knowledge enables the avoidance of operating the system in resonance zones, which affects the durability and proper operation of the device. The system parameters can be selected, regarding the dynamic properties, by using the optimization algorithms [5][6][7], modeling [19][20][21][22], or synthesis [9][10][11][12][13][14][15][16][17][18], due to an introduction of simulation tests with the use of computers. Simulation tests, belonging to the scope of theoretical tests, allow us to analyze the impact of the selected parameters on mechanical characteristics.…”

“…This article attempts to solve the problem of designing the drive system in the aspect of the desired frequency spectrum. The formalized method, based on the methods of synthesis of vibrating mechanical systems [9][10][11][12][13][14][15][16][17][18], reduces the task to a determination of dynamic parameters included in the required drive system. Using this formalized method, the parameters (mass moments of inertia of the wheels and elastic components) of the two-speed gearbox (of a specific ratio) were determined, meeting the desired dynamic properties in the form of a specific frequency spectrum.…”

Method for Tuning the Parameters of Active Force Reducing Building Vibrations—Numerical Tests

“…The reduction of vibrations comes down to the determination of parameters of the control systems in the feedback loop that meet specific vibration amplitude of a discussed material point. Conditions in which the structural and parametric identification of the system [36] subjected to vibration reduction are realized should meet the required dynamic properties in advance.…”

“…Despite many works in the field of vibration reduction of building structures, none of them deal with the reduction of the systems to the desired vibration amplitude. The authors use the methods of synthesis of mechanical systems to search for fully controlled vibration reduction methods using passive and active elements [14,[34][35][36][37]. The presented paper is the next stage of the work using synthesis methods to reduce vibrations in building structures.…”