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

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8293
Author(s):  
Andrzej Dymarek ◽  
Tomasz Dzitkowski ◽  
Krzysztof Herbuś ◽  
Piotr Ociepka ◽  
Andrzej Niedworok ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Numerical Model ◽  
Vibration Amplitude ◽  
Dynamic Properties ◽  
Maximum Amplitude ◽  
Analytical Form ◽  
Input Function ◽  
Active Force ◽  
Natural Vibrations ◽  
Richter Scale

The paper formulates a method of active reduction of structure vibrations in the selected resonance zones of the tested object. The method ensures reduction of vibrations of the selected resonance zones by determining the parameters of the active force that meets the desired dynamic properties. The paper presents a method for determining the parameters of the active force by reducing the vibrations of the structure in its resonance zones to a given vibration amplitude. For this purpose, an analytical form was formulated, which will clearly define the dynamic properties of the tested object and the force reducing the vibrations in the form of a mathematical model. The formulated mathematical model is a modified object input function, which in its form takes into account the properties of the active force reducing the vibrations. In such a case, it is possible to use the methods of mechanical synthesis to decompose the modified characteristic function into the parameters of the system and the parameters of the force being sought. In the formulated method, the desired dynamic properties of the system and the vibration reducing force were defined in such a way that the determined parameters of the active force (velocity-dependent function) had an impact on all forms of natural vibrations of the tested system. Based on the formalized method, the force reducing the vibrations of the four-story frame to the desired displacement amplitude was determined. Two cases of determining the active force reducing the vibrations to the desired vibration amplitude of the system by modifying the dynamic characteristics describing the object together with the active force were considered. For both cases, the system’s responses to the oscillation generated by harmonic force of frequencies equal to the first two forms of natural vibrations of the tested system were determined. In order to verify the determined force reducing the vibrations of the object and to create a visualization of the analyzed phenomenon, the building structure dynamics were analyzed with the use of PLM Siemens NX 12 software. The determined force parameters were implemented into the numerical model, in which the tested system was modelled, and the response time waveforms were generated with regard to the considered story. The generated waveforms were compared with the waveforms obtained in the formalized mathematical model for determining the active force reducing the vibrations. The vibrations of the tested numerical model were induced by the kinematic excitation with the maximum amplitude equal to 100 mm, which corresponds to the vibration amplitude during the earthquake with a force equal to level 5 on the Richter scale.

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

2020 ◽  
Vol 26 (17-18) ◽  
pp. 1471-1483
Author(s):  
Andrzej Dymarek ◽  
Tomasz Dzitkowski ◽  
Krzysztof Herbuś ◽  
Piotr Ociepka ◽  
Agnieszka Sękala
Keyword(s):  
Characteristic Function ◽  
Dynamic Properties ◽  
Vibration Reduction ◽  
Rational Functions ◽  
Analytical Form ◽  
Active Force ◽  
Richter Scale ◽  
Active Vibration ◽  
The Impact ◽  
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.

A Journal Bearing With Variable Geometry for the Reduction of the Maximum Amplitude During Passage Through Resonance

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Athanasios Chasalevris ◽  
Fadi Dohnal
Keyword(s):  
Film Thickness ◽  
Relative Motion ◽  
Vibration Amplitude ◽  
Journal Bearing ◽  
Dynamic Properties ◽  
Maximum Amplitude ◽  
Variable Stiffness ◽  
Fluid Film ◽  
Bearing Ring ◽  
Fluid Film Thickness

A concept for a journal bearing with variable stiffness and damping properties is developed in order to decrease the vibration amplitude of a rotor-journal bearing system during passage through resonance. The introduction of an additional fluid film thickness in the bearing is proposed in this work in order to alter the dynamic properties in the bearing. The bearing ring is divided into two parts with the upper part being fixed with the housing and the lower part being flexibly mounted by a preloaded spring in parallel with a viscous damper. This allows relative motion between the two parts of the bearing ring. The relative motion introduces an additional fluid film zone in the bearing under the passive displacement of the lower part due to increased impedance forces that are developed in the lubricant film at resonance operation. The general concept is to change the system's damping and stiffness coefficients using this extra fluid film thickness only when the system passes through its critical speed in order to quench the vibration amplitude. For rotational speeds outside of the resonant regions, the bearing is considered to be fixed in order to behave as it was designed under the nominal loading operational conditions.

The mathematical modelling of corrosion in hot dip galvanized steel reinforced concrete

2011 ◽  
Vol 2 (1) ◽  
pp. 1-12
Author(s):  
A. Hegyi ◽  
H. Vermeşan ◽  
V. Rus
Keyword(s):  
Mathematical Model ◽  
Reinforced Concrete ◽  
Numerical Model ◽  
Equation System ◽  
Galvanized Steel ◽  
Steel Reinforced Concrete ◽  
Numeric Model ◽  
Physical And Mathematical Models ◽  
Physical Phenomena ◽  
The Mathematical Model

Abstract In this paper we wish to present the numerical model elaborated in order to simulate some physical phenomena that influence the general deterioration of steel, whether hot dip galvanized or not, in reinforced concrete. We describe the physical and mathematical models, establishing the corresponding equation system, the initial and boundary conditions. We have also presented the numeric model associated to the mathematical model and the numeric methods of discretization and solution of the differential equations system that describes the mathematical model.

Prevention of Corrosion in Austenitic Stainless Steel through a Predictive Numerical Model Simulating Grain Boundary Chromium Depletion

2017 ◽  
pp. 374-389
Author(s):  
M.K. Samal
Keyword(s):  
Mathematical Model ◽  
Stainless Steel ◽  
Austenitic Stainless Steel ◽  
Numerical Model ◽  
Low Temperature ◽  
Grain Boundary ◽  
Stainless Steels ◽  
Predictive Models ◽  
Chromium Depletion ◽  
Sensitization Behavior

In this chapter, a mathematical model for rate of formation of chromium carbides near the grain boundary, which is a pre-cursor to chromium depletion and corresponding sensitization behavior in stainless steels, is presented. This model along with the diffusion equation for chromium in the grain has been used to obtain chromium depletion profiles at various time and temperature conditions. Finite difference method has been used to solve the above equations in the spherical co-ordinate system and the results of time-temperature-sensitization diagrams of four different types of alloys have been compared with those of experiment from literature. For the problem of low temperature sensitization and corresponding inter-granular corrosion in austenitic stainless steel, it is very difficult to carry out experiment at higher temperatures and justify its validity at lower operating temperatures by extrapolation. The development of predictive models is highly useful in order to design the structures for prevention of corrosion of the material in aggressive environments.

scholarly journals Studies on Dynamic Properties of Ultracapacitors Using Infinite r–C Chain Equivalent Circuit and Reverse Fourier Transform

Energies ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 4583
Author(s):  
Shailendra Rajput ◽  
Alon Kuperman ◽  
Asher Yahalom ◽  
Moshe Averbukh
Keyword(s):  
Mathematical Model ◽  
Fourier Transform ◽  
Equivalent Circuit ◽  
Dynamic Behavior ◽  
Double Layer ◽  
Electrochemical Impedance ◽  
Dynamic Properties ◽  
Internal Resistance ◽  
Simulation Software ◽  
Specific Power

The specific power storage capabilities of double-layer ultracapacitors are receiving significant attention from engineers and scientific researchers. Nevertheless, their dynamic behavior should be studied to improve the performance and for efficient applications in electrical devices. This article presents an infinite resistor–capacitor (r–C) chain-based mathematical model for the analysis of double layer ultracapacitors. The internal resistance and capacitance were measured for repetitive charging and discharging cycles. The magnitudes of internal resistance and capacitance showed approximately ±10% changes for charge-discharge processes. Electrochemical impedance spectroscopy investigations revealed that the impedance of a double-layer ultracapacitor does not change significantly in the temperature range of (−30 °C to +30 °C) and voltage range of (0.3376–2.736 V). The analysis of impedance data using the proposed mathematical model showed good agreement between the experimental and theoretical data. The dynamic behavior of the ultracapacitor was successfully represented by utilizing the proposed infinite r–C chains equivalent circuit, and the reverse Fourier transform analysis. The r–C electrical equivalent circuit was also analyzed using the PSIM simulation software to study the dynamic behavior of ultracapacitor parameters. The simulation study yields an excellent agreement between the experimental and calculated voltage characteristics for repetitive charging-discharging processes.

scholarly journals NUMERICAL MODEL OF BREAKWATER WAVE FLOWS

1988 ◽  
Vol 1 (21) ◽  
pp. 149 ◽  
Author(s):  
Alex C. Thompson
Keyword(s):  
Mathematical Model ◽  
Numerical Model ◽  
Reflection Coefficient ◽  
Water Wave ◽  
Wave Equations ◽  
Seepage Flow ◽  
Experimental Results ◽  
Simplified Model ◽  
Flow Equations ◽  
Shallow Water Wave Equations

A mathematical model of flow on a sloping breakwater face is described and results of calculations compared with some experimental results to show how the model can be calibrated. Flow above the surface of the slope is represented by the shallow water wave equations solved by a finite difference method. Flow within the breakwater is calculated by one of two methods. A solution of the linear seepage flow equations, again using finite differences or a simplified model of inflow can be used. Experimental results for runup and reflection coefficient are from tests performed at HRL Wallingford.

scholarly journals Modeling Drying of Degenerated Calluna vulgaris for Wildfire and Prescribed Burning Risk Assessment

Forests ◽  
2020 ◽  
Vol 11 (7) ◽  
pp. 759 ◽  
Author(s):  
Torgrim Log
Keyword(s):  
Mathematical Model ◽  
Numerical Model ◽  
Mass Loss ◽  
Diffusion Coefficients ◽  
Prescribed Burning ◽  
Fire Hazard ◽  
Fire Risk ◽  
Calluna Vulgaris ◽  
Fire Danger ◽  
Drying Process

Research highlights: Moisture diffusion coefficients for stems and branches of degenerated Calluna vulgaris L. have been obtained and a mathematical model for the drying process has been developed and validated as an input to future fire danger modeling. Background and objectives: In Norway, several recent wildland–urban interface (WUI) fires have been attributed to climate changes and accumulation of elevated live and dead biomass in degenerated Calluna stands due to changes in agricultural activities, i.e., in particular abandonment of prescribed burning for sheep grazing. Prescribed burning is now being reintroduced in these currently fire prone landscapes. While available wildfire danger rating models fail to predict the rapidly changing fire hazard in such heathlands, there is an increasing need for an adapted fire danger model. The present study aims at determining water diffusion coefficients and develops a numerical model for the drying process, paving the road for future fire danger forecasts and prediction of safe and efficient conditions for prescribed burning. Materials and methods: Test specimens (3–6 mm diameter) of dead Calluna stems and branches were rain wetted 48 h and subsequently placed in a climate chamber at 20 °C and 50% relative humidity for mass loss recordings during natural convection drying. Based on the diameter and recorded mass versus time, diffusion coefficients were obtained. A numerical model was developed and verified against recoded mass loss. Results: Diffusion coefficients were obtained in the range 1.66–10.4 × 10−11 m2/s. This is quite low and may be explained by the very hard Calluna “wood”. The large span may be explained by different growth conditions, insect attacks and a varying number of years of exposure to the elements after dying. The mathematical model described the drying process well for the specimens with known diffusion coefficient. Conclusions: The established range of diffusion coefficients and the developed model may likely be extended for forecasting moisture content of degenerated Calluna as a proxy for fire danger and/or conditions for efficient and safe prescribed burning. This may help mitigate the emerging fire risk associated with degenerated Calluna stands in a changing climate.

A numerical method for solving the physics-based model of IGBT with all free-carrier injection conditions in the base region

2017 ◽  
Vol 36 (6) ◽  
pp. 1653-1662 ◽  
Author(s):  
Jiajia Chen ◽  
Yuhan Ma ◽  
Shiyou Yang
Keyword(s):  
Mathematical Model ◽  
Numerical Model ◽  
Design Methodology ◽  
Free Carrier ◽  
Carrier Injection ◽  
Base Region ◽  
Content Type ◽  
Insulated Gate Bipolar Transistor ◽  
Proposed Model ◽  
Solution Methodology

Purpose The purpose of this paper is to provide an accurate model and method to simulate the transient performances of an insulated gate bipolar transistor (IGBT) in an arbitrary free-carrier injection condition. Design/methodology/approach A numerical model and method for solving the physics-based model, an ambipolar diffusion equation-based model, of an IGBT is proposed. Findings The results of the proposed model are very close to the tested ones. Originality/value A mathematical model for an IGBT considering all free-carrier injection conditions is introduced, and a numerical solution methodology is proposed.

scholarly journals Mathematical model of steady flow in a helium loop

2019 ◽  
Vol 20 (7) ◽  
pp. 704
Author(s):  
František Világi ◽  
Branislav Knížat ◽  
Marek Mlkvik ◽  
František Urban ◽  
Róbert Olšiak ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Numerical Model ◽  
Steady Flow ◽  
Gaseous Medium ◽  
Natural Circulation ◽  
Variable Density ◽  
Experimental Facility ◽  
Flowing Medium ◽  
Current State ◽  
Natural Circulation Loop

The article describes the application of a mathematical model to a natural circulation loop. A set of measurements were conducted at the experimental facility. The pressure and velocity relations were observed during the steady flow of helium. The main goal was to create a numerical model of flow capable of determining the velocity of flowing medium. The model describes the flow of highly compressed gaseous medium with variable density in direct pipelines with local resistances. At the current state, the temperature values along the loop are taken as input to the model. The article also includes the evaluation of local resistances in DHR and GFR, which significantly affects the resulting accuracy. The results from a numerical model are compared with experiments.

Analysis on location of maximum vibration amplitude in panel flutter

2019 ◽  
Vol 234 (2) ◽  
pp. 457-469 ◽  
Author(s):  
Xianzong Meng ◽  
Zhengyin Ye ◽  
Kun Ye ◽  
Cheng Liu
Keyword(s):  
Theoretical Basis ◽  
Vibration Amplitude ◽  
Dynamic Pressure ◽  
Maximum Amplitude ◽  
Displacement Function ◽  
Limit Cycle Oscillation ◽  
Panel Flutter ◽  
Mathematical Basis ◽  
Critical Dynamic ◽  
Cycle Oscillation

When the panel is under limit cycle oscillation, the location of maximum vibration amplitude always locates at 0.75 of panel length under different dynamic pressure. However, this conclusion is drawn from engineer practice without further investigations on its theoretical basis. Thus, the current study focuses on the theoretical and mathematical basis of this problem. The pattern of the location of maximum amplitude is verified at first by using three numerical methods. Then, based on the law of energy conservation, the displacement function of linear panel oscillation is derived for theoretical investigation. The linear panel consists of two structural modes. Theoretical analysis shows that, under critical dynamic pressure, the generalized displacement responses of two structural modes have opposite phase, the same vibration amplitude and the same vibration frequency. As a result, the superposition of displacement function of two structural modes, which is the displacement function of panel, leads to the occurrence of maximum vibration amplitude at 0.7 of panel length. With more structural modes considered, the location of maximum moves to 0.75 of panel length.

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