scholarly journals Description of selected pneumatic elements and systems using fractional calculus

2019 ◽  
Vol 1 (1) ◽  
pp. 43-49
Author(s):  
Daniel Pietruszczak ◽  
Artur Nowocień
Keyword(s):  
Computer Simulation ◽  
Transfer Function ◽  
Fractional Calculus ◽  
Mathematical Models ◽  
Dynamic Systems ◽  
Simulation Research ◽  
Integer Order ◽  
Frequency Domains ◽  
Model Transfer ◽  
Definition Of

The paper presents the application of fractional calculus to describe the dynamics of selected pneumatic elements and systems. In the construction of mathematical models of the analysed dynamic systems, the Riemann-Liouville definition of differintegral of non- integer order was used. For the analysed model,  transfer function of integer  and non-integer order was determined. Functions describing characteristics in frequency domains were determined,  whereas the characteristics of the elements and systems were obtained by means of computer simulation. MATLAB programme were used for the simulation research.

scholarly journals Analysis of dynamic properties of selected basic elements of automation of non-integer orders

2018 ◽  
Vol 19 (12) ◽  
pp. 514-525
Author(s):  
Mirosław Luft ◽  
Artur Nowocień ◽  
Daniel Pietruszczak
Keyword(s):  
Computer Simulation ◽  
Fractional Calculus ◽  
Dynamic Properties ◽  
Matlab Software ◽  
Simulation Research ◽  
Integer Order

The paper presents the application of the fractional calculus to describe the dynamics of selected basic elements of automation. For the analyzed models, the integer and non-integer order transmittance was determined. Relationships describing time characteristics were determined and frequency; on the path of computer simulation, the characteristics of the analyzed systems were obtained. MATLAB software was used for simulation research.

scholarly journals DEM simulation research of selected sowing unit elements used in a mechanical seeding drill

2019 ◽  
Vol 254 ◽  
pp. 02021
Author(s):  
Jacek Marcinkiewicz ◽  
Jarosław Selech ◽  
Żaneta Staszak ◽  
Łukasz Gierz ◽  
Dariusz Ulbrich ◽  
...  
Keyword(s):  
Computer Simulation ◽  
Discrete Element Method ◽  
Mathematical Models ◽  
Discrete Element ◽  
Simulation Research ◽  
Dem Simulation ◽  
Bench Tests ◽  
Modern Computer ◽  
Design Solutions ◽  
Simulation Systems

The paper presents the results of research aimed at the verification of the existing design solutions of four example sowing units for agricultural seed drills with the most frequently used types of sowing wheels. The research was conducted with the use of modern computer simulation systems based on the discrete element method (DEM) with the evaluation of the efficiency of selected design solutions in terms of achieved performance and metering uniformity. The paper includes a description of virtual research models and the employed mathematical models used for mirroring contact between seeds. Moreover, for the purpose of verification of the obtained results, bench tests were conducted using actual models of selected design solutions.

Structural-parametric model of an electroelastic actuator for nanomechanics

2020 ◽  
pp. 3-11
Author(s):  
S.M. Afonin
Keyword(s):  
Transfer Function ◽  
Piezoelectric Actuator ◽  
Transfer Functions ◽  
Piezoelectric Effect ◽  
Parametric Model ◽  
Elastic Compliance ◽  
Parametric Models ◽  
Piezo Actuator ◽  
Structural Scheme ◽  
Model Transfer

Structural-parametric models, structural schemes are constructed and the transfer functions of electro-elastic actuators for nanomechanics are determined. The transfer functions of the piezoelectric actuator with the generalized piezoelectric effect are obtained. The changes in the elastic compliance and rigidity of the piezoactuator are determined taking into account the type of control. Keywords electro-elastic actuator, piezo actuator, structural-parametric model, transfer function, parametric structural scheme

scholarly journals A remark on local fractional calculus and ordinary derivatives

2016 ◽  
Vol 14 (1) ◽  
pp. 1122-1124 ◽  
Author(s):  
Ricardo Almeida ◽  
Małgorzata Guzowska ◽  
Tatiana Odzijewicz
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Short Note ◽  
General Definition ◽  
Local Fractional Derivative ◽  
Fundamental Properties ◽  
Local Fractional Calculus ◽  
Definition Of

AbstractIn this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.

scholarly journals New Challenges Arising in Engineering Problems with Fractional and Integer Order

2021 ◽  
Vol 5 (2) ◽  
pp. 35
Author(s):  
Haci Mehmet Baskonus ◽  
Luis Manuel Sánchez Ruiz ◽  
Armando Ciancio
Keyword(s):  
Mathematical Models ◽  
Real World ◽  
Integer Order ◽  
Engineering Problems ◽  
New Challenges ◽  
Real World Problems

Mathematical models have been frequently studied in recent decades in order to obtain the deeper properties of real-world problems [...]

Effect of Spray-Wall Interaction On Thermoacoustic Instability Prediction by Flame Transfer Function and the Convective Time Delay Method

2021 ◽  
Author(s):  
Sheng Meng ◽  
Man Zhang
Keyword(s):  
Time Delay ◽  
Transfer Function ◽  
Numerical Models ◽  
Time Lag ◽  
Interaction Model ◽  
Phase Lag ◽  
Thermoacoustic Instability ◽  
Spray Flame ◽  
Wall Interaction ◽  
Definition Of

Abstract This study numerically investigates the effect of spray-wall interactions on thermoacoustic instability prediction. The LES-based flame transfer function (FTF) and the convective time delay methods are used by combining the Helmholtz acoustic solver to predict a single spray flame under the so-called slip and film spray-wall conditions. It is found that considering more realistic film liquid and a wall surface interaction model achieves a more accurate phase lag in both of the time lag evaluations compared to the experimental results. Additionally, the results show that a new time delay exists between the liquid film fluctuation and the unsteady heat release, which explains the larger phase value in the film spray-wall condition than in the slip condition. Moreover, the prediction capability of the FTF framework and the convective time delay methodology in the linear regime are also presented. In general, the instability frequency differences predicted using the FTF framework under the film condition are less than 10 Hz compared with the experimental data. However, an underestimation of the numerical gain value leads to requiring a change in the forcing position and an improvement in the numerical models. Due to the ambiguous definition of the gain value in the convective time delay method, this approach leads to arbitrary and uncertain thermoacoustic instability predictions.

The bouncing ball and the Grünwald-Letnikov definition of fractional derivative

2021 ◽  
Vol 24 (4) ◽  
pp. 1003-1014
Author(s):  
J. A. Tenreiro Machado
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Restitution Coefficient ◽  
Classical Physics ◽  
Bouncing Ball ◽  
Mechanical Experiment ◽  
Fractional Models ◽  
Definition Of

Abstract This paper proposes a conceptual experiment embedding the model of a bouncing ball and the Grünwald-Letnikov (GL) formulation for derivative of fractional order. The impacts of the ball with the surface are modeled by means of a restitution coefficient related to the coefficients of the GL fractional derivative. The results are straightforward to interpret under the light of the classical physics. The mechanical experiment leads to a physical perspective and allows a straightforward visualization. This strategy provides not only a motivational introduction to students of the fractional calculus, but also triggers possible discussion with regard to the use of fractional models in mechanics.

scholarly journals Air Temperature Control System in a Building on the Basis of Mathematical Modelling

2018 ◽  
Vol 155 ◽  
pp. 01041 ◽  
Author(s):  
Aleksandr Pilipenko ◽  
Sergei Petrov
Keyword(s):  
Computer Simulation ◽  
Control System ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Air Temperature ◽  
Temperature Control ◽  
Automated System ◽  
Temperature Control System ◽  
Heating Systems ◽  
The Cost

In the article the authors solve a crucial objective of reducing the cost of heating services through the introduction of a system, controlling boilers and heating devices, based on modelling of the building and predicting heating systems functioning and operation. The authors describe the method of mathematical modelling of heating systems of the building and represent the developed mathematical models, pledged and installed into the developed automated system. The authors have offered an automated system of dispatch control of the boilers with the elements of computer simulation and modelling.

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