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1

Transfer matrices with positive coefficients of descriptor linear systems

Kaczorek Tadeusz, Sajewski Łukasz

Journal of Automation, Electronics and Electrical Engineering

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2024

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Vol. 6, No. 1

7--17

EN

Transfer matrices with positive coefficients of descriptor positive linear continuous-time systems are addressed. Two methods of checking of the positivity of descriptor linear systems are proposed. It is shown that if the positive descriptor system is asymptotically stable then all coefficients of its transfer matrix are positive.

2

Light absorption of a polymer based single/multi junction solar cell model

Varghese Jeremiah S., Ruhneb Benhur, Moni D. Jacquline, Du John Victor H.

Przegląd Elektrotechniczny

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2022

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R. 98, nr 1

19--22

EN

In this paper, a detailed study and simulation modelling on light absorption using PDMS material in a single/multi-junction solar cells is carried out. Since PDMS material is a good absorber of light, it is used as an active layer of a solar cell. We choose PDMS because its properties, mainly exceptional intrinsic stability against thermal and ultraviolet light, induced good mechanical properties and stress over a wide range of temperatures. Good transmittance due to the absence of UV absorbers is one of its best characteristics. With the help of the transfer matrix method, which is used for optical modeling of an organic solar cell, inspired by the McGehee Group in Stanford University. The result and simulation is done using MATLAB and in the end we are going to draw a conclusion about the ideal materials that a good solar cell has to have to have good absorption.

PL

W niniejszym artykule przeprowadzono szczegółowe badania i modelowanie symulacyjne absorpcji światła przy użyciu materiału PDMS w jedno-/wielozłączowych ogniwach słonecznych. Ponieważ materiał PDMS jest dobrym pochłaniaczem światła, jest używany jako aktywna warstwa ogniwa słonecznego. Wybieramy PDMS, ponieważ jego właściwości, głównie wyjątkowa stabilność wewnętrzna w stosunku do światła termicznego i ultrafioletowego, indukowały dobre właściwości mechaniczne i naprężenia w szerokim zakresie temperatur. Dobra przepuszczalność ze względu na brak absorberów UV jest jedną z jego najlepszych cech. Za pomocą metody przeniesienia macierzy, która służy do optycznego modelowania organicznego ogniwa słonecznego, inspirowanej przez Grupę McGehee na Uniwersytecie Stanforda. Wynik i symulację wykonano przy użyciu MATLAB, a na koniec wyciągniemy wniosek na temat idealnych materiałów, które dobre ogniwo słoneczne musi mieć dobrą absorpcję.

3

Minimizing the number of layers of the quasi one-dimensional phononic structures

Garus Sebastian, Sochacki Wojciech, Kubanek Mariusz, Nabiałek Marcin

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2022

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Vol. 70, nr 1

art. no. e139394

EN

In the work, multi-criteria optimization of phononic structures was performed to minimize the transmission in the frequency range of acoustic waves, eliminate high transmission peaks with a small half-width inside of the band gap, and what was the most important part of the work – to minimize the number of layers in the structure. Two types of the genetic algorithm were compared in the study. The first one was characterized by a constant number of layers (GACL) of the phononic structure of each individual in each population. Then, the algorithm was run for a different number of layers, as a result of which the structures with the best value of the objective function were determined. In the second version of the algorithm, individuals in populations had a variable number of layers (GAVL) which required a different type of target function and crossover procedure. The transmission for quasi-one-dimensional phononic structures was determined with the use of the transfer matrix method algorithm. Based on the research, it can be concluded that the developed GAVL algorithm with an appropriately selected objective function achieved optimal solutions in a much smaller number of iterations than the GACL algorithm, and the value of the k parameter below 1 leads to faster achievement of the optimal structure.

4

Analytical and Computational Acoustic Modelling of Side Outlet Muffler and Its Extension in the Modelling of Tapered Side Outlet Muffler

Vishwakarma Sandeep Kumar, Pawar Jayappa

Archives of Acoustics

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2022

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Vol. 47, No. 4

491--499

EN

Mufflers are popular in the suppression of noise levels coming from various machinery. The most common parameters for the evaluation of the performance of mufflers are transmission loss, noise level, and insertion loss. The transmission loss is evaluated for tapered side outlet muffler using finite element analysis without considering the fluid-structure interaction. This study includes analytical modelling and acoustic modelling of the side outlet muffler and transmission loss is in excellent agreement with the reference paper. The feasibility of the acoustic model is also verified with the experimental work on simple expansion chamber muffler. The same finite element analysis is extended for the tapered side outlet muffler. The transmission loss of the tapered side outlet muffler in the given frequency range is found 8.96 dB better than the side outlet muffler. The acoustic pressure level and sound pressure level contours for the tapered side outlet muffler give a clear picture of wave propagation inside the muffler. The effect of the cut-off frequency on the transmission loss of the tapered side outlet muffler can be seen from the contours. This study can be helpful in the determination of the performance of the mufflers in terms of transmission loss, the performance of mufflers above cut-off frequency, and design improvements in the muffler to avoid the higher-order modes of the sound wave.

5

A new method for computation of positive realizations of linear discrete-time systems

Kaczorek Tadeusz

Journal of Automation Mobile Robotics and Intelligent Systems

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2021

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Vol. 15, No. 1

3--8

EN

A new method for computation of positive realizations of given transfer matrices of linear discretetime linear systems is proposed. Sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by an example.

6

Divisibility of the second-order minors of the nominators by minimal denominators of transfer matrices of cyclic fractional linear systems

Kaczorek Tadeusz

International Journal of Applied Mathematics and Computer Science

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2021

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Vol. 31, no. 4

627--633

EN

The divisibility of the second-order minors of the numerators of transfer matrices by their minimal denominators for cyclic fractional linear systems is analyzed. It is shown that all nonzero second-order minors of the numerators of the transfer matrices are divisible by their minimal denominators if and only if the system matrices of fractional standard and descriptor linear systems are cyclic. The theorems are illustrated by examples of fractional standard and descriptor linear systems.

7

Poles and zeros assignment by state feedbacks in positive linear systems

Kaczorek Tadeusz

Archives of Control Sciences

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2021

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Vol. 31, No. 3

593--605

EN

Poles and zeros assignment problem by state feedbacks in positive continuous-time and discrete-time systems is analyzed. It is shown that in multi-input multi-output positive linear systems by state feedbacks the poles and zeros of the transfer matrices can be assigned in the desired positions. In the positive continuous-time linear systems the feedback gain matrix can be chosen as a monomial matrix so that the poles and zeros of the transfer matrices have the desired values if the input matrix B is monomial. In the positive discrete-time linear systems to solve the problem the matrix B can be chosen monomial if and only if in every row and every column of the n × n system matrix A the sum of n−1 its entries is less than one.

8

Designing of quasi one-dimensional acoustic filters using genetic algorithm

Garus Sebastian, Sochacki Wojciech

Vibrations in Physical Systems

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2019

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Vol. 30, nr 2

art. no. 2019210

EN

In phononic quasi one-dimensional structures, there is a phenomenon of a phononic bandgap (PhBG), which means that waves of a given frequency do not propagate in the structure. The location and size of PhBG depend on the thickness of the layers, the type of materials used and their distribution in space. The theoretical study examined the transmission properties of quasi one-dimensional structures designed using a genetic algorithm (GA). The objective function minimized the transmission integral and integral of the absolute value of the transmission functions derivative (to eliminate high transmission peaks with a small half width) in a given frequency range. The paper shows the minimization of transmission in various frequency bands for a 40-layer structure. The distribution of multilayer structure transmission was obtained through the Transfer Matrix Method (TMM) algorithm. Structures surrounded by water were analyzed and built of layers of glass and epoxy resin.

9

Invariant properties of positive linear electrical circuits

Kaczorek Tadeusz

Poznan University of Technology Academic Journals. Electrical Engineering

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2019

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No. 97

109--123

EN

The invariant properties of the stability, reachability, and transfer matrices of positive linear electrical circuits with integer and fractional orders are investigated. It is shown that the stability, reachability and transfer matrix of positive linear systems are invariant under their integer and fractional orders.

10

Invariant properties of positive linear electrical circuits

Kaczorek Tadeusz

Archives of Electrical Engineering

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2019

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Vol. 68, nr 4

875--890

EN

The invariant properties of the stability, reachability, observability and transfer matrices of positive linear electrical circuits with integer and fractional orders are investigated. It is shown that the stability, reachability, observability and transfer matrix of positive linear systems are invariant under their integer and fractional orders.

11

Effects of viscoelastic and porous materials on sound transmission of multilayer systems

Felhi H., Trabelsi H., Taktak M., Chaabane M., Haddar M.

Journal of Theoretical and Applied Mechanics

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2018

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Vol. 56 nr 4

961--976

EN

Multilayer structures allow obtaining good performance in acoustic insulation to eliminate unwanted noise in the medium and high frequencies in many applications such as building and transport industry. In this paper, the sound transmission of multilayer systems is studied using the Transfer Matrix Method (TMM). The studied multi-layered panels include elastic, viscoelastic and porous materials. Several configurations of multilayer systems are studied, and their corresponding transmission loss T L is computed. Also, the effects of porous material characteristics are studied to evaluate the impact of each parameter.

12

High-performance quasi one-dimensional mirrors of mechanical waves built of periodic and aperiodic structures

Garus S., Sochacki W.

Journal of Applied Mathematics and Computational Mechanics

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2018

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Vol. 17, nr 4

19--24

EN

The work studied the reflectance for quasi one-dimensional phononical structures. In composite superlattices, the thickness of the layers, their arrangement and selection of constituent materials with appropriate properties such as the density and velocity of mechanical waves propagation allows for the creation of a phononic band gap (PhBG) phenomenon. PhBG is characterized by high reflectance of the mechanical wave incident on the analyzed structure, which means that the wave does not propagate in the superlattice. The paper proposes periodic and aperiodic structures characterized by a wide range of reflectance for the ultrasonic frequencies of mechanical waves and shows how the change the thickness of the layer affects the properties of the analyzed structures.

13

A new method for determination of positive realizations of linear continuous-time systems

Kaczorek T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2018

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Vol. 66, nr 5

605--611

EN

A new method for determination of positive realizations of given transfer matrices of linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are presented. A procedure for computation of the positive realizations is proposed and illustrated by an example.

14

Computation of positive realizations for descriptor linear continuoustime systems

Kaczorek T.

Autobusy : technika, eksploatacja, systemy transportowe

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2018

|

R. 19, nr 12

428--432

EN

A new method for computation of positive realizations of given transfer matrices of descriptor linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by examples.

PL

W pracy podano nową metodę wyznaczania dodatnich realizacji dla zadanych macierzy transmitacji operatorowych deskryptowych( singularnych) ciągłych układów liniowych. Sformułowano warunki konieczne i wystarczające istnienia dodatnich realizacji dla tej klasy deskryptowych ciągłych układów liniowych. Podano procedurę wyznaczania tych realizacji. Procedura ta została zlustrowana przykładami liczbowymi.

15

A new method for computation of positive realizations of fractional linear continuous-time systems

Kaczorek T.

Archives of Control Sciences

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2018

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Vol. 28, No. 4

511--525

EN

A new method for computation of positive realizations of given transfer matrices of fractional linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by examples.

16

Application of transfer relations to structural analysis of arch bridges

Zhang J.-L., Hellmich C., Mang H. A., Yuan Y., Pichler B.

Computer Assisted Methods in Engineering and Science

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2017

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Vol. 24, no. 3

199--215

EN

Transfer relations, representing analytical solutions of the linear theory of slender circular arches, have facilitated structural analysis of segmented tunnel linings. This is the motivation to apply such relations to two examples of circular arch bridges in which the bridge deck is held from the arch by equally spaced hangers. First, the number of hangers is optimized to minimize the maximum bending moment of the arch, thus allowing the latter to come as close as possible to the desired thrust-line behavior. Next, analytical solutions for a “uniform temperature change” are derived and used to demonstrate that a temperature increase of 30 K results in minor redistributions of the inner forces but in significant additional deflections. The two examples have shown that the transfer relations are useful for structural analysis of circular arch bridges, because they reduce the complexity of the analysis to that of structural systems consisting of straight beams.

17

Exact solution to the structural instability of a parallel array of mutually attracting identical simply-supported plates

Wang X., Liu L.

Archives of Mechanics

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2017

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Vol. 69, nr 3

243--256

EN

By means of the theory of elasticity, we investigate the structural instability of a parallel array of identical simply-supported plates. One plate interacts with the neighboring plates through surface attractive forces. The proposed method is based on the 2 × 2 transfer matrix for a plate and on the solution of the generalized eigenvalue problem for the plate array. Analytical expressions of the critical interaction coefficients for two, three and four interacting plates are obtained when the end-effect of the plates at the ends of the parallel array and the surface energy of the plates are ignored. The influence of the end-effect and surface energy on the critical interaction coefficient is also numerically studied. Our solution is valid whether the plates are thin or extremely thick.

18

Wave amplitudes of temperature and heat flux in the surroundings of external walls

Garbalińska H., Strzałkowski J.

Czasopismo Techniczne. Budownictwo

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2016

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Y. 113, iss. 3-B

65--73

EN

In this paper, the thermal dynamic characteristics of exterior walls with variant concrete solutions of load-bearing layer were analysed. The main aim of this study was to compare the amplitudes of wave fluctuations of internal temperature and internal heat flux depending on the construction material used. Calculations were made for partitions with a structural layer made from lightweight concrete composites, autoclaved aerated concrete and reinforced concrete. Very good damping properties were obtained for the partitions made of concrete composites. The obtained data suggests that such solutions provide much smaller fluctuations of temperature and heat flux in comparison to materials with low specific heat.

PL

W niniejszej pracy poddano analizie zbiór danych dotyczących dynamicznych charakterystyk cieplnych ścian zewnętrznych o różnie dobranej pod względem materiałowym warstwie konstrukcyjnej. Głównym celem pracy było porównanie amplitud wahań fali temperatury wewnętrznej i wewnętrznego strumienia ciepła w zależności od użytego materiału warstwy nośnej. Rozpatrzono przegrody z warstwą konstrukcyjną wykonaną z rozmaitych lekkich kompozytów betonowych, betonów komórkowych oraz betonu zbrojonego. Bardzo dobre właściwości tłumiące przegrody uzyskano dla kompozytów betonowych. Otrzymane dane wykazują, że tego typu rozwiązania zapewniają zdecydowanie mniejsze wahania fali temperatury i strumienia ciepła w porównaniu do materiałów o niskim cieple właściwym.

19

Positive electrical circuits with zero transfer matrices and their discretization

Kaczorek T.

Computer Applications in Electrical Engineering

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2016

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Vol. 14

1--13

EN

Positive continuous–time and discrete–time linear electrical circuits with zero transfer matrices are addressed. It is shown that there exists a large class of positive electrical circuits with zero transfer matrices. The electrical circuits are unreachable, unobservable and unstable for all values of the resistances, inductances and capacitances. The discrete–time linear positive electrical circuits are introduced. It is shown that: 1) the discrete–time electrical circuit is asymptotically stable for all values of the discretization step if and only if the corresponding continuous–time electrical circuit is asymptotically stable; 2) the discretization of the continuous–time electrical circuit does not change their reachability, observability and transfer matrices.

20

A new approach to the realization problem for fractional discrete-time linear systems

Kaczorek T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2016

|

Vol. 64, nr 1

9--14

EN

A new approach to the realization problem for fractional discrete-time linear systems is proposed. A procedure for computation of fractional realizations of given transfer matrices is presented and illustrated by numerical examples.