scholarly journals Fourier Variant Homogenization Treatment of Single Impulse Boundary Effect Behaviour

2020 ◽  
Vol 22 (3) ◽  
pp. 683-690
Author(s):  
Dorota Kula ◽  
Ewaryst Wierzbicki ◽  
Joanna Witkowska-Dobrev ◽  
Łukasz Wodzyński

AbstractBoundary effect behavior understood as near-boundary suppression of boundary fluctuation loads is described in various ways depending on the mathematical representation of solutions and the type of the center. In the case of periodic composites, the homogenization method is decisive here. In the framework of the Tolerance Averaging Approach, developed by prof. Cz. Woźniak leading to an approximate model of phenomena related to periodic composites this effect is described by a homogeneous part of differential equation for fluctuation amplitudes and usually this approximate description of the boundary effect behavior is restricted to a single fluctuation. In this paper, contrary to the previous elaborations, the boundary effect is developed in the variant of the tolerance thermal conductivity model in which the temperature field is represented by the Fourier expansions composed by an average temperature with infinite number of Fourier terms imposed on the average temperature as tolerance fluctuation suppressed in the framework of the boundary effect.

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 1090403-1090404
Author(s):  
Igor V. Andrianov ◽  
Vladimir I. Bolshakov ◽  
Vladyslav V. Danishevs'kyy ◽  
Dieter Weichert

2020 ◽  
Vol 22 (3) ◽  
pp. 719-726
Author(s):  
Ewaryst Wierzbicki ◽  
Dorota Kula ◽  
Łukasz Wodzyński

AbstractThe well-known parabolic Heat Transfer Equation is a simplest recognized description of phenomena related to the heat conductivity in solids with microstructure. However, it is a tool difficult to use due to the discontinuity of coefficients appearing here. The purpose of the paper is to reformulate this equation to the form that allows to represent solutions in the form of Fourier’s expansions. This equivalent re-formulation has the form of infinite number of equations with Fourier coefficients in expansion of the temperature field as the basic unknowns. The first term in Fourier representation, being an average temperature field, should satisfy the well-known parabolic heat conduction equation with Fourier coefficients as fields controlling average temperature behavior. The proposed description takes into account changes of the composite periodicity accompanying changes in the variable perpendicular to the surfaces separating components, concerning FGM - type materials and can be treated as the asymptotic version of Heat Transfer Equation obtained as a result of a certain limit passage where the cell size remains unchanged.


2020 ◽  
Vol 22 (3) ◽  
pp. 775-788
Author(s):  
Łukasz Wodzyński ◽  
Dorota Kula ◽  
Ewaryst Wierzbicki

AbstractIn the periodic composite materials temperature or displacement fluctuations suppressed in directions perpendicular to the periodicity surfaces should expect a damping reaction from the composite. This phenomenon, known as the boundary effect behavior has been investigated only in the framework of approximated models. In this paper extended tolerance model of heat transfer in periodic composites is used as a tool allows analytical investigations of highly oscillating boundary thermal loadings. It has been shown that mentioned reaction is dual – different for even and odd fluctuations.


2021 ◽  
Vol 26 (1) ◽  
Author(s):  
Artem Dmytrovych Zubkov ◽  
Denys Dmytrovych Volkov ◽  
Vitalii Semenovych Didkovkyi

This paper considers the adaptation and application of a genetic algorithm to find the parameters of the electrodynamic transducer model. The advantages and disadvantages of this method in comparison with the classical method of identification using added mass are considered. The derivation of the suitability function for estimating the identified parameters is presented, which can also be used to identify other types of electroacoustic transducers. The theory underlying genetic algorithms has been examined and shown how genetic algorithms work by assembling the best solutions from small structural elements with excellent qualities. Next, the differences between genetic and traditional algorithms were analyzed, including population population support and the use of genetic representation of solutions. After that, the strengths of genetic algorithms were described, including the possibility of global optimization and applicability to problems with complex mathematical representation or without representation at all, and noise resistance. Disadvantages were also highlighted: the need for special definitions and settings of hyperparameters, the danger of premature convergence. In conclusion, the situations when the use of genetic algorithms are listed This algorithm is not tied to a specific engineering or scientific field, which makes it universal, it is equally used in genetics and computer science. The parameters were determined using a genetic algorithm and compared with the more classical method of added mass for acoustics. The comparative table in the work illustrates the high accuracy of the genetic algorithm in comparison with the method of added mass. During the work on the practical part, also to improve the behavior of the model at frequencies higher than the resonant, it was decided to complicate the model of the electrical subsystem of the tranducer and introduce additional parameters: parallel resistance and parallel inductance. As a result, the complicated model began to correspond better to the measured values   in the entire frequency domain, and is therefore more accurate. This is an example of the convenience of using a genetic algorithm in the transition from identification of one model with specific parameters to another. The results of this work prove that the use of a genetic algorithm is appropriate for solving electroacoustic problems because its application allows to quickly experiment and identify more complex models for which the added mass method can not be applied. Also, in the future, genetic algorithm can be used to identify transducer models of in time domain, for example, nonlinear models of electrodynamic transducers or models in a state space, which is the subject of future research.This paper considers the adaptation and application of a genetic algorithm to find the parameters of the electrodynamic transducer model. The advantages and disadvantages of this method in comparison with the classical method of identification using added mass and the method of parameter selection BL are considered. The derivation of the fitness function for assessing the quality of the identified parameters is presented, which can also be used to identify other types of electroacoustic transducers. The directly measured values ​​for the application of the algorithm are the voltage at the terminals of the converter, the current through the coil of the converter and the displacement of the moving part of the converter. The undoubted advantage of the genetic algorithm compared to classical identification methods is its versatility and the ability to quickly adapt and configure for research and experimentation with different models and different types of transducers used in acoustics. This article describes the adaptation and application of a genetic algorithm to find parameters of an electrodynamic transducer model. The advantages and disadvantages of this method in comparison with the classical identification method using added mass are considered. The derivation of the fitness function for assessing quality of the identified parameters is presented, which can also be used to identify other types of electroacoustic transducer models.


1976 ◽  
Author(s):  
John Cotton ◽  
John Gallagher ◽  
Sandra Marshall

2013 ◽  
Vol 25 (1-2) ◽  
pp. 136-148
Author(s):  
I. V. Gryb

The concept of an explosion in freshwater ecosystems as a result of the release of accumulated energy, accompanied by the destruction of the steady climax successions of hydrocenoses is presented. The typification of local explosions as well as methods for assessing their risk during the development of river basins are shown. The change in atmospheric circulation, impaired phases of the hydrological regime of rivers, increasing the average temperature of the planet, including in Polesie to 0,6 ºC, deforestation leads to concentration and release of huge amounts of unmanaged terrestrial energy, which manifests itself in the form of disasters and emergencies. Hydroecological explosion is formed as a result of multifactorial external influence (natural and anthropogenic) on the water body in a certain period of time. Moreover, its level at wastewater discharge depends on the mass of recycled impurities and behaved processing capacity of the reservoir, and the mass of dumped on biocides and the possibility of the water flow to their dilution and to the utilization of non-toxic concentrations. In all these cases the preservation of "centers of life" in the tributaries of the first order – local fish reproduction areas contributed to ecosystem recovery, and the entire ecosystem has evolved from equilibrium to non-equilibrium with further restructuring after the explosion and environmental transition to a new trophic level. It means that hydroecological explosion can be researched as the logical course of development of living matter in abiotic environmental conditions, ending abruptly with the formation of new species composition cenoses and new bio-productivity. The buffer capacity of the water environment is reduced due to re-development and anthropic transformation of geobiocenoses of river basins, which leads to a weakening of life resistance. This applies particularly to the southern industrial regions of Ukraine, located in the arid zone that is even more relevant in the context of increased average temperature due to the greenhouse effect, as well as to Polesie (Western, Central and Chernihiv), had been exposed to large-scale drainage of 60-80th years, which contributed to the degradation of peatlands and fitostroma. Imposing the western trace of emissions from the Chernobyl accident to these areas had created the conditions of prolonged hydroecological explosion in an intense process of aging water bodies, especially lakes, change in species composition of fish fauna and the occurrence of neoplasms at the organismal level. Under these conditions, for the existence of man and the environment the vitaukta should be strengthened, i.e. buffer resistance and capacitance the aquatic environment, bioefficiency on the one hand and balanced using the energy deposited - on the other. This will restore the functioning of ecosystems "channel-floodplain", "riverbed-lake", reducing the energy load on the aquatic environment. Hydroecological explosions of natural origin can not be considered a pathology – it is a jump process of natural selection of species of biota. Another thing, if they are of anthropogenic origin and if the magnitude of such an impact is on the power of geological factors. Hydroecological explosions can be regarded as a manifestation of environmental wars that consciously or unconsciously, human society is waging against themselves and their kind in the river basins, so prevention of entropy increase in the aquatic environment and the prevention of hydroecological explosions is a matter of human survival. While the man - is not the final link in the development of living matter, it can develop without him, as matter is eternal, and the forms of its existence are different.


Author(s):  
Victor V. Yagov ◽  
Arslan R. Zabirov ◽  
Pavel K. Kanin ◽  
Maxim A. Lexin

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