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On multi-Jensen functions and Jensen difference
Krzysztof Ciepli\'nski 대한수학회 2008 대한수학회보 Vol.45 No.4
In this paper we characterize multi-Jensen functions f : V n→ W, where n is a positive integer, V,W are commutative groups and V is uniquely divisible by 2. Moreover, under the assumption that f : R → R is Borel measurable, we obtain representation of f (respectively, f, g, h : R → R) such that the Jensen difference [수식] (respectively, the Pexider difference [수식] takes values in a countable subgroup of R. In this paper we characterize multi-Jensen functions f : V n→ W, where n is a positive integer, V,W are commutative groups and V is uniquely divisible by 2. Moreover, under the assumption that f : R → R is Borel measurable, we obtain representation of f (respectively, f, g, h : R → R) such that the Jensen difference [수식] (respectively, the Pexider difference [수식] takes values in a countable subgroup of R.
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Analysis of the Material and Design Modifications Influence on Strength of the Cycloidal Gear System
Krzysztof Biernacki 한국정밀공학회 2015 International Journal of Precision Engineering and Vol. No.
The working unit of the hydraulic gerotor machine is a system of cycloidal gears. In the paper, ways of increasing the load-carryingcapacity of the plastic cycloidal gears have been presented. The objective has been achieved through of structural and materialmodifications. The modifications were introduced while making the numerical models of the cycloidal gear system. The fundamentalfeature of the modifications is the combination of a plastic and a steel core in the design of the cycloidal gear system. While examiningthe system, the influence of the plastic-steel combination on the stress and deformation distributions in the operation of the cycloidalgears was verified. The numerical analysis was conducted using the finite elements method. The results of the analysis show that theintroduction of the modifications strengthens the cycloidal gear system. Therefore, the conclusion that a system can work in the fluidpower gerotor machines dedicated to operating at higher working pressure p seems justified. A result of the analysis is a presentationof solutions which will enable the strengthening and a higher load-carrying capacity of the gear system. Another finding of theresearch was determination of the maximum value of working pressure p at which the hydraulic gerotor machines with the modifiedcycloidal gears can operate.
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An application of operational deflection shapes and spatial filtration for damage detection
Krzysztof Mendrok,Jeremi Wójcicki,Tadeusz Uhl 국제구조공학회 2015 Smart Structures and Systems, An International Jou Vol.16 No.6
In the paper, the authors propose the application of operational deflection shapes (ODS) for the detection of structural changes in technical objects. The ODS matrix is used to formulate the spatial filter that is further used for damage detection as a classical modal filter (Meirovitch and Baruh 1982, Zhang et al. 1990). The advantage of the approach lies in the fact that no modal analysis is required, even on the reference spatial filter formulation and other components apart from structural ones can be filtered (e.g. harmonics of rotational velocity). The proposed methodology was tested experimentally on a laboratory stand, a frame-like structure, excited from two sources: an impact hammer, which provided a wide-band excitation of all modes, and an electro-dynamic shaker, which simulated a harmonic component in the output spectra. The damage detection capabilities of the proposed method were tested by changing the structural properties of the model and comparing the results with the original ones. The quantitative assessment of damage was performed by employing a damage index (DI) calculation. Comparison of the output of the ODS filter and the classical modal filter is also presented and analyzed in the paper. The closing section of the paper describes the verification of the method on a real structure – a road viaduct.
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Krzysztof Magnucki,Pawel Jasion,Waclaw Szyc,Mikolaj Jan Smyczynski 국제구조공학회 2014 Steel and Composite Structures, An International J Vol.16 No.3
The strength and buckling problem of a five layer sandwich beam under axial compression or bending is presented. Two faces of the beam are thin aluminium sheets and the core is made of aluminium foam. Between the faces and the core there are two thin binding glue layers. In the paper a mathematical model of the field of displacements, which includes a share effect and a bending moment, is presented. The system of partial differential equations of equilibrium for the five layer sandwich beam is derived on the basis of the principle of stationary total potential energy. The equations are analytically solved and the critical load is obtained. For comparison reasons a finite element model of the beam is formulated. For the case of bended beam the static analysis has been performed to obtain the stress distribution across the height of the beam. For the axially compressed beam the buckling analysis was carried out to determine the buckling load and buckling shape. Moreover, experimental investigations are carried out for two beams. The comparison of the results obtained in the analytical and numerical (FEM) analysis is shown in graphs and figures. The main aim of the paper is to present an analytical model of the five layer beam and to compare the results of the theoretical, numerical and experimental analyses.
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Krzysztof Waśkowski 한국슬라브어학회 2021 슬라브어연구 Vol.26 No.2
The aim of the article is to reconstruct the understanding of the Polish concept of PEACE in the 16th century. Considerations – due to the material base – fall within the mainstream analyses in the field of historical semantics, although they are not subordinated to the dynamic aspect. The article tries to capture the features of the concept on the basis of the semantic properties of words, typical for an arbitrarily selected synchronous plane, and based only on a certain type of linguistic data: collocations of Polish nouns pokój [En. Peace] and mir and their textual use. The research material was excerpted from the Dictionary of the Polish Language of the 16th Century edited by Maria Renata Mayenowa. On the basis of the observed word combinations and their contexts, it can be seen that the sixteenth-century PEACE was perceived as one of the basic values, a universal and unambiguously positive state. Its positive valorisation can be determined on the basis of collocations with adjectives evaluating positively (dobry [En. good], najlepszy [En. best], najwiętszy [En. most sacred], łaskawy [En. gracious], przyjemny [En. pleasant], wdzięczny [En. grateful]) and taking into account synonymic chains (przyjacielstwo i mier [En. friendship and accord], pokój i bezpieczeństwo [En. peace and security], pokój i jedność [En. peace and unity], zdrowie i pokój [En. health and peace]). In the analysed material, no collocation with lexemes with the opposite evaluation vector has been noticed. Moreover, the excerpted linguistic data made it possible to state that although the 16th-century PEACE was considered a universal value, it was not an absolute and permanent state. This conclusion was confirmed by connections such as pokój złaman jest [En. peace was broken], zgwałcenie pokoju pospolitego [En. violation of the common peace], pokój targać [En. tearing up peace], pokój wzruszan bywa [En. peace is sometimes shaken], recorded in the texts of eminent Polish humanists of the golden age, commenting on the socio-political situation of Poland at that time. Moreover, the lexical data confirmed the internal division of the PEACE category into INDIVIDUAL PEACE and SOCIAL PEACE, which can be considered stable. The analysis of the material also made it possible to conclude that an attempt to approach PEACE holistically in the diachronic aspect requires detailed research that could become the basis of a linguistic synthesis, preceded, however, by an analysis of the literature in the field of political, social and ethical sciences. The description of the variability in understanding the concept would thus complement the state of knowledge about PEACE, developed on the basis of related disciplines within humanities and social sciences.
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Krzysztof Magnucki,Wlodzimierz Stawecki,Jerzy Lewinski 국제구조공학회 2020 Steel and Composite Structures, An International J Vol.34 No.6
The subject of the paper is a circular plate with symmetrically thickness-wise varying mechanical properties. The plate is simply supported and carries a concentrated force located in its centre. The axisymmetric bending problem of the plate with consideration of the shear effect is analytically and numerically studied. A nonlinear function of deformation of the straight line normal to the plate neutral surface is assumed. Two differential equations of equilibrium based on the principle of stationary potential energy are obtained. The system of equations is analytically solved and the maximum deflections and shear coefficients for example plates are derived. Moreover, the maximum deflections of the plates are calculated numerically (FEM), for comparison with the analytical results.
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Control of chaotic dynamics by magnetorheological damping of a pendulum vibration absorber
Krzysztof Kecik 국제구조공학회 2014 Structural Engineering and Mechanics, An Int'l Jou Vol.51 No.5
Investigations of regular and chaotic vibrations of the autoparametric pendulum absorber suspended on a nonlinear coil spring and a magnetorheological damper are presented in the paper. Application of a semi-active damper allows controlling the dangerous motion without stooping of system and additionally gives new possibilities for designers. The investigations are curried out close to the main parametric resonance. Obtained numerical and experimental results show that the semi-active suspension may reduce dangerous motion and it also allows to maintain the pendulum at a given attractor or to jump to another one. Moreover, the results show that, for some parameters, MR damping may transit to chaotic motions.
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