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1
Content available remote Formulating of reverse task of chosen class of mechatronic systems
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2012
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tom Vol. 54, nr 1
75--82
EN
Purpose: of this paper is modelling by means of the first and second category graphs and analysis of vibrating subsystem of mechatronic systems by means of the exact and approximate methods. Design/methodology/approach: Approach was to nominate the relevance or irrelevance between the characteristics obtained by means of the exact method (only for the mechanical subsystem) and the approximate method. Such formulation concerns mostly the relevance of the natural frequencies-poles of the characteristics both mechanical subsystems and mechatronic systems. Findings: are approximate solutions requiring all the conditions for torsionally vibrating mechanical and/or mechatronic systems. It is an introduction to synthesis of these systems modelled by graphs of the considered category. Research limitations/implications: is both torsional vibrating continuous mechanical subsystem and mechatronic systems of the linear continuous type. Practical implications: of this work is to present the introduction to synthesis of considered class of mechatronic bar-systems with a constant changeable cross-section. Originality/value: Originality of such formulation is focused on the use of the different category graphs for modelling and synthesising by means of the continued fraction expansion method represented by graphs of torsionally vibrating bars to the synthesis of discrete-continuous mechatronic systems.
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tom Vol. 44, nr 1
73--79
EN
Purpose: Paper describes phenomena related to the vehicle acceleration on the curve, with the high speed, considering inertia forces and driving force. Design/methodology/approach: The phenomena were investigated with three tools: classical analytical mechanics, computer simulation and tests with physical model. Findings: Simulations and physical tests led to similar results. However, new diagonal transmission system showed advantages only on slippery surface of the test track. Nevertheless such a behavior resulted in conclusion that diagonal transmission system would be useful influencing vehicle safety, specifically at slippery roads. Practical implications: There is a possibility of diagonal transmission system application for sport vehicles to improve performance. For utilitarian vehicles increasing safety is the most important aspect, especially in cooperation with ESP system. When it comes to special and military vehicles both mentioned above features are desired. Possible power-pack application is an additional advantage. Originality/value: The goal was the comparison of standard 4x4 transmission system with unconventional patented 4x4 transmission system called diagonal one.
3
Content available remote Exact and approximate analysis of mechanical and mechatronic systems
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EN
Purpose: of this paper is to compare the transients of characteristics obtained by the approximate method and exact one and to answer to the question – if the method can be used to nominate the characteristics of mechatronic systems. Design/methodology/approach: was to nominate the relevance or irrelevance between the characteristics obtained by considered methods – especially concerning the relevance of the pole values of characteristics. The main subject of the research is the continuous torsionally vibrating bar considered as a mechanical subsystem of the mechatronic system. Findings: this approach is fact, that approximate solutions fulfill all conditions for vibrating bars and some conditions only, particularly for flexibly vibrating beams. Research limitations/implications: is that linear continuous torsionally vibrating bar is considered. Practical implications: of this study is the main point is the analysis and the examination of torsionaly vibrating continuous mechatronic systems which characteristics can be nominated with similar methods only. Originality/value: of this approach relies on the comparison of the compatibility of the characteristics of the mechatronic and mechanical systems with demanded accuracy, nominated with similar method.
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Purpose: of this paper is the application of the synthesis method according to realization of mobility or immobility function into partial fraction when the level of the denominator of characteristic is higher than the level of its numerator. Design/methodology/approach: was formulated and formalized by the problem of obtaining the "new" discrete vibrating mechanical systems with branched structures. The models of mechanical systems were represented by polar graphs. The reverse problem of dynamics of defined class of vibrating mechanical systems was also formalized and solved. Findings: this study is that the same class of polar graph is a model of mechanical system with "old" and "new" branched structure. Obtaining structures of graphs as models of mechanical systems are a physical realization of dynamical characteristics, which may be considered as the immobility or mobility function. Research limitations/implications: is that the linear vibrating discrete mechanical systems with branched structures were considered. Practical implications: of this researches was that another approach was presented, which that means unclassical method of modeling of different structures of mechanical systems in form of polar graphs was used. The used method of synthesis and the obtained results can be of some value for designers of designated class of vibrating mechanical systems. Originality/value: of this paper is that the only one polar graph is obtained as a model of not only one mechanical system. The results are obtained after distribution of two dynamical characteristics into partial fraction of finding structures of mechanical systems. This approach is other than those considered elsewhere.
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Content available remote Ocena skutków zderzenia statku ze skałą
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tom nr 2
193-201
PL
Przedstawiono sposób wyznaczania sił wewnętrznych w kadłubie statku, wywołanych zderzeniem kadłuba ze skałą. Opis zjawiska zderzenia oraz ocenę jego skutków oparto na analitycznym i numerycznym całkowaniu równań ruchu kadłuba modelowanego liniowo-sprężystą, cienkościenną belką. Posługując się modelem materiału sprężysto-plastycznego oraz metodą elementów skończonych, określono także wielkości obciążeń powodujących trwałe odkształcenia dna ładowni.
EN
Stress determination in the ship's hull during the collision with a rock is presented. The description of the crash phenomena and the results assessment is based on the numerical and analytical integration of the moving equations of the hull modelled with the linear-elastic thin-walled beam. Using the elasto-plastic material model and the finite element method, the loading caused permanent deflection of the cargo hold inner bottom plating has been calculated.
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Content available remote Modified strip saturation model for a cracked piezoelectric strip
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EN
Purpose: The investigations aim to propose a model for arresting an electrical opening of a crack which weakens a narrow, poled and infinite piezoelectric strip. The edges of the strip are subjected to uniform, constant anti-plane stresses and in-plane electrical displacements. Design/methodology/approach: The loads applied at the edges of the strip open the crack in a self-similar fashion. Consequently at each tip of the crack a saturation zone protrudes. To stop the crack from further opening the rims of developed saturation zones are subjected to normal, cohesive linearly varying saturation limit electric displacement. The edges of the strip are subjected to anti-plane deformation and in-plane electrical displacement. Fourier integral transform method employed reduces the problem to the solution of a Fredholm integral equation of second kind. Findings: The electrical displacement, stress intensity factor, the saturation zone length, crack opening displacement and crack growth rate have been calculated. The results obtained presented graphically, analysed and concluded. Research limitations/implications: The ceramic used for strip is being assumed to be electrically more brittle. The investigations are carried at this level in the present paper. Also the small scale electrical yielding is considered. Consequently the developed saturation zone is proposed to lie in a line segment ahead of crack. Practical implications: Piezoelectric ceramics being widely used as transducers. Their wide utility has prompted to study many attires of such ceramic and one such attire is fracture mechanics of these ceramics. Originality/value: The paper gives an assessment of the electrical load necessary to arrest the electrical crack opening. The investigations are useful to smart material design technology where sensors and actuators are manufactured.
7
Content available remote Characteristics of discrete-continuous flexibly vibrating mechatronic system
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tom Vol. 28, nr 1
43-46
EN
Purpose: The purpose of this paper is application of approximate method of solving the task of assignment the frequency-modal analysis and characteristics of flexibly vibrating mechatronic system. Design/methodology/approach: The main approach of the subject was to formulate and solve the problem in the form of set of differential equation of motion and state equation of considered mechatronic model of object. Galerkin's solving method has been used. The considered flexibly vibrating mechanical system is a continuous beam, clamped at one of its end. Integral part of mechatronic system is a transducer, extorted by harmonic voltage excitation, to be perfectly bonded to the beam surface. Findings: The parameters of the transducer have important influence on values of natural frequencies and on form of characteristics of the discussed mechatronic system. Research limitations/implications: In the paper the linear mechanical subsystem and linear electric subsystem of mechatronic system has been considered, however for this kind of systems the approach is sufficient. Practical implications: The methods of analysis and obtained results can be base on design and investigation for this type of mechatronic systems. Originality/value: The mechatronic system formed from mechanical and electric subsystems with electromechanical bondage has been considered. This approach is different from those considered so far.
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Content available remote Crack arrest saturation model under combined electrical and mechanical loadings
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EN
Purpose: The investigation aims at proposing a model for cracked piezoelectric strip which is capable to arrest the crack. Design/methodology/approach: Under the combined effect of electrical and mechanical loadings applied at the edges of the strip, the developed saturation zone is produced at each tip of the crack. To arrest further opening of the crack, the rims of the developed saturation zones are subjected to in-plane cohesive, normal uniform constant saturation point electrical displacement. The problem is solved using Fourier integral transform method which reduces the problem to the solution of Fredholm integral equation of the second kind. This integral equation in turn is solved numerically. Findings: The expressions are derived for different intensity factors and energy release rate. A qualitative analysis of the parameters affecting the arrest of opening of the crack and fatigue crack growth with respect to strip thickness and material constants are presented graphically. Research limitations/implications: The investigations are carried out by considering the material electrical brittle. Consequently, the zones protrude along the straight lines ahead of the crack tips. And further, the small scale electrical yielding conditions are used. Practical implications: Piezoelectric materials are widely getting used nowadays, even in day to day life like piezoelectric cigarette lighter, children toys etc. And, its advance used in technology like transducers, actuators has been already in progress. So, the aspect of cracking of piezoelectric materials are of great practical importance. Originality/value: The piezoelectric material under the combined effect of electrical and mechanical loadings gives the assessment of electrical displacement which is required to arrest the crack. The various useful interpretations are also drawn from the graphs.
9
Content available remote Analysis of complex damped longitudinally vibrating systems in transportation
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EN
Purpose: of this thesis is dynamical analysis of complex systems in transportation. Analyzed systems are composed of rotatable rods. Transportation was defined as main motion of rods and the overall system. Design/methodology/approach: The dynamical flexibility method is a leading methodology for dynamic analysis of considered systems. For solving equations of motion to dynamical flexibility the Galerkins method was used. Findings: There were considered systems consisted of rods. Rods are rotated first round the origin of global reference frame simultaneously, the attached point and further ones round the end of the previous one. Charts of dynamic characteristics, in a form of dynamic flexibility as function of frequency and mathematical models were shown in this article. Research limitations/implications: All multi-body systems components were simple linear homogeneous rods, the first one as the fixed rod and next ones treated as free-free rods. Transportation was limited to plane rotational motion round the Z axis of global reference frame. Future works would consider complex systems with geometrical and physical nonlinearity. Practical implications: of presented analysis are derivation of multi-body rod systems of dynamic flexibility. Dynamic flexibility can be used in designing process. Presented mathematical models may be used for implementation in numerical applications and for automating some calculations in this type of systems. Originality/value: In the mathematical model the damping forces were taken into consideration and the dynamic flexibility of complex systems was derived.
10
Content available remote Investigation of flexibly vibrating subsystem of mechatronic system
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tom Vol. 34, nr 1
55-62
EN
Purpose: of this paper is to investigate the transients of characteristics of vibrating beams obtained by the exact and approximate methods and to answer to the question – if the method can be used to nominate the characteristics of mechatronic systems. Design/methodology/approach: was to nominate the relevance or irrelevance between the characteristics obtained by considered methods – especially concerning the relevance of the natural frequencies-poles of characteristics of mechanical part of mechatronic system. The main subject of the research is the continuous vibrating beam. Findings: this approach is fact, that approximate solutions fulfill all conditions for vibrating beams and some conditions only, particularly for vibrating beams as the subsystems of mechatronic systems. Research limitations/implications: is that linear continuous flexibly vibrating beam is considered. Practical implications: of this study is the main point is the analysis and the examination of flexibly vibrating discrete-continuous mechatronic systems which characteristics can be nominated with approximate methods only. Originality/value: of this approach relies on the comparison of the compatibility of the characteristics of the mechatronic and mechanical systems with demanded accuracy, nominated with approximate method.
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Content available remote Thermo-mechanical fatigue conditions of power plant components
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EN
Purpose: The main purpose of this work is the description of the mechanical behaviour of power plant components working under mechanical and thermal loading that cause the thermo-mechanical fatigue fracture in selected areas of the component surfaces. Design/methodology/approach: The computer modelling has been used to describe the local stress-strain behaviour of the chosen component. Findings: The values of variable in time temperature strains and stresses in selected points of the power plant header were determined. The points were located at the edges of holes through which water steam is supplied and carried away, where under use conditions the presence of cracks can be observed. That stresses and mechanical strains caused by the influence of a non-uniform temperature field may be significantly higher in comparison with the stresses and strains caused by the pressure inside the analysed component. Tensile thermal stresses of high values are created especially under conditions of sudden cooling during unsteady work of a power unit. Research limitations/implications: The possibility of applying the durability criteria currently assumed in standards still requires justification and confirmation in laboratory and industrial conditions to be closer to the real components behaviour. In such situation the presented analysis is the part of the complex investigation method which main purpose is increasing accuracy of the TMF process description and thermo-mechanical life assessment. Practical implications: The calculations carried out may constitute a basis for developing a material test parameters which would bring closer the fatigue conditions appearing locally in the analysed components. The method of stress-strain behaviour analysis used in the paper could be useful in the practical cases when the real components mechanical behaviour would be analysed. Originality/value: The main value of this paper is the own method of the mechanical behaviour analysis of the power plant component. This method includes the temperature fields analysis taking into account the boundary conditions based on the operation parameter data and the thermoplastic material model. The material stress-strain behaviour has been treated as the local phenomenon, that could be modelled by FEM.
12
Content available remote Dynamical flexibility of the free-free damped rod in transportation
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EN
Purpose: of this thesis is derivation of dynamical flexibility of the free-free rod system in transportation. The well-known problem of dynamical analysis of systems in rotational transportation was developed in this work to systems with taking into consideration damping forces. Design/methodology/approach: The dynamical flexibility method was used to analysis of the free-free rod’s vibrations. Mathematical models derived in previous articles were used to derivation of the dynamical flexibility. Considerations were done by the Galerkin’s method. Findings: There were considered systems in rotational motion treated in this thesis as main transportation. Dynamical characteristics in form of dynamical flexibility as function of frequency and mathematical models were presented in this work. Research limitations/implications: Analyzed systems were simple linear homogeneous not supported rods. Working motion was limited to plane rotational motion. Future works would consider complex systems and nonlinearity. Practical implications: of derived dynamical characteristics can easily support designing process and can be put to use in stability analysis and assigning stability zones. Thank to derived mathematical models the numerical applications can be implemented and some calculations can be automated. Originality/value: Analyzing models are rotating flexible free-free rods with taking into consideration the damping forces.
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Content available remote Description of the deformation process under thermo-mechanical fatigue
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EN
Purpose: The main problem adressed in the paper is the description of a deformation process under the conditions of mechanical and thermal interactions. Design/methodology/approach: The mathematical modelling has been used to describe the stress-strain behaviour of materials. The method of fatigue testing has been adopted to determine experimentally stress-strain characteristics. The method based on the long term own experience in thermo-mechanical investigations and new European Code-of-Practice for Thermo-Mechanical Fatigue Testing. Findings: An appropriate model description has been developed. Fatigue examinations of the P91 steel that is used in power industry, were carried out. The validation of the model has been performed. So far, experimental verification of the usefulness of the model description to determine the stress-strain characteristics' course for a selected value of the phase shift angle between the temperature and total strain cycles has been made. It has been found that the proposed model reflects the deformation process nature very well in variable temperature, strain and stress conditions. Hence, a conclusion seems to be justified that the approach presented in the paper could constitute the right basis for appropriate constitutive equations, which depict the material behaviour under thermo-mechanical conditions. Research limitations/implications: The developed description should be useful in problems of fatigue behaviour predictions of materials under different mechanical and thermal loadings in industry practical applications and in research problems connected for instance with fatigue life criteria description and validation. Originality/value: The new material characteristics have been shown in the work and the own new method of the material fatigue behaviour prediction. The work is adressed to researches interested in problems of material testing and material behaviour prediction under different loadings that we can meet in the operation practice.
14
Content available remote Prototype magnetorheological fluid damper for active vibration control system
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EN
Purpose: The paper presents a concept of a system for isolation from external vibration sources with use of a magnetorheological (MR) dampers. Design/methodology/approach: Results of experimental studies of a prototype magnetorheological damper at various magnitudes of control current and the manner of modelling electromagnetic phenomena occuring in the damper are presented in this paper. The effect of magnetic field on magnetorheological fluid is modelled by the finite element method. The mathematical model of the system as well as the damper model are outlined along with the relevant control facilities. Numerical simulations were carried out for an exemplary excitation. Findings: The elaborated damper and applied control algorithms substantially infuences the values for velocities and accelerations. Incorporation of a controllable damper into the stabilization system significantly decreases displacements of the mass to be stabilized being the results of shocks and bumps caused by excitations w(t) as a compared to similar displacement of the same mass when only a passive damper was used. Research limitations/implications: For the future research it is necessary to improve characteristics of elaborated damper in order to improve its efficiency. Practical implications: Many mechanical systems should separate from sources of vibrations. The active or semiactive vibration control systems offer a number of advantages as compared with passive systems so that better efficiency of vibration damping is assured. Originality/value: The paper presents new concept of vibration damper with magnetorheological fluids and way of its application in industrial practice.
15
Content available remote Dynamical flexibilities of mechanical rotational systems
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EN
Purpose: of this work is to present dynamical flexibilities of rotational beams and rods systems. The results of mathematical calculations were presented in the form of dynamical flexibility of analyzed systems. In final solution there were took into consideration the interactions between the major motions and local vibrations of subsystems. Design/methodology/approach: The dynamical flexibilities were derived by the Galerkin's method. The dynamical flexibilities for example numerical cases were presented onto charts of attenuation-frequency characteristics. The mathematical models were derived on the basis of known equations of motion derived in previous thesis's. Findings: After analysis of characteristics we can observe the transportation effect. We can notice additional poles on the characteristic of dynamical flexibility characteristics and after increasing angular velocity created modes symmetrically propagate from the origin mode and instead of the original mode there is created a zero's amplitude. Research limitations/implications: Analyzed systems are beams and rods in rotational motion. Motion was limited to plane motion. Future works will be connected with consideration of complex systems. Practical implications: of derived dynamical flexibilities of free-free and fixed beams and rods systems is a possibility of derivation of the stability zones of analyzed systems and derivation of eigenfrequencies and zeros in the function of angular velocity of work motion. Originality/value: Models analyzed in this thesis apply to rotating rod and beam systems with taking into consideration the transportation effect. This new approach of analyzing rod and beam systems can be put to use in modelling, analyzing and designing machines and mechanisms with rotational elements.
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EN
Purpose: The purpose of this paper is to compare the transients of characteristics obtained by the approximate and exact method and to answer to the question - if the method can be used to nominate the characteristics of mechatronic systems. Design/methodology/approach: The main approach to the problem is to nominate the relevance or irrelevance between the characteristics obtained by different methods - especially the relevance of the pole values of characteristics. The main subject of the research is the continuous torsionally vibrating bar considered as a mechanical subsystem of the mechatronic system. Findings: The values of zeroes and poles of continuous mechanical system depend on the boundary conditions. Foreseeing approximate solutions fulfill some conditions only, particularly for flexibly vibrating beams. Research limitations/implications: The linear continuous torsionally vibrating bar is considered. Practical implications: The main point is the analysis and the examination of torsionaly vibrating continuous mechatronic systems which characteristics can be nominated with approximate methods only. Originality/value: The originality of the approach relies on the comparisation of the compatibility of the characteristics of the mechatronic and mechanical systems with demanded accuracy, nominated with the same approximate method.
17
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EN
Purpose: The paper describes the method and corresponding software used for modelling and vibration analysis of mechanical systems. As an example the study on the modelling of a vibrating system in a form of a passenger car was discussed with determination of the characteristics describing its vibrations and resonance zones. Design/methodology/approach: The software described in the article uses the matrix hybrid graphs method and matrix block diagrams method for making analysis of mechanical systems vibrations. For numerical calculations the system is represented in the form as a matrix block diagram, and is analysed in detailed way in the Matlab-SIMULINK environment. Findings: Numerical software packages give possibility to analyse vibrations of mechanical systems or of their parts exposed to kinematic and dynamic excitations. Research limitations/implications: Time responses of the vibrations of the passenger car system model evoked by various types of excitations are presented, as well as the amplitude-frequency -phase characteristics (a-f-p). Originality/value: The paper constitutes the source of information into the theory and practice of mechanical vibrations as well as professional computer software as a tool enabling the determination of the time responses and the a-f-p characteristics of machine and equipment parts.
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Content available remote Influence of piezoelectric on characteristics of vibrating mechatronical system
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tom Vol. 17, nr 1-2
229--232
EN
Purpose: Application of approximate method was main purpose of work to solution task of assignment of frequency-modal analysis and characteristics of mechatronical system. Design/methodology/approach: The problem in the form of set of differential equation of motion and state equation of considered mechatronical model of object has been formulated and solved. Galerkin’s method to solving has been used. The considered torsionally vibrating mechanical system is a continuous bar of circular cross-section, clamped on one end. A ring transducer, which is the integral part of mechatronical system, extorted by harmonic voltage excitation is assumed to be perfectly bonded to the bar surface. Findings: Parameters of the transducer have important influence of values of natural frequencies and on form of characteristics of considered mechatronical system. The poles of dynamical characteristic calculated by mathematical exact method and the Galerkin’s method have approximately the same values. The results of the calculations were not only presented in mathematical form but also as a transients of examined dynamical characteristic which are function of frequency of assumed excitation. Research limitations/implications: In the paper the linear mechatronical system has been considered, but for this kind of systems the approach is sufficient. Practical implications: In article other approach is presented, that means in domain frequency spectrum the analysis has been considered. Originality/value: The mechatronical system created from mechanical and electrical subsystems with electromechanical bondage has been considered. This approach is other from considered so far. Using methods and obtained results can be value for designers of mechatronical systems.
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Content available remote Nonlinear analysis of functionally graded beams
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EN
Purpose: It is the intention of the present study to examine the effect of geometric nonlinearity on displacements and stresses in beams made of functionally graded materials (FGMs) subjected to thermo-mechanical loadings. Design/methodology/approach: The nonlinear strain-displacement relations are used to study the effect of geometric nonlinearity. Temperature distribution through the thickness of the beams in thermal loadings is obtained by solving the one-dimensional heat transfer equation. Then the equilibrium equations are obtained within the framework of the first-order shear deformatyion beam theory (FSDBT) and then solved exactly and also by using a perturbation technique. The results obtained from these two methods are compared for various loadings and boundary conditions. Findings: The numerical results showed that the nonlinearity effect on the displacements and stresses of the beams is significant. Also the effects of material constant n and the boundary conditions on the nonlinear bending behavior of the beams are determined. Research limitations/implications: The exact solution method of nonlinear equilibrium equations can only be developed for composite beams with the same boundary conditions at the ends. Practical implications: It is showed that for the maximum deflections greater than 0.3h a nonlinear solution is required. Originality/value: The paper introduces a new method to obtain analytical solution for nonlinear equilibrium equations. This method can be used in developing higher-order shear deformation and layerwise theories.
PL
W pracy przedstawiono zastosowanie zmodyfikowanej metody wymuszeń okresowych do określenia dyfuzyjności cieplnej wody. Eksperyment objął przedział temperatury od -13,6°C do +12,0°C. Dyfuzyjność cieplną wyznaczono z danych zarówno amplitudowych, jak i fazowych. W odróżnieniu od klasycznego sposobu postępowania, w obliczeniach wykorzystano nieprzybliżone zależności modelu analitycznego generujące równania przestępne. Badania potwierdziły skuteczność zastosowanej metody badań, która może być wykorzystana do zweryfikowania dotychczas publikowanych danych.
EN
The modified periodic temperature oscillation i.e. Angstrom technique at scanning mode operation has been applied to perform continuous measurements of the thermal diffusivity of water. The investigations has been done at cooling from 12,0°C to -13,6°C. The thermal diffusivity has been calculated independently from two transcendental relations based on the measured amplitude attenuation and the measured phase shift of the temperature oscillation respectively. The experiments have proved performance of the applied method for systematic studies of thermophysical properties of ice accretions. Unique results of the thermal diffusivity of water supercooled to about -5°C have been obtained also.
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