Jerzy Margielewicz - Academia.edu (original) (raw)
Papers by Jerzy Margielewicz
Sensors
The subject of the research contained in this paper is a new design solution for an energy harves... more The subject of the research contained in this paper is a new design solution for an energy harvesting system resulting from the combination of a quasi-zero-stiffness energy harvester and a two-stage flexible cantilever beam. Numerical tests were divided into two main parts-analysis of the dynamics of the system due to periodic, quasiperiodic, and chaotic solutions and the efficiency of energy generation. The results of numerical simulations were limited to zero initial conditions as they are the natural position of the static equilibrium. The article compares the energy efficiency for the selected range of the dimensionless excitation frequency. For this purpose, three cases of piezoelectric mounting were analyzed-only on the first stage of the beam, on the second and both stages. The analysis has been carried out with the use of diagrams showing difference of the effective values of the voltage induced on the piezoelectric electrodes. The results indicate that for effective energy ...
Sensors
The subject of the model research contained in this paper is a new design solution of the energy ... more The subject of the model research contained in this paper is a new design solution of the energy harvesting system with a star-shaped structure of elastic elements and variable configuration. Numerical experiments focused mainly on the assessment of the configuration of elastic elements in the context of energy harvesting efficiency. The results of computer simulations were limited to zero initial conditions as it is the natural position of the static equilibrium. The article compares the energy efficiency for the selected range of the dimensionless excitation frequency. For this purpose, four cases of elastic element configurations were compared. The results are visualized based on the diagram of RMS voltage induced on piezoelectric electrodes, bifurcation diagrams, Lyapunov exponents, and Poincaré maps, showing the impact of individual solutions on the efficiency of energy harvesting. The results of the simulations show that the harvester’s efficiency ranges from 4 V to 20 V depen...
Pain Research and Management
Mandible displacement is known to correlate with otological conditions such as pain in the ear ca... more Mandible displacement is known to correlate with otological conditions such as pain in the ear canal, hearing loss, or tinnitus. The present work aimed to determine the association between the displacement of the condyle in a temporomandibular joint, the structure and position of the petrotympanic fissure (PTF), and comorbid tinnitus in patients affected by temporomandibular joint and muscle disorder (TMD). We enrolled 331 subjects with TMD (268 women and 63 men). The average age of women was 40.8 ± 16.8 years (range 13–88), whereas the average age of the examined men was 38 ± 14 years (range 13–74). We performed imaging studies of the facial part of the skull in the sagittal plane using a volumetric imaging method and a large imaging field (FOV) of 17 cm × 23 cm. The habitual position of the mandible was determined and used as a reference. Based on the imaging results, we developed a classification for the topography and the structure of the petrotympanic fissure. Thirty-three TMD ...
Energies, 2021
A method for selecting dynamic parameters and structures of drive systems using the synthesis alg... more A method for selecting dynamic parameters and structures of drive systems using the synthesis algorithm is presented. The dynamic parameters of the system with six degrees of freedom, consisting of a power component (motor) and a two-speed gearbox, were determined, based on a formalized methodology. The required gearbox is to work in specific resonance zones, i.e., meet the required dynamic properties such as the required resonance frequencies. In the result of the tests, a series of parameters of the drive system, defining the required dynamic properties such as the resonance and anti-resonance frequencies were recorded. Mass moments of inertia of the wheels and elastic components, contained in the required structure of the driving system, were determined for the selected parameters obtained during the synthesis.
Scientific Journal of Silesian University of Technology. Series Transport, 2014
The study was carried out computer simulations of mechatronic model bridge crane, which is intend... more The study was carried out computer simulations of mechatronic model bridge crane, which is intended to theoretical evaluation of the possibility of eliminating the mechanical vibrations affecting the operator's cab driven machine. The model studies used fixed value control, the controlled variable is selected as the vertical displacement of the cab. Also included in the research model rheological model of the operator's body. We examined four overhead cranes with lifting capacity of 50T, which are classified in accordance with the directive of the European Union concerning the design of cranes, the four classes of cranes HC stiffness. The use of an active vibration isolation system in which distinguishes two negative feedback loops, very well eliminate mechanical vibration to the operator.
Scientific Journal of Silesian University of Technology. Series Transport, 2015
This paper presents an attempt of numerical description of the active vibration isolation system ... more This paper presents an attempt of numerical description of the active vibration isolation system of railway passenger car. Computer simulations were performed for different speeds of the passenger car riding along the same track. Formal basis to solve the formulated research problem was achieved by using the law and the principles of mechanics and control theory. Model results clearly indicate that the use of active vibration reduction systems in rail transport can significantly increase comfort
Sensors, 2022
The piezoelectric energy-harvesting system with double-well characteristics and hysteresis in the... more The piezoelectric energy-harvesting system with double-well characteristics and hysteresis in the restoring force is studied. The proposed system consists of a bistable oscillator based on a cantilever beam structure. The elastic force potential is modified by magnets. The hysteresis is an additional effect of the composite beam considered in this system, and it effects the modal solution with specific mass distribution. Consequently, the modal response is a compromise between two overlapping, competing shapes. The simulation results show evolution in the single potential well solution, and bifurcations into double-well solutions with the hysteretic effect. The maximal Lyapunov exponent indicated the appearance of chaotic solutions. Inclusion of the shape branch overlap parameter reduces the distance between the external potential barriers and leads to a large-amplitude solution and simultaneously higher voltage output with smaller excitation force. The overlap parameter works in th...
Advances in Mechanism and Machine Science, 2019
In this work, model tests were carried out, which are mainly focused on the identification of zon... more In this work, model tests were carried out, which are mainly focused on the identification of zones in which the motion of gear transmission occurs chaotically. To identify chaotic areas a procedure was used to estimate the largest Lyapunov exponent. The formulated gear model includes variable meshing stiffness and gear backlash characteristics, which was approximated by a logarithmic function. The method of bond graphs was used to derive differential equations of motion, on the basis of which the effect of the error of cooperation between gears and the average load transmitted by the gear was examined. It has been shown that the load conditions affecting the gears have a significant effect on the character of the model solution that maps the gear dynamics. This influence is particularly noticeable in the bifurcation diagrams of steady states. On this basis, the values of the control parameter ω have been determined, for which the Poincare cross-sections assume the geometric structu...
Streszczenie. Zagadnienia przedstawione w niniejszym artykule dotyczą oceny wlaściwości mechanicz... more Streszczenie. Zagadnienia przedstawione w niniejszym artykule dotyczą oceny wlaściwości mechanicznych liny. Punktem wyjściowym bylo przeprowadzenie badan laboratoryjnych, ktore zrealizowano w Centrum Badan i Dozoru Gornictwa Podziemnego Sp. z o.o. w Myslowicach-Brzezince. Niezbedne badania lin przeprowadzono na specjalistycznej maszynie wytrzymalościowe przy roznych wartościach wspolczynnikow bezpieczenstwa, obciązając ją cyklicznie. Na podstawie zarejestrowanych danych sporządzono charakterystyki silowo-przemieszczeniowe, bedące podstawą identyfikacji wspolczynnikow rozproszenia energii oraz charakterystyk statycznych. Slowa kluczowe: model, lina, modelowanie, identyfikacja
Energies, 2021
In this paper, the frequency broadband effect in vibration energy harvesting was studied numerica... more In this paper, the frequency broadband effect in vibration energy harvesting was studied numerically using a quasi-zero stiffness resonator with two potential wells and piezoelectric transducers. Corresponding solutions were investigated for system excitation harmonics at various frequencies. Solutions for the higher voltage output were collected in specific branches of the power output diagram. Both the resonant solution synchronized with excitation and the frequency responses of the subharmonic spectra were found. The selected cases were illustrated and classified using a phase portrait, a Poincaré section, and recurrence plot (RP) approaches. Select recurrence quantification analysis (RQA) measures were used to characterize the discussed solutions.
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2021
This paper investigates the nonlinear dynamics of a flexible tyre coupling via computer modelling... more This paper investigates the nonlinear dynamics of a flexible tyre coupling via computer modelling and simulation. The research mainly focused on identifying basins of attraction of coexisting solutions of the formulated phenomenological coupling model. On the basis of the derived mathematical model, and by assuming ranges of variability of the control parameters, the areas in which chaotic clutch movement takes place are determined. To identify multiple solutions, a new diagram of solutions (DS) was used, illustrating the number of coexisting solutions and their periodicity. The DS diagram was drawn based on the fixed points of the Poincaré section. To verify the proposed method of identifying periodic solutions, the graphic image of the DS was compared to the three-dimensional distribution of the largest Lyapunov exponent and the bifurcation diagram. For selected values of the control parameter ω, coexisting periodic solutions were identified, and basins of attraction were plotted....
Nonlinear Dynamics, 2020
This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation... more This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation. The pendulum has two degrees of freedom: a rotational angle defined in the horizontal plane and an inclination angle defined by the pendulum with respect to the vertical z axis. The results of numerical simulations are illustrated with the mathematical model in the form of multi-colored maps of the largest Lyapunov exponent. The graphical images of geometrical structures of the attractors placed on Poincaré cross sections are shown against the maps of the resolution density of the trajectory points passing through a control plane. Drawn for a steady-state, the graphical images of the trajectory of a tip mass are shown in a three-dimensional space. The obtained trajectories of the moving tip mass are referred to a constructed bifurcation diagram.
Nonlinear Dynamics, 2019
In this paper, model tests were carried out, which mainly focused on the numerical mapping of the... more In this paper, model tests were carried out, which mainly focused on the numerical mapping of the characteristics of the gear backlash. In particular, the effect of the approximation function on the value of the largest Lyapunov exponent was investigated. The generated multicoloured maps served as a criterion for verifying the results of the model tests. The analysis involved polynomial functions of the third degree, its modified structure, and the logarithmic equation. As a pattern to which the results of model tests were derived, the mathematical model of the gear was used, in which the characteristics of the backlash were modelled with a non-continuous function describing the so-called dead zone. We show that the dependencies described by polynomials imprecisely describe the dynamics of a single-stage gear transmission mechanism. Additionally, the value of the logarithmic coefficient, which approximates the backlash characteristics, for which the Poincare cross section corresponds with its model counterpart, is determined. The coefficient of the logarithmic function was optimized on the basis of
Mechanics, 2019
The paper presents the results of numerical investigations of the overhead travelling cranes load... more The paper presents the results of numerical investigations of the overhead travelling cranes load motion. The model studies assumes that the load is suspended on the inextensible rope. Conversely, its motion is triggered by an external moment. In addition, energy losses in the construction node connecting the rope to the drum are included. At the same time these losses were mapped through a linear viscous damper. The main objective was to evaluate the impact of individual mathematical model parameters on the dynamics of the transported load. The results were compared between two models: with/without crane structure vibrations included. The results were illustrated by multi-colored maps of the largest Lyapunov exponent, bifurcation diagrams, and Poincare cross-sections.
Scientific Journal of Silesian University of Technology. Series Transport, 2017
This paper presents the results of computer simulations of a gear model, where the variable stiff... more This paper presents the results of computer simulations of a gear model, where the variable stiffness of the meshing and backlash are considered. The outcome of such assumptions is a non-linear mathematical model in which chaotic phenomena can occur. During model studies, attention was paid to the identification of areas limited by the physical parameters, for which the analysed system behaved chaotically. To determine the ranges of irregular gear behaviour, numerical procedures were used to plot the bifurcation diagram, the Lyapunov exponent, the amplitude-frequency distribution and the Poincaré cross section.
Forschung im Ingenieurwesen, 2019
The aim of this work is to model the dynamics of flexible couplings. On the basis of a non-linear... more The aim of this work is to model the dynamics of flexible couplings. On the basis of a non-linear mathematical model solved by bond graph, the ranges of excitation frequency were determined, in which the movement of the couplings is chaotic. For three couplings, the 3D distributions of the largest Lyapunov exponent and correlation dimension diagram (CDD) were plotted. The proposed diagram (CDD) illustrates how the geometric structure of the attractor changes when the conditions of excitation change. The classic Poincare cross-section, completed by us with the density of points distribution, significantly enhances information about geometrical structures of strange attractors. It has been shown that in relation to large ranges of changes in the control parameter, the geometric structure of the strange attractor is stretched and curved. The areas with the highest densification of the Poincaré cross section are most often located in places where the chaotic attractor is curved. Untersuchung der nichtlinearen Dynamik flexibler Kopplungen mit Hilfe von Bondgraphen Zusammenfassung Ziel dieser Arbeit ist es, die Dynamik von elastischen Kupplungen zu modellieren. Anhand eines durch einen Bindungsgraphen gelösten nichtlinearen mathematischen Modells wurden die Bereiche der Anregungsfrequenz bestimmt, in denen die Bewegung der Kopplungen chaotisch ist. Für drei Kopplungen wurden die 3D-Verteilungen des größten Lyapunov-Exponenten und das Korrelationsdimensionsdiagramm (CDD) aufgezeichnet. Das vorgeschlagene Diagramm (CDD) zeigt, wie sich die geometrische Struktur des Attraktors ändert, wenn sich die Anregungsbedingungen ändern. Der von uns vervollständigte klassische Poincaré-Querschnitt mit der Dichte der Punkteverteilung verbessert die Informationen über geometrische Strukturen fremder Attraktoren erheblich. Es hat sich gezeigt, dass in Bezug auf große Änderungsbereiche der Steuerparameter die geometrische Struktur des seltsamen Attraktors gedehnt und gebogen wird. Die Bereiche mit der höchsten Verdichtung des Poincaré-Querschnitts befinden sich am häufigsten an Stellen, an denen der chaotische Attraktor gekrümmt ist.
Chaos, Solitons & Fractals, 2019
The aim of this work is to evaluate the dynamics of the quasi-zero stiffness vibration isolator, ... more The aim of this work is to evaluate the dynamics of the quasi-zero stiffness vibration isolator, with particular emphasis on the density distribution of Poincaré cross-section points for different conditions of the system's excitation. The research was mainly focused on model tests carried out to examine the structures representing the geometry of strange attractors of a quasi-zero stiffness vibration isolator. The analysed mechanical system consists of one main spring and two compensation springs. Energy losses are caused by friction at the connection points of the compensation springs and vibroisolated mass. On the basis of a formulated non-linear mathematical model, the ranges of variation of physical parameters of an external dynamic input for which the system motion is chaotic are identified. Taking into account three selected values of the dynamic input amplitude, a bifurcation diagram and a diagram defining the number of phase stream intersections (NPSI) with the abscissa of the phase plane are generated. Based on the diagrams, a solution is selected. The diagram proposed by us (NPSI) is an alternative method of identifying areas in which the system moves chaotically. The classic Poincaré cross-section combined by us with information about the density of point distribution on the trajectory intersection with the control plane serve as a basis for the assessment of evolution of the geometric structure of strange attractors. The evaluation of the density distribution of Poincaré cross-section points provides important information regarding the evolution of geometrical structures of strange attractors. It has been shown that in relation to large ranges of changes in the control parameter, the geometric structure of the strange attractor is stretched and curved. However, in the area of small changes in the control parameter, the evolution of the attractor' geometric structure can only be observed by analysing the density of point distribution on the Poincaré cross-section by the probability density function (PDF). The areas with the highest density of the Poincaré cross-section are usually located in places where the strange attractor is curved. Taking into account the practical application of research results, operational guidelines are formulated.
Advances in Clinical and Experimental Medicine, 2017
Background. Temporomandibular joint dysfunction is often related to excessive load in the stomato... more Background. Temporomandibular joint dysfunction is often related to excessive load in the stomatognathic system. Objectives. The objective of the model tests, using numeric calculations, was to assess the articular disc loads in the temporomandibular joints after prosthetic and pharmacological treatment of functional disorders of the masticatory organ. Material and methods. The study involved 10 patients, aged 21-48 years, of both sexes, randomly selected from a group of 120 patients treated with relaxation occlusal splints (60 patients, group I) and intramuscular injection of botulinum toxin type A (60 patients, group II), suffering from temporomandibular joint dysfunction with the dominant muscle component. In all subjects, a specialized functional examination was carried out. Treatment groups: occlusal splint therapy (group I) and intramuscular injection of botulinum toxin type A (group II). An assessment of the loads of 4 disc zones of the temporomandibular joints was carried out based on the results of clinical studies (phase I of the study), and numeric model tests (phase II). In the representatives of the study groups (5 patients in each group), measurements of occlusal forces and an evaluation of tension of the masseter and temporalis muscle were performed. Results. The results of the average load values for all evaluated zones of the right and left articular disc differ in a statistically significant way in favor of group II, with the exception of the external mid part of the discs. In the case of the anterior of the right disc, the load was lower in patients belonging to group I than in those obtained in group II. Conclusions. Botulinum toxin type A significantly reduces the loads within the temporomandibular joints, generated by masseter muscle hypertonia.
Experimental and Therapeutic Medicine, 2016
The present study aimed to determine the numeric projection of the function of the mandible and m... more The present study aimed to determine the numeric projection of the function of the mandible and muscle system during mastication. An experimental study was conducted on a healthy 47 year-old subject. On clinical examination no functional disorders were observed. To evaluate the activity of mastication during muscle functioning, bread cubes and hazelnuts were selected (2 cm 2 and 1.2/1.3 cm in diameter, respectively) for condyloid processing. An assessment of the activity of mastication during muscle functioning was determined on the basis of numeric calculations conducted with a novel software programme, Kinematics 3D, designed specifically for this study. The efficacy of the model was verified by ensuring the experimentally recorded trajectories were concordant with those calculated numerically. Experimental measurements of the characteristic points of the mandible trajectory were recorded six times. Using the configuration coordinates that were calculated, the dominant componential harmonics of the amplitude-frequency spectrum were identified. The average value of the dominant frequency during mastication of the bread cubes was ~1.16±0.06 Hz, whereas in the case of the hazelnut, this value was nearly twofold higher at 1.84±0.07 Hz. The most asymmetrical action during mastication was demonstrated to be carried out by the lateral pterygoid muscles, provided that their functioning was not influenced by food consistency. The consistency of the food products had a decisive impact on the frequency of mastication and the number of cycles necessary to grind the food. Model tests on the function of the masticatory organ serve as effective tools since they provide qualitative and quantitative novel information on the functioning of the human masticatory organ.
Sensors
The subject of the research contained in this paper is a new design solution for an energy harves... more The subject of the research contained in this paper is a new design solution for an energy harvesting system resulting from the combination of a quasi-zero-stiffness energy harvester and a two-stage flexible cantilever beam. Numerical tests were divided into two main parts-analysis of the dynamics of the system due to periodic, quasiperiodic, and chaotic solutions and the efficiency of energy generation. The results of numerical simulations were limited to zero initial conditions as they are the natural position of the static equilibrium. The article compares the energy efficiency for the selected range of the dimensionless excitation frequency. For this purpose, three cases of piezoelectric mounting were analyzed-only on the first stage of the beam, on the second and both stages. The analysis has been carried out with the use of diagrams showing difference of the effective values of the voltage induced on the piezoelectric electrodes. The results indicate that for effective energy ...
Sensors
The subject of the model research contained in this paper is a new design solution of the energy ... more The subject of the model research contained in this paper is a new design solution of the energy harvesting system with a star-shaped structure of elastic elements and variable configuration. Numerical experiments focused mainly on the assessment of the configuration of elastic elements in the context of energy harvesting efficiency. The results of computer simulations were limited to zero initial conditions as it is the natural position of the static equilibrium. The article compares the energy efficiency for the selected range of the dimensionless excitation frequency. For this purpose, four cases of elastic element configurations were compared. The results are visualized based on the diagram of RMS voltage induced on piezoelectric electrodes, bifurcation diagrams, Lyapunov exponents, and Poincaré maps, showing the impact of individual solutions on the efficiency of energy harvesting. The results of the simulations show that the harvester’s efficiency ranges from 4 V to 20 V depen...
Pain Research and Management
Mandible displacement is known to correlate with otological conditions such as pain in the ear ca... more Mandible displacement is known to correlate with otological conditions such as pain in the ear canal, hearing loss, or tinnitus. The present work aimed to determine the association between the displacement of the condyle in a temporomandibular joint, the structure and position of the petrotympanic fissure (PTF), and comorbid tinnitus in patients affected by temporomandibular joint and muscle disorder (TMD). We enrolled 331 subjects with TMD (268 women and 63 men). The average age of women was 40.8 ± 16.8 years (range 13–88), whereas the average age of the examined men was 38 ± 14 years (range 13–74). We performed imaging studies of the facial part of the skull in the sagittal plane using a volumetric imaging method and a large imaging field (FOV) of 17 cm × 23 cm. The habitual position of the mandible was determined and used as a reference. Based on the imaging results, we developed a classification for the topography and the structure of the petrotympanic fissure. Thirty-three TMD ...
Energies, 2021
A method for selecting dynamic parameters and structures of drive systems using the synthesis alg... more A method for selecting dynamic parameters and structures of drive systems using the synthesis algorithm is presented. The dynamic parameters of the system with six degrees of freedom, consisting of a power component (motor) and a two-speed gearbox, were determined, based on a formalized methodology. The required gearbox is to work in specific resonance zones, i.e., meet the required dynamic properties such as the required resonance frequencies. In the result of the tests, a series of parameters of the drive system, defining the required dynamic properties such as the resonance and anti-resonance frequencies were recorded. Mass moments of inertia of the wheels and elastic components, contained in the required structure of the driving system, were determined for the selected parameters obtained during the synthesis.
Scientific Journal of Silesian University of Technology. Series Transport, 2014
The study was carried out computer simulations of mechatronic model bridge crane, which is intend... more The study was carried out computer simulations of mechatronic model bridge crane, which is intended to theoretical evaluation of the possibility of eliminating the mechanical vibrations affecting the operator's cab driven machine. The model studies used fixed value control, the controlled variable is selected as the vertical displacement of the cab. Also included in the research model rheological model of the operator's body. We examined four overhead cranes with lifting capacity of 50T, which are classified in accordance with the directive of the European Union concerning the design of cranes, the four classes of cranes HC stiffness. The use of an active vibration isolation system in which distinguishes two negative feedback loops, very well eliminate mechanical vibration to the operator.
Scientific Journal of Silesian University of Technology. Series Transport, 2015
This paper presents an attempt of numerical description of the active vibration isolation system ... more This paper presents an attempt of numerical description of the active vibration isolation system of railway passenger car. Computer simulations were performed for different speeds of the passenger car riding along the same track. Formal basis to solve the formulated research problem was achieved by using the law and the principles of mechanics and control theory. Model results clearly indicate that the use of active vibration reduction systems in rail transport can significantly increase comfort
Sensors, 2022
The piezoelectric energy-harvesting system with double-well characteristics and hysteresis in the... more The piezoelectric energy-harvesting system with double-well characteristics and hysteresis in the restoring force is studied. The proposed system consists of a bistable oscillator based on a cantilever beam structure. The elastic force potential is modified by magnets. The hysteresis is an additional effect of the composite beam considered in this system, and it effects the modal solution with specific mass distribution. Consequently, the modal response is a compromise between two overlapping, competing shapes. The simulation results show evolution in the single potential well solution, and bifurcations into double-well solutions with the hysteretic effect. The maximal Lyapunov exponent indicated the appearance of chaotic solutions. Inclusion of the shape branch overlap parameter reduces the distance between the external potential barriers and leads to a large-amplitude solution and simultaneously higher voltage output with smaller excitation force. The overlap parameter works in th...
Advances in Mechanism and Machine Science, 2019
In this work, model tests were carried out, which are mainly focused on the identification of zon... more In this work, model tests were carried out, which are mainly focused on the identification of zones in which the motion of gear transmission occurs chaotically. To identify chaotic areas a procedure was used to estimate the largest Lyapunov exponent. The formulated gear model includes variable meshing stiffness and gear backlash characteristics, which was approximated by a logarithmic function. The method of bond graphs was used to derive differential equations of motion, on the basis of which the effect of the error of cooperation between gears and the average load transmitted by the gear was examined. It has been shown that the load conditions affecting the gears have a significant effect on the character of the model solution that maps the gear dynamics. This influence is particularly noticeable in the bifurcation diagrams of steady states. On this basis, the values of the control parameter ω have been determined, for which the Poincare cross-sections assume the geometric structu...
Streszczenie. Zagadnienia przedstawione w niniejszym artykule dotyczą oceny wlaściwości mechanicz... more Streszczenie. Zagadnienia przedstawione w niniejszym artykule dotyczą oceny wlaściwości mechanicznych liny. Punktem wyjściowym bylo przeprowadzenie badan laboratoryjnych, ktore zrealizowano w Centrum Badan i Dozoru Gornictwa Podziemnego Sp. z o.o. w Myslowicach-Brzezince. Niezbedne badania lin przeprowadzono na specjalistycznej maszynie wytrzymalościowe przy roznych wartościach wspolczynnikow bezpieczenstwa, obciązając ją cyklicznie. Na podstawie zarejestrowanych danych sporządzono charakterystyki silowo-przemieszczeniowe, bedące podstawą identyfikacji wspolczynnikow rozproszenia energii oraz charakterystyk statycznych. Slowa kluczowe: model, lina, modelowanie, identyfikacja
Energies, 2021
In this paper, the frequency broadband effect in vibration energy harvesting was studied numerica... more In this paper, the frequency broadband effect in vibration energy harvesting was studied numerically using a quasi-zero stiffness resonator with two potential wells and piezoelectric transducers. Corresponding solutions were investigated for system excitation harmonics at various frequencies. Solutions for the higher voltage output were collected in specific branches of the power output diagram. Both the resonant solution synchronized with excitation and the frequency responses of the subharmonic spectra were found. The selected cases were illustrated and classified using a phase portrait, a Poincaré section, and recurrence plot (RP) approaches. Select recurrence quantification analysis (RQA) measures were used to characterize the discussed solutions.
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2021
This paper investigates the nonlinear dynamics of a flexible tyre coupling via computer modelling... more This paper investigates the nonlinear dynamics of a flexible tyre coupling via computer modelling and simulation. The research mainly focused on identifying basins of attraction of coexisting solutions of the formulated phenomenological coupling model. On the basis of the derived mathematical model, and by assuming ranges of variability of the control parameters, the areas in which chaotic clutch movement takes place are determined. To identify multiple solutions, a new diagram of solutions (DS) was used, illustrating the number of coexisting solutions and their periodicity. The DS diagram was drawn based on the fixed points of the Poincaré section. To verify the proposed method of identifying periodic solutions, the graphic image of the DS was compared to the three-dimensional distribution of the largest Lyapunov exponent and the bifurcation diagram. For selected values of the control parameter ω, coexisting periodic solutions were identified, and basins of attraction were plotted....
Nonlinear Dynamics, 2020
This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation... more This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation. The pendulum has two degrees of freedom: a rotational angle defined in the horizontal plane and an inclination angle defined by the pendulum with respect to the vertical z axis. The results of numerical simulations are illustrated with the mathematical model in the form of multi-colored maps of the largest Lyapunov exponent. The graphical images of geometrical structures of the attractors placed on Poincaré cross sections are shown against the maps of the resolution density of the trajectory points passing through a control plane. Drawn for a steady-state, the graphical images of the trajectory of a tip mass are shown in a three-dimensional space. The obtained trajectories of the moving tip mass are referred to a constructed bifurcation diagram.
Nonlinear Dynamics, 2019
In this paper, model tests were carried out, which mainly focused on the numerical mapping of the... more In this paper, model tests were carried out, which mainly focused on the numerical mapping of the characteristics of the gear backlash. In particular, the effect of the approximation function on the value of the largest Lyapunov exponent was investigated. The generated multicoloured maps served as a criterion for verifying the results of the model tests. The analysis involved polynomial functions of the third degree, its modified structure, and the logarithmic equation. As a pattern to which the results of model tests were derived, the mathematical model of the gear was used, in which the characteristics of the backlash were modelled with a non-continuous function describing the so-called dead zone. We show that the dependencies described by polynomials imprecisely describe the dynamics of a single-stage gear transmission mechanism. Additionally, the value of the logarithmic coefficient, which approximates the backlash characteristics, for which the Poincare cross section corresponds with its model counterpart, is determined. The coefficient of the logarithmic function was optimized on the basis of
Mechanics, 2019
The paper presents the results of numerical investigations of the overhead travelling cranes load... more The paper presents the results of numerical investigations of the overhead travelling cranes load motion. The model studies assumes that the load is suspended on the inextensible rope. Conversely, its motion is triggered by an external moment. In addition, energy losses in the construction node connecting the rope to the drum are included. At the same time these losses were mapped through a linear viscous damper. The main objective was to evaluate the impact of individual mathematical model parameters on the dynamics of the transported load. The results were compared between two models: with/without crane structure vibrations included. The results were illustrated by multi-colored maps of the largest Lyapunov exponent, bifurcation diagrams, and Poincare cross-sections.
Scientific Journal of Silesian University of Technology. Series Transport, 2017
This paper presents the results of computer simulations of a gear model, where the variable stiff... more This paper presents the results of computer simulations of a gear model, where the variable stiffness of the meshing and backlash are considered. The outcome of such assumptions is a non-linear mathematical model in which chaotic phenomena can occur. During model studies, attention was paid to the identification of areas limited by the physical parameters, for which the analysed system behaved chaotically. To determine the ranges of irregular gear behaviour, numerical procedures were used to plot the bifurcation diagram, the Lyapunov exponent, the amplitude-frequency distribution and the Poincaré cross section.
Forschung im Ingenieurwesen, 2019
The aim of this work is to model the dynamics of flexible couplings. On the basis of a non-linear... more The aim of this work is to model the dynamics of flexible couplings. On the basis of a non-linear mathematical model solved by bond graph, the ranges of excitation frequency were determined, in which the movement of the couplings is chaotic. For three couplings, the 3D distributions of the largest Lyapunov exponent and correlation dimension diagram (CDD) were plotted. The proposed diagram (CDD) illustrates how the geometric structure of the attractor changes when the conditions of excitation change. The classic Poincare cross-section, completed by us with the density of points distribution, significantly enhances information about geometrical structures of strange attractors. It has been shown that in relation to large ranges of changes in the control parameter, the geometric structure of the strange attractor is stretched and curved. The areas with the highest densification of the Poincaré cross section are most often located in places where the chaotic attractor is curved. Untersuchung der nichtlinearen Dynamik flexibler Kopplungen mit Hilfe von Bondgraphen Zusammenfassung Ziel dieser Arbeit ist es, die Dynamik von elastischen Kupplungen zu modellieren. Anhand eines durch einen Bindungsgraphen gelösten nichtlinearen mathematischen Modells wurden die Bereiche der Anregungsfrequenz bestimmt, in denen die Bewegung der Kopplungen chaotisch ist. Für drei Kopplungen wurden die 3D-Verteilungen des größten Lyapunov-Exponenten und das Korrelationsdimensionsdiagramm (CDD) aufgezeichnet. Das vorgeschlagene Diagramm (CDD) zeigt, wie sich die geometrische Struktur des Attraktors ändert, wenn sich die Anregungsbedingungen ändern. Der von uns vervollständigte klassische Poincaré-Querschnitt mit der Dichte der Punkteverteilung verbessert die Informationen über geometrische Strukturen fremder Attraktoren erheblich. Es hat sich gezeigt, dass in Bezug auf große Änderungsbereiche der Steuerparameter die geometrische Struktur des seltsamen Attraktors gedehnt und gebogen wird. Die Bereiche mit der höchsten Verdichtung des Poincaré-Querschnitts befinden sich am häufigsten an Stellen, an denen der chaotische Attraktor gekrümmt ist.
Chaos, Solitons & Fractals, 2019
The aim of this work is to evaluate the dynamics of the quasi-zero stiffness vibration isolator, ... more The aim of this work is to evaluate the dynamics of the quasi-zero stiffness vibration isolator, with particular emphasis on the density distribution of Poincaré cross-section points for different conditions of the system's excitation. The research was mainly focused on model tests carried out to examine the structures representing the geometry of strange attractors of a quasi-zero stiffness vibration isolator. The analysed mechanical system consists of one main spring and two compensation springs. Energy losses are caused by friction at the connection points of the compensation springs and vibroisolated mass. On the basis of a formulated non-linear mathematical model, the ranges of variation of physical parameters of an external dynamic input for which the system motion is chaotic are identified. Taking into account three selected values of the dynamic input amplitude, a bifurcation diagram and a diagram defining the number of phase stream intersections (NPSI) with the abscissa of the phase plane are generated. Based on the diagrams, a solution is selected. The diagram proposed by us (NPSI) is an alternative method of identifying areas in which the system moves chaotically. The classic Poincaré cross-section combined by us with information about the density of point distribution on the trajectory intersection with the control plane serve as a basis for the assessment of evolution of the geometric structure of strange attractors. The evaluation of the density distribution of Poincaré cross-section points provides important information regarding the evolution of geometrical structures of strange attractors. It has been shown that in relation to large ranges of changes in the control parameter, the geometric structure of the strange attractor is stretched and curved. However, in the area of small changes in the control parameter, the evolution of the attractor' geometric structure can only be observed by analysing the density of point distribution on the Poincaré cross-section by the probability density function (PDF). The areas with the highest density of the Poincaré cross-section are usually located in places where the strange attractor is curved. Taking into account the practical application of research results, operational guidelines are formulated.
Advances in Clinical and Experimental Medicine, 2017
Background. Temporomandibular joint dysfunction is often related to excessive load in the stomato... more Background. Temporomandibular joint dysfunction is often related to excessive load in the stomatognathic system. Objectives. The objective of the model tests, using numeric calculations, was to assess the articular disc loads in the temporomandibular joints after prosthetic and pharmacological treatment of functional disorders of the masticatory organ. Material and methods. The study involved 10 patients, aged 21-48 years, of both sexes, randomly selected from a group of 120 patients treated with relaxation occlusal splints (60 patients, group I) and intramuscular injection of botulinum toxin type A (60 patients, group II), suffering from temporomandibular joint dysfunction with the dominant muscle component. In all subjects, a specialized functional examination was carried out. Treatment groups: occlusal splint therapy (group I) and intramuscular injection of botulinum toxin type A (group II). An assessment of the loads of 4 disc zones of the temporomandibular joints was carried out based on the results of clinical studies (phase I of the study), and numeric model tests (phase II). In the representatives of the study groups (5 patients in each group), measurements of occlusal forces and an evaluation of tension of the masseter and temporalis muscle were performed. Results. The results of the average load values for all evaluated zones of the right and left articular disc differ in a statistically significant way in favor of group II, with the exception of the external mid part of the discs. In the case of the anterior of the right disc, the load was lower in patients belonging to group I than in those obtained in group II. Conclusions. Botulinum toxin type A significantly reduces the loads within the temporomandibular joints, generated by masseter muscle hypertonia.
Experimental and Therapeutic Medicine, 2016
The present study aimed to determine the numeric projection of the function of the mandible and m... more The present study aimed to determine the numeric projection of the function of the mandible and muscle system during mastication. An experimental study was conducted on a healthy 47 year-old subject. On clinical examination no functional disorders were observed. To evaluate the activity of mastication during muscle functioning, bread cubes and hazelnuts were selected (2 cm 2 and 1.2/1.3 cm in diameter, respectively) for condyloid processing. An assessment of the activity of mastication during muscle functioning was determined on the basis of numeric calculations conducted with a novel software programme, Kinematics 3D, designed specifically for this study. The efficacy of the model was verified by ensuring the experimentally recorded trajectories were concordant with those calculated numerically. Experimental measurements of the characteristic points of the mandible trajectory were recorded six times. Using the configuration coordinates that were calculated, the dominant componential harmonics of the amplitude-frequency spectrum were identified. The average value of the dominant frequency during mastication of the bread cubes was ~1.16±0.06 Hz, whereas in the case of the hazelnut, this value was nearly twofold higher at 1.84±0.07 Hz. The most asymmetrical action during mastication was demonstrated to be carried out by the lateral pterygoid muscles, provided that their functioning was not influenced by food consistency. The consistency of the food products had a decisive impact on the frequency of mastication and the number of cycles necessary to grind the food. Model tests on the function of the masticatory organ serve as effective tools since they provide qualitative and quantitative novel information on the functioning of the human masticatory organ.