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  1. 7 Vibrations in Physical Systems
  2. 5 Bulletin of the Polish Academy of Sciences. Technical Sciences
  3. 4 Mechanics and Mechanical Engineering
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  5. 2 Energy Policy Journal
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  1. 4 Awrejcewicz J.
  2. 3 Dąbrowski A.
  3. 3 Pielorz A.
  4. 3 Starosta R.
  5. 2 Balcerzak M.
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1
Content available Modeling and energy recovery from a system with two pseudo-levitating magnets
Mitura Andrzej, Kecik Krzysztof
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2022
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Vol. 70, nr 4
art. no. e141721
EN
In this paper, a model of an electromagnetic system with two levitating magnets is presented. Modeling was performed using the results of experiments. The data obtained make it possible to fit the magnetic forces between two magnets using a 5th order polynomial. The time series show that dry friction constitutes an important part of damping forces. The differential equations of motion consider strong nonlinearities of magnetic and damping forces. These terms cause the nonlinear hardening effect. The energy recovered by magnetic induction is dissipated in the resistors. Numerical simulations show that resistance has an impact on magnet dynamics and energy recovery. From the resonance characteristics obtained, optimal resistance is determined when energy recovery is the highest.
2
Content available Investigation to the influence of additional magnets positions on four-magnet bi-stable piezoelectric energy harvester
Li Xinxin, Huang Kexue, Li Zhilin, Xiang Jiangshu, Huang Zhenfeng, Mao Hanling, Cao Yadong
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2022
|
Vol. 70, nr 1
art. no. e140151
EN
To enhance the harvesting performance of a bi-stable piezoelectric energy harvester (BEH), this work proposes a four-magnet BEH (FBEH). FBEH consists of a piezoelectric cantilever beam with a tip magnet, a fixed magnet and two movable magnets. The two movable magnets relative to the fixed magnet can move in both horizontal and vertical directions. A nonlinear distributed parameter model of FBEH is derived through the Hamilton principle. The effects of the excitation frequency and amplitude as well as the horizontal and vertical gap on the harvesting performance are mainly investigated by using the bifurcation diagram, phase diagram, Poincaré map and output power. Numerical simulations demonstrate that the proposed FBEH decreases the potential barrier and creates a higher than typical bi-stable one when subjected to lower excitation amplitudes and frequencies.
3
Content available Nonlinear homogeneous dynamical system of fully cracked concrete beam
Mohan G., Pandey U. K.
Journal of Achievements in Materials and Manufacturing Engineering
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2021
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Vol. 106, nr 1
5--19
EN
Purpose: Purpose of this paper is the theoretical formulation of elasto-dynamics behaviour of fully cracked concrete beams for two-degree of freedom (DOF) dynamical system. Such modelled system is demonstrated by a new class of two-DOF conservative, fully-nonlinear systems known as nonlinear homogeneous dynamical (NHD) systems. Design/methodology/approach: The theoretical formulation of Two-DOF dynamical system has been developed by using the fundamental concept of structural analysis. Further, the behaviour of such class of conservative dynamical system has been concluded by using MATLAB. Findings: Findings can be distinguished into two aspects. First, when subjected to service loads, reinforced concrete structures possess tension cracks. Due to load variation with time leads the breathing action (opening-closing-reopening) of existing cracks and the behaviour of such structures are nonlinearly-elastic. Second, such class of fully nonlinear dynamical system possess dependence of stiffness coefficients on nodal displacements. Research limitations/implications: The mechanism behind such class of fully nonlinear dynamical system is not yet fully explored. Practical implications: Practical implications are related to the structural response of fully cracked concrete beam to different earthquake excitation, especially to understand the response of such nonlinear homogeneous elasto-dynamical system with two-DOF concrete beam. Originality/value: Elasto-dynamics of fully cracked concrete beams.
4
Content available Rotor dynamics - four open questions
Kiciński Jan
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2021
|
Vol. 69, nr 6
art. no. e139791
EN
Despite many years of development in the field of rotor dynamics, many issues still need to be resolved. This is due to the fact that turbomachines, even those with low output power, have a very complex design. The author of this article would like to signal these issues in the form of several questions, to which there are no precise answers. The questions are as follows: How can we build a coherent dynamic model of a turbomachine whose some subsystems have non-linear characteristics? How can we consider the so-called prehistory in our analysis, namely, the relation between future dynamic states and previous ones? Is heuristic modelling the future of rotor dynamics? What phenomena may occur when the stability limit of the system is exceeded? The attempt to find answers to these questions constitutes the subject of this article. There are obviously more similar questions, which encourage researchers from all over the world to further their research.
5
Content available Nonlinear double-beam system dynamics
Koziol Piotr, Pilecki Rafał
Archives of Civil Engineering
|
2021
|
Vol. 67, nr 2
337--353
EN
Double-beam model is considered in many investigations both theoretical and typically engineering ones. One can find different studies concerning analysis of such structures behaviour, especially in the cases where the system is subjected to dynamic excitations. This kind of model is successfully considered as a reliable representation of railway track. Inclusion of nonlinear physical and geometrical properties of rail track components has been justified by various computational studies and theoretical analyses. In order to properly describe behaviour of real structures their nonlinear properties cannot be omitted. Therefore a necessity to search appropriate analytical nonlinear models is recognized and highlighted in published literature. This paper presents essential extension of previously carried out double-beam system analysis. Two nonlinear factors are taken into account and parametrical analysis of the semi-analytical solution is undertaken with special emphasis on different range of parameters describing nonlinear stiffness of foundation and layer between beams. This study is extended by preliminary discussion regarding the dynamic effects produced by a series of loads moving along the upper beam. A new solution for the case of several forces acting on the upper beam with different frequencies of their variations in time is presented and briefly discussed.
PL
Model belki podwójnej jest często wykorzystywany w budowie układów wielowarstwowych opisujących zjawiska związane z ruchomymi obciążeniami. Nieliniowe i stochastyczne właściwości tych układów wpływają znacząco na ich dynamiczne zachowania, co zostało potwierdzone zarówno eksperymentalnie, jak i w wyniku badań teoretycznych. Dlatego wskazana jest szczegółowa analiza czułości rozważanych modeli na różne parametry, przed ich zastosowaniem do badania rzeczywistych konstrukcji. W artykule rozważany jest problem odpowiedzi układu belki podwójnej na system sił poruszających się wzdłuż górnej belki ze stałą prędkością i różnymi częstotliwościami, przy założeniu różnych wartości parametrów opisujących nieliniową sztywność dwóch warstw: podłoża i warstwy łączącej belki. Otrzymane semi-analityczne rozwiązanie dla opisanego przypadku jest znaczącym rozszerzeniem poprzednio opublikowanych rezultatów. Założenie dotyczące występowania dwóch nieliniowości prowadzi do konieczności zastosowania szeregu analitycznych aproksymacji, włączając dekompozycję Adomiana i falkową estymację szukanego rozwiązania. Te nakładające się przybliżenia czynią całą procedurę bardziej skomplikowaną i dlatego kontrolowanie zbieżności rozwiązań jest trudniejsze niż w przypadku poprzednio rozważanych uproszczonych modeli. Analiza parametryczna, wykonana dla szerokiego zakresu różnych parametrów, pokazuje, że nieliniowość warstwy pomiędzy belkami wpływa bardziej znacząco na zachowanie układu, w porównaniu do podobnego założenia dotyczącego podłoża. Analiza przedstawiona w artykule może być traktowana jako kolejny etap określenia zakresu stosowalności modelu i zbadania możliwości jego zastosowania w inżynierii kolejowej, w odniesieniu do dwuwarstwowego modelu toru kolejowego, opartego na układzie belki podwójnej, w którym pierwsza warstwa opisuje szyny, a druga modeluje warstwę podkładów. Takie podejście do modelowania drogi szynowej zostało już wcześniej poddane walidacji razem z hybrydową semi-analityczną metodą rozwiązania opartą o aproksymacje wykorzystujące filtry falkowe typu „coiflet”. Rozszerzenie tego modelu o wprowadzenie dodatkowej nieliniowości, stanowi ważny element badań w zakresie analizy dynamiki dróg szynowych.
6
Content available Differentiating fallers from nonfallers using nonlinear variability analyses of data from a low-cost portable footswitch device: a feasibility study
Gonabadi Arash, Antonellis Prokopios, Malcolm Philippe
Acta of Bioengineering and Biomechanics
|
2021
|
Vol. 23, no. 2
139--145
EN
Purpose: Falls are one of the main causes of injuries in older adults. This study evaluated a low-cost footswitch device that was designed to measure gait variability and investigates whether there are any relationships between variability metrics and clinical balance tests for individuals with a history of previous falls. Methods: Sixteen older adults completed a history of falls questionnaire, three functional tests related to fall risk, and walked on a treadmill with the footswitch device. We extracted the stride times from the device and applied two nonlinear variability analyses: coefficient of variation and detrended fluctuation analysis. Results: The temporal variables and variability metrics from the footswitch device correlated with gold-standard measurements based on ground reaction force data. One variability metric (detrended fluctuation analysis) showed a significant relationship with the presence of past falls with a sensitivity of 43%. Conclusion: This feasibility study demonstrates the basis for using low-cost footswitch devices to predict fall risk.
7
Content available Ciągły nieliniowy układ belki podwójnej jako wiarygodny model dynamiki drogi kolejowej
Kozioł Piotr, Pilecki Rafał
Zeszyty Naukowo-Techniczne Stowarzyszenia Inżynierów i Techników Komunikacji w Krakowie. Seria: Materiały Konferencyjne
|
2020
|
Nr 2 (121)
67--74
PL
Współczesny transport kolejowy napotyka na nowe wyzwania związane z rosnącymi wymogami bezpieczeństwa. Te stają się konieczne z powodu spodziewanego rozwoju skutkującego wysokimi prędkościami pociągów i częstotliwością połączeń, razem z trudnościami w planowaniu nowych linii umiejscowionych w rejonach o warunkach geotechnicznie wymagających. Utrzymanie istniejących trakcji staje się równie ważne ponieważ ich intensywne użytkowanie prowadzi do szybszej degradacji i zmniejszonej efektywności. Rozważając stan infrastruktury będącej w użyciu jeszcze kilka lat temu, można zauważyć, że poszukiwanie nowych metod analizy tworzonych układów jest obecnie nawet bardziej istotne. Poza problemami związanymi z wytrzymałością i zużyciem, należy zwracać uwagę na dynamiczne właściwości konstrukcji, głównie ze względu na ich rosnące znaczenie w odniesieniu do wpływu nieliniowych i stochastycznych charakterystyk. Nowe materiały używane w konstrukcjach drogi kolejowej mają bardzo często nieliniowe właściwości fizyczne, w sposób oczywisty potwierdzone i zbadane laboratoryjnie. Jednak ich wpływ na odpowiedź dynamiczną układów transportowych pozostaje dotychczas niewystarczająco zbadany. Obecny artykuł opisuje podejście do analitycznego modelowania dynamiki drogi kolejowej oparte na układach „wielobelkowych” posiadających nieliniowe właściwości. Wstępne wyniki obliczeniowe pokazujące dynamikę układu powiązaną z ruchomym obciążeniem złożonym z sił zmieniających się z różnymi częstotliwościami mogą być uważane za oryginalny wkład prezentowały w artykule.
EN
Recent rail transportation meets new challenges associated with increasing safety requirements. These become a strong necessity due to expected development resulting in high speeds of trains and frequency of connections, along with difficulties in planning and construction of new lines placed in demanding geotechnical conditions. Maintenance of existing tracks becomes equally important as their more intensive use leads to faster degradation and decreased efficiency. Seeking new methods of analysis for newly developed systems is even more important compared to study the infrastructure being operational yet a few years ago. Besides the issues of strength and wear, one should pay attention to the dynamic properties of structures, mainly due to their increasing importance in terms of stochastic and nonlinear features influence. New materials used in rail track structures have very often nonlinear physical characteristics which are obviously confirmed and determined in laboratory conditions. However their effects on the dynamic response of transportation systems remain insufficiently unexplored so far. This paper describes an idea of rail track dynamics analytical modelling based on multibeam systems possessing nonlinear stiffness. Preliminary computational examples of the system dynamics arising from a load consisting of forces with varying frequencies can be recognized as a novelty of presented study.
8
Content available remote On size-dependent large-amplitude free oscillations of FGPM nanoshells incorporating vibrational mode interactions
Yi Hongwei, Sahmani Saeid, Safaei Babak
Archives of Civil and Mechanical Engineering
|
2020
|
Vol. 20, no. 2
257--279
EN
At nanoscale, surface free energies of the atoms located on the free surfaces of structures significantly affect their mechanical characteristics. In this study, nonlinear large-amplitude free vibration response of nanoshells prepared from functionally graded porous materials (FGPM) is investigated by taking into account surface stress size effects and vibrational mode interactions. Non-classical shell model is constructed on the basis of the Gurtin–Murdoch type of the surface theory of elasticity having the capability of capturing surface stress size dependency. The accuracy of nonlinear vibration analysis is improved by incorporating the interaction of the main vibration mode and the first, third and fifth symmetric oscillation modes. Moreover, the closed-cell Gaussian-Random field scheme is put to use to extract the mechanical characteristics of FGPM nanoshell. Multiple timescales technique is then applied to achieve surface stress elastic-based nonlinear frequency of FGPM nanoshell analytically for different interactions between vibrational modes. It is revealed that by incorporating the interactions of the main vibration mode and higher symmetric oscillation modes, the behavior of the backbone curves belongs to the nonlinear free oscillation response of FGPM nanoshells changes from hardening to softening schema. It is found that when only the main vibration mode is taken into account, surface elasticity effects makes an enhancement in the significance of the hardening schema. However, by considering the interactions of higher symmetric oscillation modes, surface elasticity effects makes a reduction in the significance of the softening schema.
9
Content available remote Nonlinear coupled moving-load excited dynamics of beam-mass structures
Ghayesh M. H., Farokhi H., Zhang Y., Gholipour A.
Archives of Civil and Mechanical Engineering
|
2020
|
Vol. 20, no. 2
207--217
EN
Investigated in this paper is the first on the moving-load-caused nonlinear coupled dynamics of beam-mass systems. A constant value load excites the beam-mass system where its position on the beam-mass system changes periodically. The energy contribution of the moving load is included via a virtual work formulation. The kinetic energy of the mass together with the beam as well as energy stored in the beam after deflection is formulated. Hamilton’s principle gives nonlinear equations of the beam-mass system under a moving load in a coupled transverse/longitudinal form. A weighted-residual-based discretisation gives a 20 degree of freedom which is numerically integrated via continuation/time integration along with Floquet theory techniques. The resonance dynamics in time, frequency, and spatial domains is investigated. As we shall see, torus bifurcations are present for some beam-mass structure parameters as well as travelling waves. A finite element analysis is performed for a simpler linear version of the problem for to-some-extend verifications.
10
Content available Chaos synchronization of uncertain coronary artery systems through sliding mode
Qian D. W., Xi Y. F., Tong S. W.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2019
|
Vol. 67, nr 3
455--462
EN
The chaotic phenomena of coronary artery systems are hazardous to health and may induce illness development. From the perspective of engineering, the potential harm can be eliminated by synchronizing chaotic coronary artery systems with a normal one. This paper investigates the chaos synchronization problem in light of the methodology of sliding mode control (SMC). Firstly, the nonlinear dynamics of coronary artery systems are presented. Since the coronary artery systems suffer from uncertainties, the technique of derivative-integral terminal SMC is employed to achieve the chaos synchronization task. The stability of such a control system is proven in the sense of Lyapunov. To verify the feasibility and effectiveness of the proposed method, some simulation results are illustrated in comparison with a benchmark.
11
Content available Two approaches in the analytical investigation of the spring pendulum
Sypniewska-Kamińska G., Starosta R., Awrejcewicz J.
Vibrations in Physical Systems
|
2018
|
Vol. 29
art. no. 2018005
EN
Dynamics of the nonlinear spring pendulum is analysed using two asymptotic approaches. The multiple scale method is commonly applied with using two time scales. The purpose of the research is to justify the introduction of an additional third scale. Results of the analysis clearly show that introducing the third scale improve correctness of the approximate analytical solution. The obtained results allow for qualitative and quantitative analysis of the behavior of the studied system with a high accuracy. Calculations are made both in the neighbourhood of the resonance and also far from it.
12
Content available Model and dynamical analysis of a tattooing device
Sarbinowski F., Starosta R.
Vibrations in Physical Systems
|
2018
|
Vol. 29
art. no. 2018004
EN
The paper presents the physical model of the tattooing device. The model is described by three degrees of freedom and a series of linear and nonlinear dynamic parameters and excitation, whose values are determined – depending on the available data and resources – by analytical, numerical and experimental methods. There are also presented a solution of motion equations and the assessment of the impact of individual parameters on the nature of solutions, and moreover, it is indicated a modification of the structure, the use of which results in decrease the amplitudes of the body structure vibrations.
13
Content available The impact of primary suspension stiffness of 2-axle bogie of MKIII passenger car on its dynamical behaviour
Zboiński K., Golofit-Stawińska M.
Transport Problems
|
2018
|
T. 13, z. 1
135--146
EN
This article presents results of the study on the impact of stiffness in vehicle primary suspension for lateral direction kzy and longitudinal direction kzx. The study was carried out for 2-axle bogie of MKIII passenger car. The problem was solved by numerical tests performed with the simulation software for dynamics of vehicle-track system. Performed study consisted in varying both stiffness types through change of their values from 0.001 to 1000 times as compared to nominal value.
14
Content available Iterative methods for efficient sampling-based optimal motion planning of nonlinear systems
Ha J. S., Choi H. L., Jeon J. H.
International Journal of Applied Mathematics and Computer Science
|
2018
|
Vol. 28, no. 1
155--168
EN
This paper extends the RRT* algorithm, a recently developed but widely used sampling based optimal motion planner, in order to effectively handle nonlinear kinodynamic constraints. Nonlinearity in kinodynamic differential constraints often leads to difficulties in choosing an appropriate distance metric and in computing optimized trajectory segments in tree construction. To tackle these two difficulties, this work adopts the affine quadratic regulator-based pseudo-metric as the distance measure and utilizes iterative two-point boundary value problem solvers to compute the optimized segments. The proposed extension then preserves the inherent asymptotic optimality of the RRT* framework, while efficiently handling a variety of kinodynamic constraints. Three numerical case studies validate the applicability of the proposed method.
15
Content available Mathematical modeling of traveling autosolitons in fractional-order activator-inhibitor systems
Datsko B., Gafiychuk V.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2018
|
Vol. 66, nr 4
411--418
EN
In the article, basic properties of traveling spatially nonhomogeneous auto-wave solutions in nonlinear fractional-order reactiondiffusion systems are investigated. Such solutions, called autosolitons, arise in a stability region of the system and can coexist with the spatially homogeneous states. By a linear stability analysis and computer simulation, it is shown that the order of the fractional derivative can substantially change the properties of such auto-wave solutions and significantly enrich nonlinear system dynamics. The results of the linear stability analysis are confirmed by computer simulations of the generalized fractional van der Pol-FitzHugh-Nagumo model. A common picture of traveling auto-waves including series in time-fractional two-component activator-inhibitor systems is presented. The results obtained in the article for the distributed system have also been of interest for nonlinear dynamical systems described by fractional ordinary differential equations.
16
Content available Locking the movement of persons on the bridge crane
Kuľka Jozef, Mantič Martin, Kopas Melichar, Faltinová Eva
Advances in Science and Technology. Research Journal
|
2018
|
Vol. 12, no 2
260--265
EN
This article describes the design of a horizontal rope system for increasing the safety of work and movement on a specific device operating in height. This system is designed to be installed on a conventional existing crane footbridge or crane track structure and this system enables a free pass along the rope, without unclamp of spring hook on prolongation rope. The calculation was made by non-linear dynamic FEM analysis.
17
Content available remote The fastest, simplified method of estimation of the largest Lyapunov exponent for continuous dynamical systems with time delay
Balcerzak M., Pikunov D.
Mechanics and Mechanical Engineering
|
2017
|
Vol. 21, nr 4
985--994
EN
This paper focuses on the applications of the new method of estimation of the Largest Lyapunov exponent. The method has been adapted to continuous dynamical systems with time delay. The paper presents efficiency of the new method in comparison with classical algorithms of LLE estimation. Computation times and convergence rates have been compared with the typically used method. It has been revealed in this paper that for the van der Pol oscillator, application of the new method increases the efficiency of calculations by 28% comparing to the classic one. Therefore, authors claim that the method presented in this paper is the fastest one in the assumed range of applications.
18
Content available remote Application of the Lyapunov Exponent Based on Current Vibration Control Parameter (CVC) in Control of an Industrial Robot
Szaniewski M., Dąbrowski A., Balcerzak M., Zawiasa P.
Mechanics and Mechanical Engineering
|
2015
|
Vol. 19, nr 1
51--61
EN
Controlling dynamics of industrial robots is one of the most important and complicated tasks in robotics. In some works[3,7], there are algorithms of the manipulators steering with flexible joints or arms. However, introducing them to calculation of trajectory results in complicated equations and a longer time of counting. On the other hand, works [4,5,6]show that improvement of the tool path is possible thanks to the previousidentification of the robot errors and their compensation. This text covers application of Largest Lyapunov Exponent (LLE) as a criterion for control performance assessment (CPA) in a real control system. The main task is to find a simple and effective method to search for the best configuration of a controller in a control system. In this context, CPA criterion based on calculation of LLE by means of a new method [9–11] is presented in the article.
19
Content available remote Dynamical system analysis of unstable flow phenomena in centrifugal blower
Garcia D., Stickland M., Liśkiewicz G.
Zeszyty Naukowe. Cieplne Maszyny Przepływowe - Turbomachinery / Politechnika Łódzka
|
2014
|
nr 145
43--46
EN
Methods of dynamical system analysis were employed to analyze unsteady phenomena in the centrifugal blower. Pressure signals gathered at different control points were decomposed into their Principal Components (PCs) by means of Singular Spectrum Analysis (SSA). Certain number of PCs was considered in the analysis based on their statistical correlation. Projection of the original signal onto its PCs allowed to draw the phase trajectory that clearly separated non-stable blower working conditions from its regular operation.
20
Content available remote Analiza, modelowanie oraz prognozowanie stanu i rozwoju kryzysowej sytuacji socjalno-politycznej : pewne rozważania wstępne
Kurbanowicz-Ramazanow S., Stemplewska L.
Studia i Materiały / Europejska Uczelnia Informatyczno-Ekonomiczna w Warszawie
|
2014
|
Nr 2(8)
77--100
PL
W pracy po raz pierwszy przedstawiono pewne rozważania wstępne dotyczące analizy i modelowania stanu socjalno-politycznego głębokiego kryzysu na podstawie supersystemu typu „Majdan”. Pokazano możliwość stosowania podejścia entropii i zaprezentowano jedno ogólne podejście budowy integralnego nieliniowego dynamicznego modelu interakcji w złożonym systemie o wielu agentach typu „Majdan” na podstawie równania logistycznego oraz jego szczególne przykłady.
EN
This paper presents some preliminary considerations on the analysis and modeling of socio-political state of deep crisis based on “Maidan” supersystem. The possibility of using entropy approach is shown and a general approach of building an integral nonlinear dynamic model of interaction in a complex system with multiple agents of “Maidan” type based on the logistic equation is presented as well as its specific examples.
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