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Przeglądaj Materiały konferencyjne, referaty (WM) wg Autor "Awrejcewicz, Jan"
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Pozycja Anisotropic friction sliding rule influence on the mechanical systems dynamics(Wydawnictwo Politechniki Łódzkiej, 2021) Wijata, Adam; Stańczyk, Bartosz; Awrejcewicz, JanAnisotropic friction can produce friction force which is not collinear with a sliding direction. How much friction deviates from a sliding direction is described with a so-called sliding potential or equivalently a sliding rule. A sliding potential is often described with an ellipse or a superellipse. In this paper we propose an oval curve which provides piecewise continuous mathematical description for a sliding rule and fits better to the experimental results than a typical superepllipse. For an exemplary mechanical system it is shown, that an anisotropic sliding potential can lead to an unstable equilibrium position in the system. Furthermore, for what parameters the unstable equilibrium occurs differs between sliding potential models. We have tested four different geometrical models of sliding potential in this regard.Pozycja Conditions Regulating Tumor Cell Behaviour in Biological Systems with Memory of States(Wydawnictwo Politechniki Łódzkiej, 2021) Dzyubak, Larysa; Dzyubak, Oleksandr; Awrejcewicz, JanFor biological systems with memory of states there were found conditions which regulate tumor cell behaviour. These conditions depend on parameters of the multi-parametric space. Based on the Masing–Bouc-Wen’s framework, the state memory in the biological system was simulated by means of supplemental state variables (internal variables). The additional state variables were introduced into the generalized non-linear multi-scale diffusion cancer invasion model and the chaotic cancer attractors were found. To quantify chaotic cancer attractors, the technique based on the wandering trajectories analysis was applied.Pozycja Construction and 3D model of stand for investigating a non-ideal forcing in a nonlinear chain dynamics of self-excited oscillators with friction(Wydawnictwo Politechniki Łódzkiej, 2021) Rogala, Patryk; Olejnik, Paweł; Awrejcewicz, JanThe research involves application and research on a non-ideal forcing to modelling and identification of vibrating systems with friction. It is still an innovative approach in the numerical analysis of vibrations of mechatronic machines and devices. This will allow to make a much real numerical modelling and more efficient identification of nonlinear dynamic phenomena observed in vibrating systems with friction, and thus, a better modelling of such phenomena in computer programs. To obtain the goal, initial 3D model of the mechanical stand was made in the CAD software. Based on the 3D model, real stand will be built, and experiments will be held to obtain data that will be necessary to ensure correctness of the mathematical model, which also will be studied and developed.Pozycja Design and simulation of a lower limb exoskeleton with linear electric actuators(Wydawnictwo Politechniki Łódzkiej, 2021) Grzelczyk, Dariusz; Jarzyna, Olga; Awrejcewicz, JanIn the present study, we proposed and investigated a relatively simple and inexpensive construction of a lower limb exoskeleton driven by linear electric actuators and controlled by an Arduino microcontroller board. Moreover, to study crucial kinematic and dynamic parameters of the proposed device, we developed a general, three-dimensional simulation model of the exoskeleton in Mathematica software. To control individual joints of the investigated exoskeleton, we employed time histories of human joint angles in normal gait, recorded with the use of a motion capture system. As a result, we developed a novel human gait generator, which can be used to produce rhythmic movements in hip, knee and ankle joints of both limbs. Finally, the developed control approach was verified with the use of the constructed prototype of the exoskeleton.Pozycja Dynamic analysis of functionally graded sandwich shells resting on elastic foundations(Wydawnictwo Politechniki Łódzkiej, 2021) Tetyana, Shmatko; Lidiya, Kurpa; Awrejcewicz, JanFree vibrations of sandwich shallow shells resting on elastic foundations are investigated. It is assumed that shell consists of three layers of the different thickness. Different schemes of arrangement of layers are considered. Namely, the core is made of ceramics or metals , and the upper and lower layers are made of FGM. The volume fractions of metal and ceramic are described by the power law. Shear deformation shell theory of the first (FSDT) that includes interaction with elastic foundations is applied. To study shells with an arbitrary plan form the R-functions theory combined with the variational Ritz method are used. Validation of the proposed method and developed software has been examined on test problems for FG shell with rectangular plan form. New results for shallow shells with complex plan form were obtained. Effects of the power law index, boundary conditions, thickness of core and face sheet layers, elastic foundations on fundamental frequencies are studied in this work.Pozycja Dynamics of Energy Harvesting Mechanical System in the Vicinity of 1:1 Resonance(Wydawnictwo Politechniki Łódzkiej, 2021) Puzyrov, Volodymyr; Awrejcewicz, Jan; Losyeva, NataliyaEnergy harvesting provides a useful way to power electronic devices without using batteries or electrical wiring. Energy harvesting can be defined as the conversion of environmental energy, such as mechanical, thermal, light energies into usable electrical energy. Conventional mechanical energy harvesting devices use a line harvester to generate electricity through vibrations or other mechanical motion. However, linear generators generate significant power in a narrow band around resonance, and the power is limited by the internal damping factor and the driving force at the resonant frequency. Such devices implementing a linear (resonant) generator cannot generate sufficient specific power. In present paper the mechanical system is considered which consists of two coupled oscillators (nonlinear absorber connected with primary mass) and a piezoelectric element attached. Two goals are pursued: the mitigation of the responses of the main mass and maximizing the amount of energy extracted from vibrations. The influence of nonlinear stiffness's component is discussed. It is shown that the piezoelectric element allows the effective energy harvesting and at the same has very limited influence on reducing the amplitude of oscillations of the main mass.Pozycja Energy flow control in a system of coupled pendulums using magnetic field(Wydawnictwo Politechniki Łódzkiej, 2021) Pilipchuk, Valery; Polczyński, Krystian; Bednarek, Maksymilian; Awrejcewicz, JanIn the presented work, we proposed a methodology of controlling the resonance energy exchange in mechanical systems by creating appropriate electromagnetic fields around the system’s structural subcomponents. It has been shown theoretically and confirmed experimentally that properly guided magnetic fields can effectively change mechanical potentials in such a way that the energy flow between the oscillators takes the desired direction. In particular, a model of two weakly coupled pendulums subjected to an electromagnetic load using a specific set of descriptive functions was considered. The developed control strategies are based on the observation that, in the case of antiphase oscillation, the energy is moving from the pendulum, which is in the repelling magnetic field, to the oscillator not subjected to magnetic field. The advantage of the suggested control strategy is that the temporal rate of inputs is dictated by the speed of beating, which is relatively slow compared to the carrying oscillations.Pozycja Estimation the Domain of Attraction for a System of Two Coupled Oscillators with Weak Damping(Wydawnictwo Politechniki Łódzkiej, 2021) Awrejcewicz, Jan; Puzyrov, Volodymyr; Losyeva, Nataliya; Savchenko, Nina; Nikolaieva, OksanaWhen solving a wide class of problems of nonlinear dynamics, the stability property of a given system regime is a prerequisite for design. An important role is played by the concept of the domain of attraction (DoA) of the equilibrium point (or limit cycle). However, as a rule, this domain is difficult to find and describe in explicit form. Therefore, the search for DoA estimate has been a fundamental problem in the control theory since the middle of the last century. Currently, methods based on Lyapunov functions predominate in the literature. We have studied the problem of obtaining the estimates of the DoA for equilibrium of the mechanical systems. The method for using Lyapunov function of special kind for a system with polynomial right-hand side to find the estimates for DoA is proposed. This procedure is illustrated by the example of a mechanical system which consists of two coupled nonlinear oscillators with weak damping.Pozycja Geometrically nonlinear vibrations of double-layered nanoplates(Wydawnictwo Politechniki Łódzkiej, 2021) Awrejcewicz, Jan; Mazur, OlgaThe geometrically nonlinear vibrations of simply supported double-layered graphene sheet systems are considered in the presented manuscript. The interaction between layers is taken into account due to van der Waals forces. The investigation is based on the nonlocal elasticity theory, Kirchhoff plate theory and von Kármán theory. The governing equations are used in mixed form by introducing the stress Airy function. The analytical presentation of the nonlinear frequency ratio for in-phase vibration and anti-phase vibration modes is presented. It is shown that the nonlocal parameter included in the compatibility equation can significantly change the vibrating characteristics.Pozycja Identification of the model parameters based on the ambiguous branches of resonance response curves(Wydawnictwo Politechniki Łódzkiej, 2021) Sypniewska-Kamińska, Grażyna; Awrejcewicz, JanA concept of the method of determining the parameters describing the damping and the nonlinearity, which can be of physical or geometrical nature, is presented in the paper. The main idea is explained regarding mechanical systems with one degree of freedom, however, the method can be also employed to identification for systems with two DoF provided that the couplings are weak and the resonances do not occur simultaneously. The analysis of stationary resonance states can be reduced only then to the third-degree equation, which is a necessary condition for the applicability of this method. Numerical simulations, which are carried out, confirm the usefulness and accuracy of the method.Pozycja Influence of a relatively high frequency structure vibrations on the dynamics of real stick-slip motion(Wydawnictwo Politechniki Łódzkiej, 2021) Olejnik, Paweł; Górniak vel Górski, Adrian; Cebulak, Maciej; Awrejcewicz, JanThe work concerns the research on the impact of structure vibrations on the dynamics of frictional contact of bodies moving in relation to each other and remaining in frictional contact, causing a stick-slip motion. A literature review was carried out, describing mainly the phenomena concerning friction, but also the dynamics of vibrations and non-ideal energy sources that induce system oscillations. In the next step an experimental station for investigation of friction equipped with a new subsystem inducing high-frequency vibrations is presented to propose a modified physical model of the investigated frictional system. After analysing the most important factors influencing the behavior of the tested system, a mathematical description was prepared, which in theory showed the potential influence of the attached subsystem on the dynamics of the movement of the tested object - the frictional connection. Various methods of implementing the unbalance of rotors, being the source of highfrequency excitation, have been considered. At the final stage, a series of measurements of the displacement of the vibrating block on the moving belt was performed with the highfrequency excitation turned on and off. The prepared graphs were used to analyse the dynamics of frictional contact and the impact of non-autonomous vibrations on the occurrence of the stick-slip phenomenon.Pozycja Influence of fractional order parameter on the dynamics of different vibrating systems(Lodz University of Technology Press, 2021) Zafar, Azhar Ali; Awrejcewicz, JanIn this work, we will investigate the fractional differential equations associated to different vibration phenomena. More specifically, we will discuss Bagley-Torvik equation, composite fractional relaxation differential equation and the motion of a linear oscillator using fractional derivative operator in the sense of Atangana-Baleanu. In order to be consistent with the physical systems the value of the fractional parameter that characterizes the existence of fractional structures in the system, lies within unit interval. The solutions of the non-integer order differential equation are obtained and expressed in terms of generalized functions depending upon the fractional parameter. The classical cases could be recovered by making the limit of fractional parameter approaches to unity. Moreover, we will analyze and compare the control of the fractional order parameter on the dynamics of the models and useful conclusions are recorded.Pozycja Magnetic oscillator under excitation with controlled initial phase(Wydawnictwo Politechniki Łódzkiej, 2021) Polczyński, Krystian; Bednarek, Maksymilian; Awrejcewicz, JanThe work contains the results of numerical simulations of the dynamics of a magnetic pendulum system subjected to excitation with a varying initial phase. A magnetic pendulum consists of a magnet fixed to the end of its arm and an electric coil below it. The initial phase of the excitation is presented as a linear function of the dynamic variable of the system, which is the angular position of the pendulum. The obtained basins of attraction indicate the occurrence of multi-periodic solutions in the system depending on the changes in the parameters of this system. The periodicities of the observed solutions are quantified mostly by odd numbers.Pozycja Mathematical Modelling of an extended Swinging Atwood Machine(Wydawnictwo Politechniki Łódzkiej, 2021) Yakubu, Godiya; Olejnik, Paweł; Awrejcewicz, JanAn extended model for a variable-length pendulum’s mechanical application is being derived from the Swinging Atwood Machine (SAM). An electrical component consisting of an electromagnet and armature coil is attached on the link connected to the counterweight mass on the left-hand side of the modified SAM to provide an excitation force for the system when an electric current is induced. The extended SAM presents a novel SAM concept being derived from a variable-length double pendulum with a suspension between the two pendulums. The equations of motion are simulated to see the trajectory of the two pendulums. The results of original numerical simulations show some compact regions of attraction at some regimes. Therefore, the extended SAM’s nonlinear dynamics presented in the current work can be thoroughly studied, and more modifications can be achieved. The new technique can reduce residual vibrations through damping when the desired level of the crane is reached. It can also be used in simple mechatronic and robotic systems.Pozycja Nonlinear Dynamics of Forced Oscillator Subjected to a Magnetic Interaction(Wydawnictwo Politechniki Łódzkiej, 2021) Skurativskyi, Sergii; Kudra, Grzegorz; Witkowski, Krzysztof; Wasilewski, Grzegorz; Awrejcewicz, JanIt is considered the system composed of a cart moving along a linear rolling bearing with harmonic excitation produced by a stepper motor with an unbalanced disk. The magnetic field is generated by a pair of non-point neodymium magnets, one of which is mounted on the cart, whereas another one is fixed on the guide out of the axis of oscillations. The mathematical model for the cart dynamics is derived where the scaled point dipoles approximation of magnetic interaction is used. The numerical and bifurcation analysis of the model presented is carried out and compared to the experimental results.Pozycja Parametric Vibrations of a System of Oscillators Connected with Periodically Variable Stiffness(Wydawnictwo Politechniki Łódzkiej, 2021) Kudra, Grzegorz; Witkowski, Krzysztof; Seth, Soumyajit; Polczyński, Krystian; Awrejcewicz, JanThe work is a part of a larger project concerning investigations of different configurations of connected oscillators with direct and parametric forcing sources. Among others, we present preliminary numerical studies of dynamics of a system composed of two oscillators connected with periodically variable stiffness. Each of the oscillators is connected to the fixed support with the use of a nonlinear magnetic spring. Based on the derived mathematical equations of the parametric system, a bifurcation plot was calculated for different shaft speeds. Bifurcation analysis shows both the ranges of periodic and chaotic motion. As an additional part, we will realize this kind of mechanical system from an electrical point of view, and we shall observe the phenomena experimentally.Pozycja Research of the dynamics of a physical pendulum forced with an electromagnetic field(Wydawnictwo Politechniki Łódzkiej, 2021) Ogińska, Ewelina; Grzelczyk, Dariusz; Awrejcewicz, JanIn this paper, both experimental and numerical results of the dynamics of a pendulum with a neodymium magnet and an aerostatic bearing are presented. The experimental stand includes the pendulum with the neodymium magnet at the end of the rod, whereas four electric coils are placed underneath. The pivot of the pendulum is supported on the aerostatic bearing. As a result, dry friction resistance in the pivot joint can be negligible and it has only a viscous character. The electric current with a given frequency and duty cycle and of a square waveform flows through the coils. Interaction between the neodymium magnet and the electric coils leads to the forced angular motion of the pendulum with the neodymium magnet. Both mathematical and physical models with experimentally confirmed system parameters are derived. The results of the simulation and experiment showed rich dynamics of the system, including various types of regular motion (multi-periodicity) and chaos.Pozycja Vibration of the system with nonlinear springs connected in series(Wydawnictwo Politechniki Łódzkiej, 2021) Awrejcewicz, Jan; Starosta, Roman; Sypniewska-Kamińska, GrażynaSolution of the problem and qualitative analysis of the forced vibration of the spring pendulum containing nonlinear springs connected in series is made in the paper. The method of multiple scales in time domain (MMS) has been employed in order to carry out the analytical computations. The MMS allows one, among others, to predict the resonances which can appear in the systems. The approximate solution of analytical form has been obtained for vibration at main resonance.