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2024 | Book

Perspectives in Dynamical Systems I — Applications

DSTA, Łódź, Poland, December 6–9, 2021

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About this book

This proceedings volume gathers selected, peer-reviewed papers presented at the Dynamical Systems Theory and Applications International Conference - DSTA 2021, held virtually on December 6-9, 2021, organized by the Department of Automation, Biomechanics, and Mechatronics at Lodz University of Technology, Poland. This volume concentrates on studies on applications, while Volume II focuses on numerical and analytical approaches.
Being a truly international conference, this 16th iteration of DSTA received submissions from authors representing 52 countries. The program covered both theoretical and experimental approaches to widely understood dynamical systems, including topics devoted to bifurcations and chaos, control in dynamical systems, asymptotic methods in nonlinear dynamics, stability of dynamical systems, lumped mass and continuous systems vibrations, original numerical methods of vibration analysis, nonsmooth systems, dynamics in life sciences and bioengineering, as well as engineering systems and differential equations.
DSTA conferences aim to provide a common platform for exchanging new ideas and results of recent research in scientific and technological advances in modern dynamical systems. Works contained in this volume can appeal to researchers in the field, whether in mathematics or applied sciences, and practitioners in myriad industries.

Table of Contents

Frontmatter
Control of Bubbling Phenomenon in Bipolar SPWM Inverters

Significant growth in the adoption of electric cars and non–conventional energy sources has led to an increase in the use of power electronic converters, in particular, the power inverter system. However, in some cases its performance has been affected by a phenomenon known as bubbling, which consists on a significant distortion of the output waveforms by phase restricted high frequency oscillations. As a consequence, in this paper we propose to vary the frequency of the SPWM to control the bubbling phenomenon reported in the inverter systems. Our proposed strategy was successfully applied to these inverters with a very relevant advantage, it does not require any physical or structural change to the system configuration, only an appropriate tuning of the ramp frequency signal. This process was performed by using a bifurcation perspective and detecting the frequency values for which the bubbling phenomenon and other nonlinear dynamics of the systems are suppressed.

Anderson Fabian Abella, José D. Morcillo, Fabiola Angulo
Drive-by-Wire of a Converted into Electric Car Syrena 105 Enabling Hardware-In-Loop Tests of Driving

In this work, replacing an electronic throttle pedal and a driver in an electric car converted into electric by a hardware-in-loop workbench is described, highlighting the advantage of drive-by-wire feature that appeared after conversion. Drive-by-wire facilitates replacing a driver by Hardware-In-Loop (HIL) workbench, as instead of simulating a mechanical pedal depression by a servomechanism, electric signals can be transmitted directly from the workbench. The one-pedal-driving feature of the motor controller used in the car, allows for performing a variety of road tests replacing only the electronic throttle pedal. Hardware interventions in the car are described and sample HIL test results are presented.

Paweł Adamski, Paweł Olejnik
Analysis of the Influence of Tyre Cross-Sectional Parameters on the Stability of a Nonlinear Bicycle Model with Elliptic Toroidal Wheels

In this work, the stability of a bicycle with elliptic toroidal wheels is analysed in detail. The influence of the tyre cross-sectional parameters on the self-stability velocity range of the steady forward motion is studied. The bicycle multibody model is based on a well-acknowledged bicycle benchmark, which has been extensively used in several works. The nonlinear equations of motion, constituting a Differential-Algebraic Equations (DAE) system, are derived and linearized along the steady forward motion. The robustness of the linearization approach allows obtaining the resulting Jacobian matrix as a function of the tyre cross-sectional parameters. Therefore, a sensitivity analysis of the eigenvalues with the wheels’ geometric parameters is performed. Different scenarios are considered, and the influence of the tori aspect ratios and the elliptic cross-sections are illustrated with various stability regions.

A. G. Agúndez, D. García-Vallejo, E. Freire
Finite Dimensional Modeling of an Elastic Rib

Finite dimensional modeling is the most important method of modeling biological objects. Our goal was to apply this method to build thorax models for patients with pectus carinatum. We presented a workflow for building finite element models from CT scans with the focus on using free open-source software, including 3D Slicer and Ansys Student.We also developed a mechanical model of a flat rib under load and proposed a method for its parameters’ identification. The rib is modeled by five rigid rods connected by torsion springs. We took into account the compliance in costovertebral joint by including to the model two cylindrical springs that connect the head of the rib with fixed perpendicular planes (which models that corresponding vertebra is fixed). There is also a torsion spring in the head of the rib that hinders the rotation of the rib in costovertebral joint. The load is applied to the free end of the last rod in the system.We obtained the equations of equilibrium for the described system. Stiffnesses’ identification was made from the assumption that small displacements of the first rod’s free end and displacements of non-fixed end of homogeneous isotropic linear elastic curved beam are equal.

Ivan Alpatov, Marat Dosaev, Vitaly Samsonov, Ekaterina Vorobyeva, Vadim Dubrov
Transient Solutions for a Pendulum Coupled to a DC Motor

The present text analyzes the influence of the inductance and the rotor inertia on the dynamics of a pendulum vertically moved by a DC motor through a yoke-scotch mechanism. The analysis also includes the influence of the mass on the tip of the pendulum. Time histories for the position and speed of the pendulum are presented, and the phase portraits demonstrate the type of motion and the amplitudes. The motor speed is affected by the pendulum characterizing a nonideal excitation. The results point that amplitude and speed in the pendulum increase when the mass on the pendulum increases. A small influence of the rotor inertia is found, and no influence of the inductance is present in steady state regions. Higher values for the mass of the pendulum provokes a lower speed in the motor, larger values for the rotor inertia diminish the final speed of the motor, but the inductance does not affect the final speed of the DC motor in the present analysis.

Rafael Henrique Avanço, Danilo Antonio Zanella, Raibel de Jesus Arias Cantillo, Américo Cunha Jr, José Manoel Balthazar, Angelo Marcelo Tusset
Remarks on the Dynamics of a DC Motor Moving a Cart Horizontally

The present text analyzes the dynamics of a DC motor coupled to a cart moved horizontally with a yoke scotch mechanism. The common concept about the inductance in DC motors is the influence in the transient region. The start in DC motors depend on the current and the inductance, but when it reaches a steady state the influence of the inductance diminishes and the current approaches to a mean value determined by the voltage set and the speed of the motor. However, when the motor speed fluctuates, the current may not be a constant and the inductance maybe needs to be considered. The results in the present analysis use different values for the mass moved by the yoke scotch, what causes a variable load acting over the DC motor provoking fluctuations on the speed. The conclusion is that in some specific cases it is necessary to consider the inductance of DC motors but in most of cases the inductance may be neglected without loss in the numerical results.

Rafael Henrique Avanço, Danilo Antonio Zanella, Raibel de Jesus Arias Cantillo, Américo Cunha Jr, José Manoel Balthazar, Angelo Marcelo Tusset
Nonlinear Dynamics, Stability and Control Strategies: Mathematical Modeling on the Big Data Analyses of Covid-19 in Poland

Detailed numerical data on covid-19 epidemic have been collected since February 2020, and now >200 countries and regions are presented in online databases. A brief review of the data analyses and mathematical modelling for different countries is given. The time series on four “waves” of pandemic in 16 provinces of Poland are analyzed. Statistical regularities, self- and cross-correlations, common and different features in the regions are revealed. Spectral analysis of oscillating components and phase curves demonstrated non-linear quasi-regular and chaotic dynamics. Based on the comparative analyses of the 7-day averaged curves, the non-linear SEIDQRV model with time delay was estimated as the most proper mathematical model. Material parameters of the model for each “wave” and region have been used for stability analysis and controllability of the pandemic. The reproduction number for each region/wave have been obtained as the stability criterion for the systems of equations of the SIR, SIRS, SEIR, SEIRS, SEIDQR models with and without time delay. Sensitivity of the models to different control functions (social restrictions, lockdown measures, availability/quality of medical treatment, vaccination level) revealed different sets of the most influencing parameters in different provinces and waves. The results are compared for similar data for Poland and other European countries. It is shown; the nonlinear dynamics and best control strategies differ at the level of the country and its regions that needs more complex local governmental measures against further development of the pandemic.

Liliya Batyuk, Natalia Kizilova
Energy Pulse: Competitive and Accessible Application for Monitoring Electricity Consumption

The present work brings to the reader’s attention the advantages and features of the Energy Pulse application. The application encapsulates a full solution for real-time monitoring of electrical power use and execution of fractional control in the form of individualized alerts to lower the cost of the monthly bill at the Faculty of Electrical Engineering buildings, the Swimming Complex from the Technical University of Cluj-Napoca, the Faculty of Building Services Engineering, and from Marasti Student Campus dormitories.

Alexandru G. Berciu, Eva H. Dulf, Dacian I. Jurj, Levente Czumbil, Dan D. Micu
Global Sliding Mode Control for a Fully Actuated Non-planar Hexarotor Aerial Vehicle

This work is concerned with the attitude and position control of a fully actuated non-planar hexarotor aerial vehicle equipped with reversible fixed rotors. The complete nonlinear dynamics of the vehicle is modeled in a state error formulation with six degrees of freedom (DOF), being three for position and three others for attitude, while the control input is also a six-DOF quantity defined in terms of the resultant force and torque acting on the system. A control law is designed using an unit-vector global sliding mode control strategy, which ensures robustness against bounded force and torque disturbances during the entire flight since the sliding condition is guaranteed from the initial time. Furthermore, the proposed controller also ensures global exponential stability for both the closed-loop translational and rotational dynamics. Using computational simulations, the designed control law is compared with an inverse-dynamic stabilizing control, showing to be effective and to perform much better.

José Agnelo Bezerra, João Francisco Silva Trentin, Davi A. Santos
Measurement of Dynamic Parameters of Composite Lighting Columns

The paper presents the results of measurements of the dynamic parameters of full-scale composite lighting columns in a laboratory. The object of the research was two types of composite columns 9.0 m high. The columns were made of GFRP (Glass Fiber Reinforced Polymer) or G/BFRP (Glass/Basalt Fiber Reinforced Polymer) composites. The results obtained in the measurements allow for comparing the modal parameters of the new types of lighting columns in the context of the use of basalt fibers. The results of the measures for elements with and without a lamp are presented.

Artur Borowiec, Daniel Szynal, Łukasz Szyszka
Stability Analysis of Mobile Crane During Wind Induced Load Sway

This paper concerns the analysis of the stability of a mobile crane, taking into account the deformability of the cable system and the influence of external forces. The deformability of the rope was introduced by the use of the Kelvin-Voigt model, while the wind force was determined by the formula for the aerodynamic resistance. Tracking the center of mass of the entire system with respect to the tipping contour was chosen as the stability criterion. Several cases of the working cycle with different duration or parameters of wind force were analyzed. The results are presented in the form of the projection of the center of mass on the plane of rotation. The influence of issues such as the spherical movement of the load, wind pressure or rope deformation on the criterion of work safety was determined.

Dawid Cekus, Paweł Kwiatoń
Assessing the Effect of Different Configurations of Inerter-Based Devices for Structural Vibration Control

In order to control vibration-prone structures, the vibrations mitigation effect of well-known passive control systems such as Tuned Mass Dampers (TMDs) can be enhanced by using a mass amplification device called inerter. In this study, the behavior of this device and its influence on the response of vibration-prone systems are investigated by analyzing different configurations in a civil engineering context, finding optimized parameters, and assessing the performance of various systems with the inerter in different positions. Indeed, the position of the device can strongly influence the benefits obtained from the structural control design. Therefore, a more critical analysis is proposed with respect to previous studies on the use of inerter-based devices for vibration control, with the aim of consistently investigating the exploitation of these innovative systems in practical applications.

Miriam Chillemi, Thomas Furtmüller, Christoph Adam, Antonina Pirrotta
A Study of an Electro-Hydraulic Servo Actuator Control System to Compensate for Badly Damped Vibrations

The purpose of this study is to develop an electro-hydraulic servo actuator (EHSA) control system to compensate for badly damped vibrations by a spring-damping device (SDD). The EHSA controls the extension and retraction of the telescopic boom of a hydraulic manipulator with three degrees of freedom (3-DoF), subjected to the cyclic impact force generated by a hydraulic breaker. A solution was applied, in which the actuator barrel was rigidly mounted on the manipulator’s main boom, and the actuator piston rod was flexibly connected to the manipulator’s telescopic boom by an SDD acting as a vibroisolator. A hydraulic breaker is mounted on the telescopic boom to crush large rocks (oversize) on a Blake jaw crusher conveyor. The purpose of the EHSA control system was to compensate for vibrations that were badly damped by SDD. The dynamic system of the EHSA-SDD based on the Hammerstein model was identified using a third-order polynomial function for the nonlinear static subsystem, and an autoregressive model with exogenous input (ARX) for the dynamic linear subsystem. A modified recursive least squares (RLS) method with variable estimation was used to identify the EHSA-SDD control system. Based on the estimated autoregressive variables, the quality index of the EHSA-SDD control system was minimized. A test stand was built, on which the designed EHSA-SDD control system excited by the cyclic excitation force generated by a hydraulic breaker was verified.

Ryszard Dindorf, Piotr Wos
Slide of a Flat Body on Elastic Supports Under the Action of a Small Lateral Force

A plane-parallel motion of a dynamically asymmetric body with two elastic supports on a plane with dry friction is considered in the presence of a lateral pulling force. The mechanical system is somewhat analogous to the sliding of a body along an inclined plane. The equations of motion compose a dynamic system of variable structure. The motion is considered, during which one or both supports slide, depending on the value of the coefficient of friction. An estimate is given for the value of the friction coefficient at which only one support slides. It is shown that during the transition from rest to the equilibrium position, the center of mass of the system acquires a nonzero horizontal velocity even if the pulling force is less than the force required to start sliding of a rigid inelastic body.

Marat Dosaev, Vitaly Samsonov
Seismic Response of Adjacent Steel Frames Linked by Friction Dampers

When an earthquake happens, besides of some direct effects on the structures, some indirect factors can lead to damage to the structure. One of these indirect factors is pounding that occurs between two adjacent structures because of out-of-phase vibration. The simplest way for the elimination of earthquake-induced pounding is to have a proper gap between the two structures. However, this method is not applicable in all cases, and we should search for other methods that can reduce the pounding effects. Linking the two adjacent structures with different elements like friction dampers (FDs) is one of the applicable strategies that can be studied. A friction damper (FD) absorbs energy by friction, and the slip force is the most important factor in these dampers. In this study, the effect of pounding on adjacent frames with different heights and also the effect of considering friction dampers with optimum slip force that are distributed uniformly in the stories, have been discussed. It is concluded that pounding finally results in decreasing of the responses of the low-rise frame and in increasing of the responses of the high-rise frame. It is also revealed that linking the dampers does not reduce pounding effects in all cases, and their performance in reducing or increasing of responses of the frames belongs to characteristics of the adjacent frames and the acceleration time history.

Mehdi Ebadi-Jamkhaneh, Masoud Ahmadi, Denise-Penelope N. Kontoni
Optimization of the Two-Mass Oscillators Regarding the Accumulation of Energy at Mechanical Resonance

In the considered two-mass oscillator, the excitation force acts on one mass (small mass) and the reception of the energy occurs on the second mass (bigger mass). The two-mass oscillator will be optimized with respect to the maximal energy accumulation of the second mass. The stiffness values of particular connecting spring elements, the mass values, and the amplitude of the excitation force will be used as parameters of the optimization process.

Wieslaw Fiebig, Adam Dmochowski
Dynamical Analysis and Control of Parametric Surface Waves in a Nonlinear and Non-ideally Excited Tank

In this work, we revisited and investigated the nonlinear parametric resonance of free surface oscillations of fluid inside a tank excited by a non-ideal power source with limited power supply. Numerical analysis of nonlinear dynamics is presented as phase portrait diagrams, power spectrum and maximum Lyapunov exponents to determine the regions in which the resonant sloshing vibrations have a chaotic or periodic behavior. We also present a State Dependent Riccatti Equation (SDRE) control design that can reduce the chaotic movement to a stable condition. The SDRE technique is based on the Linear Quadratic Regulator (LQR) and it has the characteristic of separating nonlinearity from the system and applying feedback control.

Maria Aline Gonçalves, José Manoel Balthazar, Elżbieta Jarzȩbowska, Angelo Marcelo Tusset, Mauricio Aparecido Ribeiro, Hilson Henrique Daum
Influence of a Cracked Rod in the Dynamics of a Planar Slider-Crank Mechanism

A simplified model of a slider-crank mechanism with a cracked rod is obtained through Lagrange’s theory and used to investigate perturbations on the system’s dynamic response caused by the presence of an open and non-propagating crack. The open crack is modelled as a massless spring. To further evaluate the influence of crack presence, crack depth and position, torque and pressure forces, the dynamic response of the damaged mechanism is compared to the health system. Results show, for all cases, a significant difference in the kinematic and dynamic response of both healthy and damaged systems.

Tomé S. N. Guenka, Marcela R. Machado
On the Local Stability of Braking Dynamics of a Slip-Controlled Two-Axle Vehicle with Multiple Time-Delays

Improving vehicle safety is one of the most challenging tasks of nowadays. During braking appropriate slip control of the wheel is essential to ensure proper performance regarding brake distance or lateral vehicle handling characteristics. Modern electronically controlled brake systems are equipped with several sensors, actuators and electronic control units (ECU), and there is a communication network that provides a connection between these nodes of the control system. As the speed of information is finite, and the communication protocol needs time to send and receive information packages, there is communication delay in the system that can be the root cause of performance and stability issues. The aim of the present research is to perform a local stability analysis on a two-axle vehicle model that is equipped with a slip controller in the presence of communication delay. Steady-state and dynamic brush models are used, and a PID controller is used for slip regulation. Communication delay is modelled as a constant time-delay, and as a time-varying time-delay that can model the effect of sampling as well. Boundaries of stability are determined in terms of the controller gains, stability maps are constructed, and finally the practical invariance of these stability maps for different other parameters are investigated.

Ádám Horváth, Péter Béda
Energy Recovery Hybrid System with the Flywheel

The coupling of drive units of electric and hybrid vehicles with flywheel-based kinetic energy recovery systems is one of the best suitable options to reduce fuel energy usage. It is also a convenient method to reduce greenhouse gas emissions, by the way. The essence of the work is to design a hybrid traction system cooperating with a flywheel that collects kinetic energy during vehicle braking. The proposed solution characterizes higher efficiency than known and used regenerative braking systems for energy recovery.

Jacek Jackiewicz
Motion Tracking of a Rigid-Flexible Link Manipulator in a Controller Failure Condition

The paper presents its contribution to tracking control of systems in failure work conditions. The example we examine is a three link planar manipulator with rigid and flexible links, for which one of actuators fails during its work. The work task for the manipulator is defined by the programmed constraints. The CoPCoD method is used to derive the reference motion dynamics and the tracking control after failure of one of manipulator actuators.

Elżbieta Jarzębowska, Krzysztof Augustynek, Andrzej Urbaś
Nonlinear Dynamics of a 2DOF Magneto-Mechanical Harvester

The nonlinear two-degree-of-freedom (2DOF) harvester system based on magnetic levitation is modelled and investigated. The equations of motions have been derived while taking into account magnetic nonlinearity. The experimental relationships of magnetic forces versus the distance between the magnets were determined. Based on these dependencies a strongly nonlinear model of a system with two degrees of freedom was proposed. A proper configuration of transducer parameters can improve energy harvesting. Therefore, an effort is made to assess the influence of electromechanical coupling and coil resistance. Finally, the obtained results allowed the determination of nonlinear effects in the investigated system.

Krzysztof Kecik, Andrzej Mitura
Dynamics of a Low-Inertia Ball Located Between Two Rotating Planes with Viscous Friction

The problem of the motion of a low-inertia ball between two horizontal uniformly rotating planes with linear viscous friction is considered. The center of mass of the ball coincides with its geometric center, the central inertia tensor of the ball is spherical. Two cases of low inertia of the ball are investigated: in the first case the mass of the ball is constant and concentrated near its center, in the second case the mass of the ball is small. In both cases the equations of motion of the ball have the form of the Tikhonov’s type equations with a small parameter in the left-hand side. The dynamics of the ball on an arbitrary finite time interval in the limit as the central moment of inertia of the ball tends to zero is studied.

Alexander Koshelev, Eugene Kugushev, Tatiana Shahova
Determination of the Loading of an Open Car with Filler in the Center Sill

The dynamic loading in the bearing structure of an open car can be decreased by means of the application of fillers in the center sill. The research included the mathematic modelling of the dynamic loading of an open car. The calculation was made for elastic, viscous, and elastic-viscous fillers. The results of calculation demonstrated that the application of viscous or elastic-viscous fillers is the most optimal technological solution in terms of decreasing the dynamic loading of an open car. The article presents the results of the computer modelling of the dynamic loading on the bearing structure of an open car. The authors determined the numerical values and the acceleration fields for the frame of an open car. The dynamic loading models were verified with an F-test. It was found that the hypothesis on adequacy was not rejected. The article also presents the results of the strength calculation for the bearing structure of an open car. The maximum equivalent stresses were concentrated in the contact area between the center sill and the body bolster beam; they amounted to 298.5 МPа, which was 9% lower than the stresses in the frame without filler. The research can be used by those who are concerned about the designing of innovative structures of freight cars and improving the operational efficiency.

Alyona Lovska, Oleksij Fomin, Grzegorz M. Szymański, Dmytro Skurikhin
Determination of Global Damping and Stiffness Coefficients of Journal Foil Bearing

For the few last years, in modern low-power generation systems, a demand for oil-free compressors has appeared. This high speed turbomachinery with a nominal speed of tens of thousands rpm strongly depends on the proper rotordynamic design. It is especially important when the foil bearings are taken to consideration. These compliant surface gas bearings are a class of hydrodynamic bearings that use the ambient gas as their working fluid and, thus, require no dedicated lubrication system. On the other hand, due to their relatively low damping, a designer should analyze thoroughly described in the dynamics of the rotor-bearing-casing system in the whole operating rpm range. The foil bearings, although simple in design, indicate complex behaviour resulting from Coulomb friction between their elements. This Coulomb friction affects the damping and stiffness of a given bearing support. So far, many more or less reliable numerical models of this phenomenon have been built and described in the literature. The research approach presented in this paper is different. The authors suggested obtaining the data experimentally from the bearing isolated on a test bench, where, the shaft is stationary (fixed), and the gas film is not present. The shaker excites the bearing sleeve while the damping and stiffness are provided to the system by the foil structure. The information collected about the bearing’s global coefficients can be implemented afterwards to the rotordynamic software as a tabular data. This will allow to prepare reliable models that will shorten the design process of newly developed compressors with these oil-free supports.

Jakub Łagodziński, Eliza Tkacz, Zbigniew Kozanecki
Tuned Liquid Column Damper Inerter (TLCDI) for Wind-Induced Vibration Control of Fixed-Base Structures

In this paper, the optimal design of a novel passive control device, defined as Tuned Liquid Column Damper Inerter (TLCDI), is investigated to control wind-induced vibrations of structural systems. Due to inherent nonlinearities, a complex numerical solution scheme is commonly required to optimally design the device. Therefore, to provide a straightforward optimization procedure, a statistical linearization approach is employed to minimize the stochastic response of a single degree of freedom system. Under the assumption of a Gaussian white noise excitation of wind loading type, and considering some additional hypotheses, a closed form solution of the optimal parameters of TLCDI is achieved. The validity of the proposed expressions is assessed by comparing results with those obtained from a more computationally demanding iterative method.

Masnata Chiara, Alberto Di Matteo, Christoph Adam, Antonina Pirrotta
A Vibro-Impact Oscillator-Based Energy Harvester

This study analyses the dynamics and energy generation from a vibro-impact based piezoelectric energy harvester. The configuration comprises of primary bimorph undergoing base excitation and impacts two secondary unimorphs on either side. Hamilton’s principle is used to develop governing equations of piecewise smooth linear dynamical system. The dynamics and harvesting performance of the system under study are characterized through numerical simulations. The impact is modelled as spring on contact. The effect of gap between the unimorphs and stiffness of contacting spring on the power and bandwidth are discussed in this study.

Shubhanshu Maheshwari, Aravindan Muralidharan, Shaikh Faruque Ali, Grzegorz Litak
Simple Suppression Method of Impact Oscillations Between a Pantograph and an Overhead Rigid Conductor Line

Wave-like wear on the surface of a conductor line in a railway current collection system often makes a pantograph separate from the conductor line. In the present study, we propose a simple method to suppress the contact loss between a pantograph and a conductor line. The current collection system can be modeled as a one-degree-freedom spring mass system. A flexible beam is added to this system to produce higher natural frequencies. In experiments, we found that the contact loss is strongly suppressed in a certain range of excitation frequency.

Naoto Nishiyama, Kiyotaka Yamashita
Anti-vibration Knob for the Motorcycle, Customizable on the Basis of the Driver’s Ergonomics

Anyone, young or adult who has ridden a motorcycle for several kilometers, will remember an unpleasant tingling sensation in the hand. The vibrations induced on humans while riding a motorcycle cause this tingling and other uncomfortable sensation. Several more or less serious pathologies are caused by exposure to these vibrations, a very common example is Carpal Tunnel Syndrome. Recent studies on the control of structural vibrations, whose excellent results published in international journals of high impact, have stimulated interest in developing these methods of analysis also for biomechanical structures, such as those of the bone skeleton of the hand. In particular, by analyzing the vibrations induced on humans while driving a motorcycle, it was decided to design and manufacture knobs with anti-vibration material made according to the anthropometric characteristics of the driver’s hand. Experimental investigations assess the efficiency of the anti-vibration knob (Italian Patent Application No. 102021000004691 filed on 01.03.2021), reducing the magnitude of stresses in the most damaging frequency range for the driver.

Antonina Pirrotta, Andrea Evola, Alberto Di Matteo, Antonio Galvano, Antonio Russo
Design of a Vibration Absorber System for Tremor Reduction in Parkinson Patients Using a Cluster Based Algorithm

Parkinson disease is a neuro degenerative disorder caused by the deficiency of dopamine in the brain and influences the brain control of muscles, leading to tremor (shaking), slow muscle movement and motion balancing problems. The treatment of Parkinson disease using passive control devices such as Dynamic Vibration Absorber has received considerable attention in recent times. In this work a new optimization algorithm termed as the Cluster Based Algorithm (CBA), developed by the authors for the design optimization of dynamical systems, is used to design the absorber system. It is seen that the designed absorber parameters which when attached to the primary system (Human hand) resulted in reduction of steady state amplitude. Moreover, it is also seen that absorber parameter sets converge to a cluster in the parameter space. Parameter cluster gives the designer more freedom to choose a parameter set satisfying the design considerations.

V. P. Premchand, Bipin Balaram, Ajith K. Mani, A. S. Sajith, M. D. Narayanan
Numerical Analysis of Nonlinear Dynamics of an Offshore Platform for Energy Harvesting

In this work, we numerically investigate the nonlinear model that describes the displacement of an offshore platform under ocean wave action. However, we have coupled a piezoceramic based system for the possible analysis of the generated energy that the system can produce. And so, a proposal for a pilot model for energy collection. For our analysis we investigate the behavior of the attraction basins described by the initial conditions of the system dynamics. Thus, we identified that the attraction basins have the sifting phenomenon with the variation of the parameter p. Other analyzes performed were the Maximum Lyapunov Exponent to determine the parametric set for dynamic regions where the system is in a chaotic or periodic regime. This behavior affects energy production, as the values that determine the maximum power have a positive LME exponent. We also determined the chaotic and periodic phase map as we observed in the results.

Mauricio A. Ribeiro, Angelo Marcelo Tusset, Wagner B. Lenz, José Manoel Balthazar, Grzegorz Litak
Dynamic Investigation of a Rolling Locomotion System Based on a Tensegrity Structure with Spatially Curved Compressed Members

In this paper a compliant tensegrity structure based on spatially curved compressed members is presented. Due to an internal variation of the prestress state the shape of the structure can be controlled. In particular, a modification of a cylindrical outer shape to a conical form is achieved. Regarding to the applications in mobile robotics this approach enables a steerable two-dimensional rolling locomotion system. Beside the consideration of the underlying non-holonomic constraints a simplified mechanical model an the corresponding equations of motion are derived for a predefined actuation principle. Various numerical simulations are evaluated focusing on the corresponding locomotion behavior. Based on these results a reliable actuation strategy to navigate in two dimensions is proposed.

Philipp Schorr, Markus Ebnet, Klaus Zimmermann, Valter Böhm
Fractional Order Controllers for Twin Rotor Aerodynamical System

The twin-rotor aerodynamical system (TRAS) is a highly nonlinear system with a cross-coupling effect. The input variables of the system are the two voltages applied to the motors. There are 4 output signals, the angular azimuth and pitch velocities of the motors and the vertical and horizontal positions. Although several controllers are published in the literature for this system, all solutions are with great complexity. The novelty of this work consists in the design of fractional order controllers using two innovative, ease to use methods. In this way, after a complete decoupling, the individual outputs are controlled by individual performant controllers, thus giving the subsystems a high degree of independence. The two controllers are designed for the velocity of the azimuth and pitch motor. The control loop is implemented and tested on the physical TRAS laboratory equipment, yielding results comparable with any complex solution already acknowledged. In order to highlight the special performances of the two fractional order controller design method, a comparison is also offered.

Magdalena Sangeorzan, Eva H. Dulf
Heart Rate Effects on Intracranial Aneurysm Hemodynamic

In the modern world, vascular diseases are associated with a high mortality rate. The knowledge of provenance mechanisms is critical to understanding their progress. Hemodynamics englobes important biomechanical factors intervening in different vascular diseases, especially intracranial aneurysms, where the hemodynamic environment actively influences their genesis, growth, and rupture.In the present study, we assess the influence of the feeding frequency variation on different hemodynamic parameters inside intra-aneurysmal circulation, using computational fluid dynamics (CFD) combined with patient-specific MRI images.The patient-specific model of Internal Carotid Artery (ICA) aneurysm was reconstructed from (Three-dimensional Time Of Flight Magnetic Resonance Imaging) 3D TOF MRI images. Navies-Stokes equations are solved inside the geometry using the finite-elements method. We carried out Twenty-seven simulations using different inlet flow rate frequencies to assess the influence of this change on hemodynamics in the aneurysm.The Variation of the feeding frequency Boundary condition revealed the disturbance of the overall hemodynamic parameters assessed intracranial aneurysm (IA). The increase of the inlet frequency allowed observing the disturbance of the association between flow and pressure inside the aneurysmal sac. This dissociation can be related to the stagnation increase inside the aneurysmal dome in response to feeding frequency. Moreover, the flow profiles have been affected by the disturbance of flow pressure association, which allowed the observation of fluctuating pressure values with multiple high-pressure values on the aneurysmal sac and the peri-aneurismal segment.The intra-aneurysmal flow is influenced highly by the feeding inlet frequency, which imbalance the pressure-flow stability causing an unfavourable hemodynamic environment inside the aneurysmal sac leading to growth or the rupture of the aneurysm.

Djalal Sekhane, Karim Mansour
Parametric Vibrations of a System of Oscillators Connected with Periodically Variable Stiffness

In this paper, we have considered a mechanical system consisting of two coupled oscillators. The mechanical design has the effects of magnetic and resistance forces. The spring constant of the system is periodically varying. By appropriately choosing the parameter values, we have numerically shown that the system’s state variables, such as the displacements and the velocities, under the effects of different forces, lead to some nonlinear behaviors, like a transition from the fixed point attractor to the chaotic attractor through the periodic and quasi-periodic attractors. These numerically obtained results will be helpful when the mechanical system is studied in a real experimental rig.

Soumyajit Seth, Grzegorz Kudra, Krzysztof Witkowski, Krystian Polczyński, Jan Awrejcewicz
Transversal Straining of Pressurized Pipeline Caused by Vibration of Damaged Foundation

A deformation model of buried pipeline under complicated geotechnical conditions of soil slit fracture is developed. The classical theory of rods on an elastic foundation and the membrane theory of shells are used. The influence of the contingency of cyclic discontinuities of transversal displacement in damaged foundation on the stressed state and limit equilibrium of pressurized pipe has been studied in quasi-static and dynamic statement with analytical methods. It is assumed that the frequency of kinematic perturbation does not exceed the cutoff frequency of the system.

Ivan Shatskyi, Mykola Makoviichuk, Maksym Vaskovkyi
Development of a Mathematical Model for the Functioning of a River Port Discharge Point

The current stage in the development of transportation in river ports is characterized by an increase in requirements for the timing of cargo delivery, quality of transportation, reduction of costs for transport and storage operations. In the transportation system, transport hubs are the central link, since cargo delivery begins and ends in them, processes of transhipment of cargo from one mode of transport to another take place.Should be noted that transhipment operations at the port are among the most time-consuming and difficult work on river and sea transport, the implementation of which is impossible without the use of modern information technologies and automated systems. Since the use of such systems can reduce the time and increase the quality of cargo handling.A mathematical model of a discharge point at the port is explicated, which describes the process of its functioning, is a state graph for a transport node. To calculate the probabilities of all possible states of this system, a system of algebraic equations is used. This allows to simplify the calculation of the possibility of transition from one state to another, which are determined by the state of trucks, since the solution of the resulting system of linear algebraic equations is not difficult and can be implemented in any mathematical program package.The waiting and maintenance times of trucks A and B are determined, with calculated by the ratio of the probabilities of the system states, quantitative values can be considered as justification for deciding on determining the efficiency of the transport system.

Viktor Strelbitskyi, Stanislaw Rajba, Nataliia Punchenko, Nadiia Kazakova, Rafal Szklarczyk, Ruslana Ziubina
Identification of Parameters of Mechanical Vibrating Systems Using the Amplitude-Frequency Relationship in Analytical Form

The subject of the paper is the concept of a method serving to the determination of the parameters that describe the damping and nonlinear elastic properties of mechanical vibrating systems. The possibility of the identification is provided by the analytical form of the relationship between the amplitude and frequency of periodic steady oscillations in the main resonance. The dependence is obtained using the multiple scale method (MSM) in the domain of time. The proposed method applies only when this dependency reduces to an algebraic equation of the third degree. The considerations for a single degree of freedom system described by the Duffing equation explain the main idea of the identification. However, under certain assumptions, the method can also be employed for systems with several degrees of freedom. The numerical simulations of the real experiment were carried out and discussed. The results confirm the usefulness and accuracy of the method and lead to practical conclusions determining the conditions for performing measurements.

Grażyna Sypniewska-Kamińska, Jan Awrejcewicz
Energy Harvesting from a Portal Frame with a Shape Memory Alloy

In this work, the investigation of energy harvesting for a portal frame structure is presented. A Shape Memory Alloy (SMA) and a piezoelectric material are coupled to the portal frame. The structure is excited by a non-ideal DC motor of limited power supply attached to its rigid body. The energy harvesting is carried through the piezoelectric material, which is mathematically represented by a nonlinear electromechanical coupling model. The behavior of the SMA is described by a system of differential equations that consider the martensite fraction and the temperature as the state variables thermodynamically constrained to the mechanical ones. Numerical results demonstrate the significant influence of both piezoelectric material and Shape Memory Alloy in the behavior of the system and energy harvesting. In addition, it is highlighted that the use of the SMA makes the vibrations of the structure possible to be controlled. In addition, for specific values of the elastic stiffness of Shape Memory Alloy, the harvested energy is increased.

Angelo Marcelo Tusset, Dim Pires, Giane G. Lenzi, Itamar Iliuk, Rodrigo T. Rocha, José Manoel Balthazar
Nonlinear Dynamic Vibration Absorber Applied in a High-Speed Elevator System

In this work, the horizontal response of a 4 degree-of-freedom vertical transport model excited by rail-guide deformations, and with a nonlinear dynamic vibration absorber is numerically investigated. The levels of the vibration and comfort in cabin, and the efficiency of using a nonlinear dynamic vibration absorber to reduce cabin vibrations, is numerical analyzed. The lateral displacement of the cabin is considered by an external disturbance that represents the deformations and misalignment of the rails-guide. The levels of lateral accelerations of the elevator and the levels of comfort felt by passengers are analyzed in accordance with ISO 2631 and BS 6841. The results of numerical simulations demonstrated that the configuration of the appropriate parameters of the DVA is essential to ensure a better level of comfort to passengers, and that the increase in speed associated with the use of nonlinear dynamic vibration absorber can improve the level of comfort reducing accelerations in the cabin.

Angelo Marcelo Tusset, Marcos Gonçalves, Calequela J. T. Manuel, José Manoel Balthazar, Giane G. Lenzi
The Influence of the Load Modelling Methods on Dynamics of a Mobile Crane

A mathematical model for the dynamics analysis of a mobile crane is presented in the paper. The proposed model of a mobile crane is in the form of a tree structure of a kinematic chain with closed-loop subchains. The carried load is treated in the two cases, as a lumped mass and a rigid body. The formulated model takes also into account the flexibility of wheels, outriggers, drives and rope(s). Dry friction in joints is also considered. The formalism of joint coordinates and homogeneous transformation matrices are used to describe the kinematics of the crane. The equations of motion are derived using the Lagrange equations of the second kind. These equations are supplemented by the Lagrange multipliers and constraint equations formulated for each cut-joint.

Andrzej Urbaś, Krzysztof Augustynek, Vasyl Martsenyuk
A Nonlinear Analysis of an Aeroelastic Three Degrees of Freedom Model

The aeroelastic typical section, also known as the three degrees of freedom (3DoF) aeroelastic model, is a common way to start studying aeroelastic systems, especially when there are nonlinearities that can be isolated. There is a lack of research using cubic springs controlling aileron deflection and considering Peters’ unsteady loading acting on the model simultaneously. The model presented here have two linear springs (one commanding the vertical displacement and the other commanding the pitch angle) and one nonlinear cubic spring for aileron deflection. Peters’ unsteady model is used to define the lift and aerodynamic moment, forces used in the flutter analysis. In addition, this model is validated for very flexible surfaces, such as helicopter blades. With the numerical simulated time series, the 0–1 test is performed, as well as the Takens reconstruction and the determination of the Lyapunov exponent. The 0–1 test result is compared to the Lyapunov exponent, as part of their validation for aeroelastic systems subjected to structural nonlinearities. With this validation, in future work, these methodologies shall be applied in a more complex aeroelastic system, which will be a flat plate clamped at the root.

Michelle F. Westin, Roberto G. A. da Silva, José Manoel Balthazar
Hydraulic Levelling Control System Technology of Brick-Laying Robot

The article presents a hydraulic control system for the auto-levelling of a mobile bricklaying robot platform. To stabilize the position of the robotic bricklaying system, four extendable hydraulic supporting legs were used. For the correct operation of the robot, its horizontal position is important. To control the self-levelling process, the system uses a two-axis tilt sensor and proportional directional control valves. After the target practical test, the results show that this method is a simple and reliable adjustment and perfectly realizes the precise and fast levelling of the hydraulic platform of the bricklaying robot. It can also be used for other multi-point automatic levelling systems.

Piotr Wos, Ryszard Dindorf
Correlation of Biomechanical Performance Measures with Speed, Acceleration and Deceleration in Human Overground Running

Earlier research results suggest that certain optimization processes take place in the human nervous system during body movement including locomotion. These processes might employ a combination of cost functions that make adaptation possible to the changing conditions, such as terrain or to certain intentions such as maintaining locomotion speed. We focus on the exploration of the changes in human body kinematics and kinetics, related to well-defined cost functions, such as energy dissipation, energy conservation or energy accumulation. These cost functions are in analogy with deceleration, constant speed locomotion and acceleration. Hence, we collected measurement data of eight athletes with five different tasks: (1) slow, (2) convenient, (3) high speed running, (4) acceleration and (5) deceleration. Correlation tests showed that the effect of varying speed and acceleration can be distinguished. The variation in running speed can be effectively indicated by the knee angle, the relative horizontal position of the center of mass and the center of foot pressure (CoM-CoP distance), the loading rate, the peak tibial shock, the foot angle and the shank angle, while the variation in the acceleration can be indicated by the angle of the trunk, the CoM-CoP distance, the average ground reaction force angle and the horizontal force components in the joints.

Liliána Zajcsuk, Ambrus Zelei
Energy Exchanges in a Nonlinear Meta-Cell

Energy exchanges between particles of a two degrees of freedom-dof meta-cell are studied. The nondimensionalized equations of the system are presented and then complexified. Only the first harmonics of the system are kept before applying a time multiple scales method. Detection of system dynamics at different time scales leads to the clarification of the slow invariant manifold and characteristic points of the system. Finally, frequency response curves of the system are presented and quasi-analytical responses are confronted with numerical ones obtained by time direct integration.

Camila da Silveira Zanin, Alireza Ture Savadkoohi, Sébastien Baguet, Régis Dufour
Dynamics of an Economic Growth Model with New Stylized Facts

The last two decades’ social and economic events have proven the importance of feedback mechanisms for determining the income dynamics of the countries of the world. The first feedback mechanism is the neglected endogenous population: the inverse relationship between income and population growth. The second feedback mechanism is—partly as a consequence of the previous one—aging society: the simultaneous reduction of labour force and increasing economic cost of the dependency ratio, additionally, the lower technological adaptability of the aging society to new technological innovations. The third feedback mechanism is the rising functional income inequality: the increasing relative income share of the rich. The result of this study is the following: the potential qualitative growth effects of three new stylized facts that emerged in recent literature—(1) aging society, (2) endogenous population growth, and (3) varying share of factors income—were investigated in a growth framework by simulations. The consequence of these mechanisms is a qualitatively new national and global income path in the twenty-first century compared to that of the twentieth century. The results of these feedback mechanisms question not only the stability of social and economic performance but the sustainability of these systems, as well.

Ádám János Zsiros, Zsombor Ligeti
Non-smooth Models of Wheel-Road Interactions Based on Piecewise-Linear luz(…) and tar(…) Projections

Vehicle modeling is often practiced on the concept of partial models created independently to describe the dynamics of longitudinal movements (related to the drive and braking processes), the dynamics of lateral movements (related to the vehicle steering processes), the dynamics of vertical movements (related to the effects of road unevenness and suspension operation). The paper presents a set of three innovative non-smooth dynamical models describing the interaction of a pneumatic wheel with a road in terms of the longitudinal, lateral and vertical dynamics of the vehicle motion. They are based on a simple two-mass substitute physical model. The presented mathematical models use piecewise-linear luz(…) and tar(…) projections. Thanks to these projections and their mathematical apparatus, the developed models are useful for a simplified description and analysis of strong nonlinear non-smooth processes, including the most difficult ones related to wheel locking, sudden wheel slip, or wheel detachment from the road surface.

Dariusz Żardecki
Metadata
Title
Perspectives in Dynamical Systems I — Applications
Editor
Jan Awrejcewicz
Copyright Year
2024
Electronic ISBN
978-3-031-56492-5
Print ISBN
978-3-031-56491-8
DOI
https://doi.org/10.1007/978-3-031-56492-5

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