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  • 1. Adolfsson, J.
    et al.
    Dankowicz, H.
    Nordmark, Arne B.
    KTH, Superseded Departments, Mechanics.
    3D passive walkers: Finding periodic gaits in the presence of discontinuities2001In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 24, no 2, p. 205-229Article in journal (Refereed)
    Abstract [en]

    This paper studies repetitive gaits found in a 3D passive walking mechanism descending an inclined plane. By using direct numerical integration and implementing a semi-analytical scheme for stability analysis and root finding, we follow the corresponding limit cycles under parameter variations. The 3D walking model, which is fully described in the paper, contains both force discontinuities and impact-like instantaneous changes of state variables. As a result, the standard use of the variational equations is suitably modified. The problem of finding initial conditions for the 3D walker is solved by starting in an almost planar configuration, making it possible to use parameters and initial conditions found for planar walkers. The walker is gradually transformed into a 3D walker having dynamics in all spatial directions. We present such a parameter variation showing the stability and the amplitude of the hip sway motion. We also show the dependence of gait cycle measurements, such as stride time, stride length, average velocity, and power consumption, on the plane inclination. The paper concludes with a discussion of some ideas on how to extend the present 3D walker using the tools derived in this paper.

  • 2. Alekseev, A.A
    et al.
    Kozlov, Alexander
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Shalfeev, V.D
    Chaotic regime and synchronous response in frequency controlled oscillator1994In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 5, no 1, p. 71-77Article in journal (Refereed)
  • 3.
    Farré, Gerard
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Sardanyes, Josep
    Guillamon, Antoni
    Fontich, Ernest
    Coexistence stability in a four-member hypercycle with error tail through center manifold analysis2017In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 90, no 3, p. 1873-1883Article in journal (Refereed)
    Abstract [en]

    Establishing the conditions allowing for the stable coexistence in hypercycles has been a subject of intensive research in the past decades. Deterministic, time-continuous models have indicated that, under appropriate parameter values, hypercycles are bistable systems, having two asymptotically stable attractors governing coexistence and extinction of all hypercycle members. The nature of the coexistence attractor is largely determined by the size of the hypercycle. For instance, for two-member hypercycles the coexistence attractor is a stable node. For larger dimensions more complex dynamics appear. Numerical results on so-called elementary hypercycles with and species revealed, respectively, coexistence via strongly and weakly damped oscillations. Stability conditions for these cases have been provided by linear stability and Lyapunov functions. Typically, linear stability analysis of four-member hypercycles indicates two purely imaginary eigenvalues and two negative real eigenvalues. For this case, stability cannot be fully characterized by linearizing near the fixed point. In this letter, we determine the stability of a non-elementary four-member hypercycle which considers exponential and hyperbolic replication terms under mutation giving place to an error tail. Since Lyapunov functions are not available for this case, we use the center manifold theory to rigorously show that the system has a stable coexistence fixed point. Our results also show that this fixed point cannot undergo a Hopf bifurcation, as supported by numerical simulations previously reported.

  • 4.
    Fredriksson, Mats H.
    et al.
    KTH, Superseded Departments, Mechanics.
    Borglund, Dan
    KTH, Superseded Departments, Aeronautical Engineering.
    Nordmark, Arne B.
    KTH, Superseded Departments, Mechanics.
    Experiments on the Onset of Impacting Motion Using a Pipe Conveying Fluid1999In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 19, no 3, p. 261-271Article in journal (Refereed)
    Abstract [en]

    The transition from stable periodic nonimpacting motion to impacting motion, due to variations of parameters, is observable in a wide range of vibro-impact systems. Recent theoretical studies suggest a possible scenario for this type of transition. A key element in the proposed scenario is fulfilled if the oscillatory motion involved in the transition is born in a supercritical Hopf bifurcation. If the onset of impacting motion is close to the Hopf bifurcation, the impacting motion is likely to be chaotic. A numerical simulation of a system of articulated pipes conveying fluid is used to illuminate the theory. An experimental setup is presented, where a cantilevered pipe conveying fluid is unilaterally constrained. Results from experiments are found to be in good qualitative agreement with the theory.

  • 5.
    Hedberg, Claes
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Collisions, mutual losses and annihilation of pulses in a modular nonlinear medium2017In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 90, no 3, p. 2083-2091Article in journal (Refereed)
    Abstract [en]

    One of the most important sections of nonlinear wave theory is related to the collisions of single pulses. These often exhibit corpuscular properties. For example, it is well known that solitons described by the Korteweg–de Vries equation and a few other conservative model equations exhibit properties of elastic particles, while shock waves described by dissipative models like Burgers’ equation stick together as absolutely inelastic particles when colliding. The interactions of single pulses in media with modular nonlinearity considered here reveal new physical features that are still poorly understood. There is an analogy between the single pulses collision and the interaction of clots of chemical reactants, such as fuel and oxidant, where the smaller component disappears and the larger one decreases after a reaction. At equal “masses” both clots can be annihilated. In this work various interactions of two and three pulses are considered. The conditions for which a complete annihilation of the pulses occurs are indicated. © 2017 The Author(s)

  • 6. Hedberg, Claes
    et al.
    Rudenko, Oleg
    Interaction between low and high-frequency Modes in a Nonlinear System: Gas-Filled Cylinder Covered by a movable Piston2003In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 32, no 4, p. 405-416Article in journal (Refereed)
    Abstract [en]

    A simple mechanical system containing a low-frequency vibration mode and set of high-frequency acoustic modes is considered. The frequency response is calculated. Nonlinear behaviour and interaction between modes is described by system of functional equations. Two types of nonlinearities are taken into account. The first one is caused by the finite displacement of a movable boundary, and the second one is the volume nonlinearity of gas. New mathematical models based on nonlinear equations are suggested. Some examples of nonlinear phenomena are discussed on the base of derived solutions.

  • 7. Ibragimov, N. H.
    et al.
    Kolsrud, Torbjörn
    KTH, Superseded Departments, Mathematics.
    Lagrangian approach to evolution equations: Symmetries and conservation laws2004In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 36, no 1, p. 29-40Article in journal (Refereed)
    Abstract [en]

    We show that one can apply a Lagrangian approach to certain evolution equations by considering them together with their associated equations. Consequently, one can employ Noether's theorem and derive conservation laws from symmetries of coupled systems of evolution equations. We discuss in detail the linear and non-linear heat equations as well as the Burgers equation and obtain new non-local conservation laws for the non-linear heat and the Burgers equations by extending their symmetries to the associated equations. We also provide Lagrangians for non-linear Schrodinger and Korteweg-de Vries type systems.

  • 8. Ibragimov, Nail H.
    Laplace type invariants for parabolic equations2002In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, p. 125-133Article in journal (Refereed)
    Abstract [en]

    The Laplace invariants pertain to linear hyperbolic differential equations with two independent variables. They were discovered by Laplace in 1773 and used in his integration theory of hyperbolic equations. Cotton extended the Laplace invariants to elliptic equations in 1900. Cotton's invariants can be obtained from the Laplace invariants merely by the complex change of variables relating the elliptic and hyperbolic equations. To the best of my knowledge, the invariants for parabolic equations were not found thus far. The purpose of this paper is to fill this gap by considering what will be called Laplace type invariants (or seminvariants), i.e. the quantities that remain unaltered under the linear transformation of the dependent variable. Laplace type invariants are calculated here for all hyperbolic, elliptic and parabolic equations using the unified infinitesimal method. A new invariant is found for parabolic equations.

  • 9. Ibragimov, Nail H.
    et al.
    Kovalev, Vladimir
    Pustovalov, V.V.
    Symmetries of integro-differential equations: A survey of methods illustrated by the Benny equations2002In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, p. 135-153Article in journal (Refereed)
    Abstract [en]

    Classical Lie group theory provides a universal tool for calculating symmetry groups for systems of differential equations. However Lie's method is not as much effective in the case of integral or integro-differential equations as well as in the case of infinite systems of differential equations. This paper is aimed to survey the modern approaches to symmetries of integro-differential equations. As an illustration, an infinite symmetry Lie algebra is calculated for a system of integro-differential equations, namely the well-known Benny equations. The crucial idea is to look for symmetry generators in the form of canonical Lie-Backlund operators.

  • 10. Ibragimov, Nail H.
    et al.
    Magri, F.
    Geometric proof of Lie's linearization theorem2004In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 36, no 1, p. 41-46Article in journal (Refereed)
    Abstract [en]

    S. Lie found in 1883 the general form of all second-order ordinary differential equations transformable to the linear equation by a change of variables and proved that their solution reduces to integration of a linear third-order ordinary differential equation. He showed that the linearizable equations are at most cubic in the first-order derivative and described a general procedure for constructing linearizing transformations by using an over-determined system of four equations. We present here a simple geometric proof of the theorem, known as Lie's linearization test, stating that the compatibility of Lie's four auxiliary equations furnishes a necessary and sufficient condition for linearization.

  • 11. Ibragimov, Nail H.
    et al.
    Svirshchevskii, SR
    Lie-Backlund symmetries of submaximal order of ordinary differential equations2002In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, p. 155-166Article in journal (Refereed)
    Abstract [en]

    It is well known that the maximal order of Lie-Backlund symmetries for any nth-order ordinary differential equation is equal to n-1, and that the whole set of such symmetries forms an infinite-dimensional Lie algebra. Symmetries of the order pless than or equal ton - 2 span a linear subspace (but not a subalgebra) in this algebra. We call them symmetries of submaximal order. The purpose of the article is to prove that for n less than or equal to 4 this subspace is finite-dimensional and it's dimension cannot be greater than 35 for n=4, 10 for n=3 and 3 for n=2. In the case n=3 this statement follows immediately from Lie's result on contact symmetries of third-order ordinary differential equations. The maximal values of dimensions are reached, e.g., on the simplest equations y((n))=0.

  • 12.
    Kozlov, Alexander
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Osipov, G.V
    Shalfeev, V.D
    impulse suppression of chaotic oscillations1996In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 1, p. 113-120Article in journal (Refereed)
    Abstract [en]

    The methods of nonconstant feedback impulse control of chaos are introduced. the approach is based on the similarity of the return of the dissipative continuoustime systems with one dimensional maps. The metods are illustrated for the chua´s circuit Rössler oscillator, and phase-locked loop system.

  • 13.
    Kozlov, Alexander
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Shalfeev, V.D
    Controlling chaotic oscillations in delayed phase-locked loop1994In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 2, no 2, p. 36-48Article in journal (Refereed)
  • 14.
    Lundström, Niklas L. P.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    How to find simple nonlocal stability and resilience measures2018In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 93, no 2, p. 887-908Article in journal (Refereed)
    Abstract [en]

    Stability of dynamical systems is a central topic with applications in widespread areas such as economy, biology, physics and mechanical engineering. The dynamics of nonlinear systems may completely change due to perturbations forcing the solution to jump from a safe state into another, possibly dangerous, attractor. Such phenomena cannot be traced by the widespread local stability and resilience measures, based on linearizations, accounting only for arbitrary small perturbations. Using numerical estimates of the size and shape of the basin of attraction, as well as the systems returntime to the attractor after given a perturbation, we construct simple nonlocal stability and resilience measures that record a systems ability to tackle both large and small perturbations. We demonstrate our approach on the Solow-Swan model of economic growth, an electro-mechanical system, a stage-structured population model as well as on a high-dimensional system, and conclude that the suggested measures detect dynamic behavior, crucial for a systems stability and resilience, which can be completely missed by local measures. The presented measures are also easy to implement on a standard laptop computer. We believe that our approach will constitute an important step toward filling a current gap in the literature by putting forward and explaining simple ideas and methods, and by delivering explicit constructions of several promising nonlocal stability and resilience measures.

  • 15.
    Luneno, Jean-Claude
    et al.
    Luleå tekniska universitet, Material- och solidmekanik.
    Aidanpää, Jan-Olov
    Luleå tekniska universitet, Material- och solidmekanik.
    Use of nonlinear journal-bearing impedance descriptions to evaluate linear analysis of the steady-state imbalance response for a rigid symmetric rotor supported by two identical finite-length hydrodynamic journal bearings at high eccentricities2010In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 62, no 1-2, p. 151-165Article in journal (Refereed)
    Abstract [en]

    This paper concerns the investigation of validity limits of linear models in predicting rotor trajectory inside the bearing clearance for a rigid symmetric rotor supported by two identical journal bearings operating at high eccentricities. The inherent nonlinearity of hydrodynamic journal bearings becomes strong for eccentricities grater than 60% of the bearing clearance where most existing linear models are not able to accurately predict the rotor trajectory. The usefulness of nonlinear journal-bearing impedance description method in this investigation is due to the analytical formulations of the linearised bearing coefficients, and the analytical nonlinear bearing models. These analytically derived bearing coefficients do not require any numerical differentiation (or integration) and are therefore more accurate for large eccentricities. The analytically derived nonlinear bearing models markedly decrease the simulation time while valid for all L/D (length to diameter ratios) and all eccentricities. The results contained in this paper show that linear models derived from the nonlinear impedance descriptions of the Moes-cavitated (π-film) finite-length bearing can predict the steady-state imbalance response of a symmetric rigid rotor supported by two identical journal bearings at high eccentricities. This is, however, only the case when operating conditions are below the threshold speed of instability and when the system has period-one solutions. The error will become larger closer to the resonance speed.

  • 16. Luneno, Jean-Claude
    et al.
    Aidanpää, Jan-Olov
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Use of nonlinear journal-bearing impedance descriptions to evaluate linear analysis of the steady-state imbalance response for a rigid symmetric rotor supported by two identical finite-length hydrodynamic journal bearings at high eccentricities2010In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 62, no 1-2, p. 151-165Article in journal (Refereed)
    Abstract [en]

    This paper concerns the investigation of validity limits of linear models in predicting rotor trajectory inside the bearing clearance for a rigid symmetric rotor supported by two identical journal bearings operating at high eccentricities. The inherent nonlinearity of hydrodynamic journal bearings becomes strong for eccentricities grater than 60% of the bearing clearance where most existing linear models are not able to accurately predict the rotor trajectory. The usefulness of nonlinear journal-bearing impedance description method in this investigation is due to the analytical formulations of the linearised bearing coefficients, and the analytical nonlinear bearing models. These analytically derived bearing coefficients do not require any numerical differentiation (or integration) and are therefore more accurate for large eccentricities. The analytically derived nonlinear bearing models markedly decrease the simulation time while valid for all L/D (length to diameter ratios) and all eccentricities. The results contained in this paper show that linear models derived from the nonlinear impedance descriptions of the Moes-cavitated (π-film) finite-length bearing can predict the steady-state imbalance response of a symmetric rigid rotor supported by two identical journal bearings at high eccentricities. This is, however, only the case when operating conditions are below the threshold speed of instability and when the system has period-one solutions. The error will become larger closer to the resonance speed.

  • 17.
    Medvedev, Alexander
    et al.
    Department of Information Technology, Uppsala University, Uppsala, Sweden.
    Mattsson, Per
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Electronics.
    Zhusubaliyev, Zhanybai T.
    Department of Computer Science, Southwest State University, Kursk, Russian Federation.
    Avrutin, Viktor
    Institute for Systems Theory and Automatic Control, University of Stuttgart, Stuttgart, Germany.
    Nonlinear dynamics and entrainment in a continuously forced pulse-modulated model of testosterone regulation2018In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 94, no 2, p. 1165-1181Article in journal (Refereed)
    Abstract [en]

    Dynamical behaviors arising in a previously developed pulse-modulated mathematical model of non-basal testosterone regulation in the human male due to continuous exogenous signals are studied. In the context of endocrine regulation, exogenous signals represent, e.g., the influx of a hormone replacement therapy drug, the influence of the circadian rhythm, and interactions with other endocrine loops. This extends the scope of the autonomous pulse-modulated models of endocrine regulation to a broader class of problems, such as therapy optimization, but also puts it in the context of biological rhythms studied in chronobiology. The model dynamics are hybrid since the hormone metabolism is suitably captured by a continuous description and the control feedback is implemented in a discrete (i.e., event-based) manner by the hypothalamus of the brain. It is demonstrated that the endocrine loop with an exogenous signal entering the continuous part can be equivalently described by proper modifications in the pulse modulation functions of the autonomous model. The cases of a constant and a harmonic exogenous signal are treated in detail and illustrated by the results of bifurcation analysis. According to the model, adding a constant exogenous signal only reduces the mean value of testosterone, which result pertains to the effects of hormone replacement therapies under intact endocrine feedback regulation. Further, for the case of a single-tone harmonic positive exogenous signal, bistability and quasiperiodicity arise in the system. The convergence to either of the stationary solutions in a bistable regime is shown to be controlled by the phase of the exogenous signal thus relating this transition to the phenomenon of jet lag.

  • 18.
    Medvedev, Alexander
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Mattsson, Per
    Zhusubaliyev, Zhanybai T.
    Avrutin, Viktor
    Nonlinear dynamics and entrainment in a continuously forced pulse-modulated model of testosterone regulation2018In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 94, no 2, p. 1165-1181Article in journal (Refereed)
  • 19.
    Nordmark, Arne B.
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Biomechanics.
    Piiroinen, P. T.
    Simulation and stability analysis of impacting systems with complete chattering2009In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 58, no 1-2, p. 85-106Article in journal (Refereed)
    Abstract [en]

    This paper considers dynamical systems that are derived from mechanical systems with impacts. In particular we will focus on chattering-accumulation of impacts-for which local discontinuity mappings will be derived. We will first show how to use these mappings in simulation schemes, and secondly how the mappings are used to calculate the stability of limit cycles with chattering by solving the first variational equations.

  • 20.
    Rudenko, Oleg
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering. Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering.
    Hedberg, Claes
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering. Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science. Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering. Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences. Blekinge Institute of Technology, Department of Telecommunications and Mathematics.
    A new equation and exact solutions describing focal fields in media with modular nonlinearity2017In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 89, no 3, p. 1905-1913Article in journal (Refereed)
    Abstract [en]

    Brand-new equations which can be regarded as modifications of Khokhlov–Zabolotskaya–Kuznetsov or Ostrovsky–Vakhnenko equations are suggested. These equations are quite general in that they describe the nonlinear wave dynamics in media with modular nonlinearity. Such media exist among composites, meta-materials, inhomogeneous and multiphase systems. These new models are interesting because of two reasons: (1) the equations admit exact analytic solutions and (2) the solutions describe real physical phenomena. The equations model nonlinear focusing of wave beams. It is shown that inside the focal zone a stationary waveform exists. Steady-state profiles are constructed by the matching of functions describing the positive and negative branches of exact solutions of an equation of Klein–Gordon type. Such profiles have been observed many times during experiments and numerical studies. The non-stationary waves can contain singularities of two types: discontinuity of the wave and of its derivative. These singularities are eliminated by introducing dissipative terms into the equations—thereby increasing their order. © 2017 The Author(s)

  • 21. Rudenko, Oleg
    et al.
    Hedberg, Claes
    Nonlinear Dynamics of Grains in a Liquid-Saturated Soil2003In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 35, no 2, p. 187-200Article in journal (Refereed)
    Abstract [en]

    A new kind of nonlinearity of inertial type caused by accelerated motion of interacting particles is described. The model deals with an ensemble of grains immersed into a vibrating fluid. First, the nonlinear vibration of two connected grains is studied. The temporal behaviours of displacement and velocity, as well as spectrum of vibration, are analysed. Numerical simulations are performed. Then an infinite chain of grains is considered and the corresponding differential-difference equation is derived. For the continuum limit the inhomogeneous nonlinear wave equation is solved and temporal profiles are calculated. A new resonant phenomenon is described and the resonant curves are constructed.

  • 22.
    Rudenko, Oleg
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Hedberg, Claes
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    The quadratically cubic Burgers equation: an exactly solvable nonlinear model for shocks, pulses and periodic waves2016In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 85, no 2, p. 767-776Article in journal (Refereed)
    Abstract [en]

    A modified equation of Burgers type with a quadratically cubic (QC) nonlinear term was recently pointed out as a new exactly solvable model of mathematical physics. However, its derivation, analytical solution, computer modeling, as well as its physical applications and analysis of corresponding nonlinear wave phenomena have not been published up to now. The physical meaning and generality of this QC nonlinearity are illustrated here by several examples and experimental results. The QC equation can be linearized and it describes the experimentally observed phenomena. Some of its exact solutions are given. It is shown that in a QC medium not only shocks of compression can be stable, but shocks of rarefaction as well. The formation of stationary waves with finite width of shock front resulting from the competition between nonlinearity and dissipation is traced. Single-pulse propagation is studied by computer modeling. The nonlinear evolutions of N- and S-waves in a dissipative QC medium are described, and the transformation of a harmonic wave to a sawtooth-shaped wave with periodically recurring trapezoidal teeth is analyzed. © 2016 The Author(s)

  • 23.
    Sjoberg, M.
    et al.
    KTH, Superseded Departments, Vehicle Engineering.
    Kari, Leif
    KTH, Superseded Departments, Vehicle Engineering.
    Nonlinear isolator dynamics at finite deformations: An effective hyperelastic, fractional derivative, generalized friction model2003In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 33, no 3, p. 323-336Article in journal (Refereed)
    Abstract [en]

    In presenting a nonlinear dynamic model of a rubber vibration isolator, the quasistatic and dynamic motion influences on the force response are investigated within the time and frequency domain. It is found that the dynamic stiffness at the frequency of a harmonic displacement excitation, superimposed upon the long term isolator response, is strongly dependent on static precompression, dynamic amplitude and frequency. The problems of simultaneously modelling the elastic, viscoelastic and friction forces are removed by additively splitting them, modelling the elastic force response by a nonlinear, shape factor based approach, displaying results that agree with those of a neo-Hookean hyperelastic isolator at a long term precompression. The viscoelastic force is modeled by a fractional derivative element, while the friction force governs from a generalized friction element displaying a smoothed Coulomb force. A harmonic displacement excitation is shown to result in a force response containing the excitation frequency and its every other higher-order harmonic, while using a linearized elastic force response model, whereas all higher-order harmonics are present for the fully nonlinear case. It is furthermore found that the dynamic stiffness magnitude increases with static precompression and frequency, while decreasing with dynamic excitation amplitude-eventually increasing at the highest amplitudes due to nonlinear elastic effects-with its loss angle displaying a maximum at an intermediate amplitude. Finally, the dynamic stiffness at a static precompression, using a linearized elastic force response model, is shown to agree with the fully nonlinear model except at the highest dynamic amplitudes.

  • 24.
    Sun, Da
    et al.
    National University of Singapore, Singapore, Singapore.
    Naghdy, Fazel
    University of Wollongong, Wollongong, Australia.
    Du, Halping
    University of Wollongong, Wollongong, Australia.
    Time domain passivity control of time-delayed bilateral telerobotics with prescribed performance2017In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 87, p. 1253-1270Article in journal (Refereed)
    Abstract [en]

    A novel approach applying the extended prescribed performance control (PPC) and the wavebased time domain passivity approach (wave-based TDPA) to teleoperation systems is proposed. With the extended PPC, a teleoperation system can synchronize position, velocity and force. Moreover, by combining with the extended wave-based TDPA, the overall system’s passivity is guaranteed in the presence of arbitrary time delays. The system’s stability and performance are analyzed by using Lyapunov functions. The method is validated through experimental work based on a 3-DOF bilateral teleoperation system. The experimental results showthat the proposed control algorithm can robustly guarantee the master–slave system’s passivity and simultaneously provide high tracking performance of position, velocity and measured force signals.

  • 25.
    Thiery, Florian
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Product and Production Development.
    Aidanpää, Jan-Olov
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Product and Production Development.
    Nonlinear vibrations of a misaligned bladed Jeffcott rotor2016In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 86, no 3, p. 1807-1821Article in journal (Refereed)
    Abstract [en]

    This paper describes the numerical and experimental investigation of the nonlinear vibration of a bladed Jeffcott rotor. The nonlinearity in the system is due to discontinuities caused by multiple contacts with an outer ring as well as the nonlinear deformation of the massless blades. Contacts occur since the rotor shaft is initially misaligned by displacing the outer ring in one direction. The aim of the paper is to develop a simple model of bladed rotor and verify whether the global dynamics of the numerical simulations can be observed experimentally. The experimental rig and data acquisition are presented in detail together with the experimental procedures. The results between the numerical simulation and experiments are compared in terms of bifurcation diagrams and waterfall plots. An overall correlation is observed between the numerical and experimental study in the case of stiff blades, with differences mainly in localized frequency ranges due to parameter variation.

  • 26. Zhang, Tongqian
    et al.
    Meng, Xinzhu
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Song, Yi
    The dynamics of a high-dimensional delayed pest management model with impulsive pesticide input and harvesting prey at different fixed moments2011In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 64, no 1-2, p. 1-12Article in journal (Refereed)
    Abstract [en]

    In this paper, a delayed pest control model with stage-structure for pests by introducing a constant periodic pesticide input and harvesting prey (Crops) at two different fixed moments is proposed and analyzed. We assume only the pests are affected by pesticide. We prove that the conditions for global asymptotically attractive 'predator-extinction' periodic solution and permanence of the population of the model depend on time delay, pulse pesticide input, and pulse harvesting prey. By numerical analysis, we also show that constant maturation time delay, pulse pesticide input, and pulse harvesting prey can bring obvious effects on the dynamics of system, which also corroborates our theoretical results. We believe that the results will provide reliable tactic basis for the practical pest management. One of the features of present paper is to investigate the high-dimensional delayed system with impulsive effects at different fixed impulsive moments.

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