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Accepted Manuscripts

BASIC VIEW  |  EXPANDED VIEW
Guest Editorial  
Dumitru Baleanu, Tamas Kalmar Nagy, Themistoklis Sapsis and Hiroshi Yabuno
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4040569
Guest Editorial
TOPICS: Nonlinear dynamics
research-article  
Akira Saito
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4040540
This paper deals with the forced response analysis of chains of thin elastic beams that are subject to periodic external loading and frictionless intermittent contact between the beams. Our study shows that the beams show nonlinear resonances whose frequencies are the same as the linear resonant frequencies if all the beams have the same stiffness. Furthermore, it is also shown that small gaps between the beams and small deviation, or mistuning in the stiffness of each beam can cause drastic changes in the nonlinear resonant frequencies of the system dynamics. The system is modeled as a semi-discrete system of piecewise-linear oscillators with multiple degrees of freedom that are subject to unilateral constraints, which is derived from a finite element discretization of the beams. The resulting equations of motions are solved by a second-order numerical integration scheme, and steady-state solutions are sought for various driving frequencies. Results of parametric studies with respect to the gaps between the beams and the number of beams are presented to discuss how these parameters affect the resonant behavior of the system.
TOPICS: Resonance, Chain, Stiffness, Finite element analysis, Steady state, System dynamics, Degrees of freedom
research-article  
Akira Saito
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4040540
This paper deals with the forced response analysis of chains of thin elastic beams that are subject to periodic external loading and frictionless intermittent contact between the beams. Our study shows that the beams show nonlinear resonances whose frequencies are the same as the linear resonant frequencies if all the beams have the same stiffness. Furthermore, it is also shown that small gaps between the beams and small deviation, or mistuning in the stiffness of each beam can cause drastic changes in the nonlinear resonant frequencies of the system dynamics. The system is modeled as a semi-discrete system of piecewise-linear oscillators with multiple degrees of freedom that are subject to unilateral constraints, which is derived from a finite element discretization of the beams. The resulting equations of motions are solved by a second-order numerical integration scheme, and steady-state solutions are sought for various driving frequencies. Results of parametric studies with respect to the gaps between the beams and the number of beams are presented to discuss how these parameters affect the resonant behavior of the system.
TOPICS: Resonance, Chain, Stiffness, Finite element analysis, Steady state, System dynamics, Degrees of freedom
research-article  
Tamas Kalmar-Nagy and Balázs Sándor
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4040410
We present a new approach to the construction of first integrals for second order autonomous systems without invoking a Lagrangian or Hamiltonian reformulation. We show and exploit the analogy between integrating factors of first order equations and their Lie point symmetry and integrating factors of second order autonomous systems and their dynamical symmetry. We connect intuitive and dynamical symmetry approaches through one-to-one correspondence in the framework proposed for first order systems. Conditional equations for first integrals are written out, as well as equations determining symmetries. The equations are applied on the simple harmonic oscillator and a class of nonlinear oscillators to yield integrating factors and first integrals.
TOPICS: Construction, Harmonic oscillators
research-article  
Nader Dolatabadi, Stephanos Theodossiades and Steve J Rothberg
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4040239
Piston impacts against the cylinder liner are the most significant sources of mechanical noise in internal combustion engines. Traditionally, the severity of impacts is reduced through the modification of physical and geometrical characteristics of components in the piston assembly. These methods effectively reduce power losses at certain engine operating conditions. Frictional losses and piston impact noise are inversely proportional. Hence, reduction in power loss leads to louder piston impact noise. An alternative method that is robust to fluctuations in engine operating conditions is anticipated to improve the engine's NVH performance, whilst exacerbation in power loss remains within the limits of conventional methods. The concept of Targeted Energy Transfer (TET) through the use of Nonlinear Energy Sinks (NES) is relatively new and its application in automotive powertrains has not been demonstrated yet. In this paper, a TET device is conceptually designed and optimised through a series of parametric studies. The dynamic response and power loss of a piston model equipped with this nonlinear energy sink is investigated. Numerical studies have shown a potential in reducing the severity of impact dynamics by controlling piston's secondary motion.
TOPICS: Design, Internal combustion engines, Optimization, Pistons, Noise (Sound), Engines, Manufacturing, Fluctuations (Physics), Dynamics (Mechanics), Energy transformation, Cylinders, Dynamic response
research-article  
Astitva Tripathi and Anil Bajaj
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4040261
Electrostriction is a recent actuation mechanism which is being explored for a variety of new micro- and millimeter scale devices along with macro-scale applications such as artificial muscles. The general characteristics of these materials and the nature of actuation lends itself to possible production of very rich nonlinear dynamic behavior. In this work, principal parametric resonance of the second mode in in-plane vibrations of appropriately designed electrostrictive plates is investigated. The plates are made of an electrostrictive polymer whose mechanical response can be approximated by Mooney Rivlin model, and the induced strain is assumed to have quadratic dependence on the applied electric field. A Finite Element Method formulation is used to develop mode shapes of the linearized structure whose lowest two natural frequencies are designed to be close to be in 1:2 ratio. Using these two structural modes and the complete Lagrangian, a nonlinear two-mode model of the electrostrictive plate structure is developed. Application of a harmonic electric field results in in-plane parametric oscillations. The nonlinear response of the structure is studied using averaging on the two-mode model. The structure exhibits 1:2 internal resonance and large amplitude vibrations through the route of parametric excitation. The principal parametric resonance of the second mode is investigated in detail, and the time-response of the averaged system is also computed at few frequencies to demonstrate stability of branches. Some results for the case of principal parametric resonance of the first mode are also presented.
TOPICS: Resonance, Vibration, Plates (structures), Electric fields, Finite element methods, Stability, Muscle, Mode shapes, Excitation, Polymers, Oscillations
research-article  
Sen Zhang, Yi Cheng Zeng and Zhi Jun Li
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4039980
y using a simple state feedback control technique and introducing two new nonlinear functions into a modified Sprott B system, a novel 4D no-equilibrium hyper-chaotic system with grid multi-wing hyper-chaotic hidden attractors is proposed in this paper. One remarkable feature of the new presented system is that it has no equilibrium points and therefore, Shil'nikov theorem is not suitable to demonstrate the existence of chaos for lacking of hetero-clinic or homo-clinic trajectory. But grid multi-wing hyper-chaotic hidden attractors can be obtained from this new system. The complex hidden dynamic behaviors of this system are analyzed by phase portraits, the time domain waveform, Lyapunov exponent spectra and the Kaplan-York dimension. In particular, the Lyapunov exponent spectra are investigated in detail. Interestingly, when changing the newly introduced nonlinear functions of the new hyper-chaotic system, the number of wings increases. And with the number of wings increasing, the region of the hyper-chaos is getting larger, which proves that this novel proposed hyper-chaotic system has very rich and complicated hidden dynamic properties. Furthermore, A corresponding improved module-based electronic circuit is designed and simulated via Multisim software. Finally, the obtained experimental results are presented, which are in agreement with the numerical simulations of the same system on the Matlab platform.
TOPICS: Equilibrium (Physics), Wings, Attractors, Spectra (Spectroscopy), Chaos, Circuits, Computer software, Matlab, State feedback, Computer simulation, Dimensions, Trajectories (Physics), Theorems (Mathematics)
research-article  
Samuel Jung, Tae-Yun Kim and Wan-Suk Yoo
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4039838
Dynamic relaxation (DR) is the most widely used approach for static equilibrium analyses. Specifically, DR compels dynamic systems to converge to a static equilibrium through the addition of fictitious damping. DR methods are classified by the method in which fictitious damping is applied. Conventional DR methods use a fictitious mass matrix to increase the fictitious damping while maintaining numerical stability. There are many calculation methods for the fictitious mass matrix; however, it is difficult to select the appropriate method. In addition, these methods require a stiffness matrix of a model, which makes it difficult to apply nonlinear models. To resolve these problems, a new DR method that uses continuous kinetic damping is proposed in this study. The proposed method does not require the fictitious mass matrix and any tuning coefficients, and it possesses a second-order convergence rate. The aforementioned advantages are unique and significant when compared to those of conventional methods. The stability and convergence rate were analyzed by using an eigenvalue analysis and demonstrated by simulating nonlinear models of a pendulum and cable. Simple but representative models were used to clearly demonstrate the features of the proposed DR method and to enable the reproducibility of the verification results.
TOPICS: Algorithms, Damping, Relaxation (Physics), Equilibrium (Physics), Stability, Cables, Dynamic systems, Eigenvalues, Numerical stability, Pendulums, Stiffness, Computational methods
research-article  
Manashita Borah
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4039841
This paper proposes new fractional-order models of seven non-equilibrium or stable equilibrium systems and investigates the existence of chaos and hyperchaos in them. It thereby challenges the conventional generation of chaos that involves starting the orbits from the vicinity of unstable manifold. This is followed by the discovery of coexisting hidden attractors in fractional dynamics. All the seven newly proposed fractional-order chaotic systems (FOCSs) ranging from minimum fractional dimension (n_f) of 2.76 to 4.95, exhibit multiple hidden attractors, such as periodic orbits, stable foci, and strange attractors, often coexisting together. To the best of the author's knowledge, this phenomenon of prevalence of fractional-order (FO) coexisting hidden attractors in multidimensional FOCSs is reported for the first time. These findings have significant practical relevance because the attractors are discovered in real-life physical systems such as the FO homopolar disc dynamo, FO memristive system, FO model of the modulation instability in a dissipative medium, etc., as analysed in this work. Numerical simulation results confirm the theoretical analyses and comply with the fact that multistability of hidden attractors does exist in the proposed FO models.
TOPICS: Attractors, Chaos, Equilibrium (Physics), Disks, Dynamics (Mechanics), Computer simulation, Dimensions, Manifolds, Theoretical analysis
research-article  
Pitcha Khamsuwan, Teerawat Sangpet and Suwat Kuntanapreeda
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4039681
This paper deals with the problem of master-slave synchronization of fractional-order chaotic systems with input saturation. Sufficient stability conditions for achieving the synchronization are derived from the basis of a fractional-order extension of the Lyapunov direct method, a new lemma of the Caputo fractional derivative, and a local sector condition. The stability conditions are formulated in Linear Matrix Inequality (LMI) forms and therefore are readily solved. The fractional-order chaotic Lorenz and hyperchaotic Lü systems with input saturation are utilized as illustrative examples. The feasibility of the proposed synchronization scheme is demonstrated through numerical simulations.
TOPICS: Stability, Computer simulation, Chaos synchronization, Linear matrix inequalities, Synchronization
research-article  
Han Kyul Joo, Mustafa Mohamad and Themistoklis Sapsis
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4039309
We characterize the complex, heavy-tailed probability distribution functions (pdf) describing the response and its local extrema for structural systems subjected to random forcing that includes extreme events. Our approach is based on the recent probabilistic decomposition-synthesis technique, where we decouple rare events regimes from the background fluctuations. The result of the analysis has the form of a semi-analytical approximation formula for the pdf of the response (displacement, velocity, and acceleration) and the pdf of the local extrema. For special limiting cases (lightly damped or heavily damped systems) our analysis provides fully analytical approximations. We also demonstrate how the method can be applied to high dimensional structural systems through a two-degrees-of-freedom structural system undergoing rare events due to intermittent forcing. The derived formulas can be evaluated with very small computational cost and are shown to accurately capture the complicated heavy-tailed and asymmetrical features in the probability distribution many standard deviations away from the mean, through comparisons with expensive Monte-Carlo simulations.
TOPICS: Simulation, Fluctuations (Physics), Engineering simulation, Approximation, Displacement, Statistical distributions, Excitation
Technical Brief  
Edmon Perkins and Timothy Fitzgerald
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4038895
For stochastic systems, the Fokker-Planck equation (FPE) is used to describe the system dynamics. The FPE is a partial differential equation, which is a function of all the variable in state space and of time. To solve the FPE, several methods are used, including finite elements, moment neglect methods, and cumulant neglect methods. This paper will study the cumulant neglect equations, which are derived from the FPE. It will be shown that the cumulant neglect method, while being a useful and popular tool for studying the system response, introduces several nonphysical artifacts. This paper extends the continuation method technique, typically employed on nonlinear deterministic systems, to a stochastic system. Employing the continuation method to stochastic systems in this way could further develop a bifurcation theory of stochastic systems.
TOPICS: System dynamics, Finite element analysis, Bifurcation, Fokker-Planck equation, Partial differential equations, Stochastic systems
research-article  
Carla Pinto and Ana Carvalho
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4038643
We introduce a fractional order model for HIV dynamics where time-varying drug-exposure and drug-resistance are assumed. We derive conditions for the local and global asymptotic stability of the disease-free equilibrium. We find periodic stable endemic states for certain parameter values, for sinusoidal drug efficacies and when considering a density dependent decay rate for the $T$ cells. Other classes of periodic drug-efficacies are considered and the effect of the phases of these functions on the dynamics of the model are also studied. The order of the fractional derivative plays an important role in the severity of the epidemics.
TOPICS: Dynamics (Mechanics), Drugs, Density, Stability, Equilibrium (Physics), Diseases
research-article  
Touria Karite, Ali Boutoulout and Delfim F. M. Torres
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4038450
We investigate exact enlarge controllability for time fractional diffusion systems of Riemann-Liouville type. The Hilbert uniqueness method is used to prove exact enlarge controllability for both cases of zone and pointwise actuators. A penalization method is given and the minimum energy control is characterized.
TOPICS: Diffusion (Physics), Actuators, Differential equations
research-article  
Nicholas Candelino and Nader Jalili
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4038331
There have been a variety of attempts to model the quasi-static and high energy impact dynamics of vertically-aligned carbon nanotube pads. However, very little work has focused on identifying the behavior at the mid-level frequencies that may occur in materials handling or vibration suppression applications. Moreover, the existing models are predominantly very complex, and yet provide only a very rough approximation of the bulk behavior. While several of the existing models make attempts at ascribing physical relevance, an adequate first principles approach has yet to be demonstrated. In this work, a close-fitting continuous model of these mid-frequency dynamics is developed utilizing a combination of phenomenological and identification based methodologies. First, a set of specially fabricated carbon nanotube pads are preconditioned and subjected to various position controlled compression experiments. The measured position and force responses are used to develop load-displacement curves, from which several characteristic features are identified. Based on these observations, a preliminary version of the proposed model is introduced. This simplified model is then systematically refined in order to demonstrate completely both the modeling approach and parameter identification scheme. The accuracy of the model is demonstrated through a comparison between the modeled and experimental responses including a normalized vector correlation of >0.998 across all sets of sinusoidal experimental data. A brief analysis utilizing a Lyapunov linearization approach follows, as well as a discussion of the advantages and limitations of the final model.
TOPICS: Modeling, Carbon nanotubes, Experimental analysis, Dynamics (Mechanics), Materials handling, Surface roughness, Stress, Compression, Displacement, Vibration suppression, Approximation, Fittings
research-article  
Albert C.J. Luo and Siyu Guo
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4038204
In this paper, the analytical solutions of periodic evolutions of the periodically diffused Brusselator are obtained through the general harmonic balanced method. Stable and unstable solutions of period-1 and period-2 evolutions in the Brusselator are discussed. Stability and bifurcations of the periodic evolution are determined by the eigenvalue analysis, and the corresponding Hopf bifurcations are presented on the analytical bifurcation tree of periodic motion. Numerical simulations of stable period-1 and period-2 motions of Brusselator are completed. The harmonic amplitude spectrums show harmonic effects on periodic motions, and the corresponding accuracy of approximate analytical solutions can be prescribed specifically.
TOPICS: Stability, Computer simulation, Bifurcation, Eigenvalues
Technical Brief  
Chandan Kumar and Somnath Sarangi
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037995
Planar dynamics of a rotor supported by long hydrodynamic journal bearing is investigated theoretically. An analytical model of the long journal bearing system is numerically integrated for analysis of fixed point and periodic oscillations. The nonlinearities in the system arise due to a nonlinear fluid film force acting on the journal. The influences of three dimensionless parameters viz. bearing parameter, unbalance, and rotor speed on the dynamic behavior of the rotor bearing system is studied and compared with the short journal bearing. For the same bearing parameter, short bearing has large operating speed compared to a long bearing. Results are presented in the form of a bifurcation diagram and Poincare´ map of the oscillations based on numerical computation. The considered unbalanced system shows periodic, multiperiodic and quasi-periodic motion in different speed range. Jumping phenomenon is also observed for a high value of bearing parameter with unbalance.
TOPICS: Fluid-dynamic forces, Bearings, Rotors, Dynamic response, Journal bearings, Oscillations, Dynamics (Mechanics), Fluid films, Bifurcation, Computation
research-article  
Li Ma and Changpin Li
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037930
This paper is devoted to investigating the relation between Hadamard-type fractional derivatives and finite part integrals in Hadamard sense, that is to say, the Hadamard-type fractional derivative of a given function can be expressed by the finite part integral of a strongly singular integral which does not exist. Besides, our results also cover that some fundamental properties on absolutely continuous functions, and the logarithmic series expansion formulas at the right end point of interval for functions in certain absolutely continuous spaces.
TOPICS: Space

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