Accepted Manuscripts

James Oshea, Paramsothy Jayakumar, Dave Mechergui, Ahmed A. Shabana and Liang Wang
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4039059
The floating frame of reference (FFR) formulation is widely used in the analysis of deformable bodies in multibody system (MBS) simulations. The modeling of deformable bodies requires the use of elastic degrees of freedom, which can increase the model size significantly. Therefore, modal reduction techniques have been proposed in order to define a proper set of assumed body deformation modes at a preprocessing stage. Crucial to the proper definition of these modes when the finite element (FE) FFR formulation is used is the understanding of the concept of the reference conditions, which define the nature of the deformable body coordinate system. Substructuring techniques, such as the Craig-Bampton method, on the other hand, have been proposed to allow for efficiently modeling assemblies and reducing model dimensionality. However, it is important to distinguish between substructuring techniques, which aim at obtaining efficient model assembly, and coordinate reduction and the reference conditions that define the problem to be solved. In this study, the appropriateness and generality of using the Craig-Bampton method in MBS implementation is discussed. It is shown that, when a set of reference conditions are not applied at a preprocessing stage, the Craig-Bampton transformation leads to the free-free modes of deformation as well as the natural frequencies associated with these modes.
TOPICS: Dynamics (Mechanics), Multibody systems, Modeling, Deformation, Manufacturing, Simulation, Degrees of freedom, Engineering simulation, Finite element analysis
Liangqiang Zhou and Fangqi Chen
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4039060
Subharmonic bifurcations and chaotic dynamics are investigated both analytically and numerically for a class of ship power system. Chaos arising from heteroclinic intersections is studied with the Melnikov method. The critical curves separating the chaotic and non-chaotic regions are obtained. The chaotic feature on the system parameters is discussed in detail. It is shown that there exist chaotic bands for this system. The conditions for subharmonic bifurcations with O type or R type are also obtained. It is proved that the system can be chaotically excited through finite subharmonic bifurcations with O type, and it also can be chaotically excited through infinite subharmonic bifurcations with R type. Some new dynamical phenomena are presented. Numerical simulations are given, which verify the analytical results.
TOPICS: Dynamics (Mechanics), Power systems (Machinery), Bifurcation, Ships, Chaos, Computer simulation
Hao Dong, Bin Zhao and J.H. Xie
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4038991
The application of Hopf bifurcation is essential to rail vehicle dynamics because it corresponds to the linear critical speed. In engineering, researchers always wonder which vehicle parameters are sensitive to it. Usually the numerical method is applied to solve it with one by one parameter trying. With the nonlinear singularity theory's development, it has been widely applied in many other engineering areas. This paper mainly studies the singularity theory applied in nonlinear rail vehicle dynamics. Firstly, the bifurcation norm forms of wheelset and bogie system are respectively deduced. Then the universal unfolding is obtained and the influences of perturbation on bifurcation are investigated. By the analysis of a simple bar-spring system, the relationship between the unfolding and original perturbation parameters can be found. But this may be difficult to calculate for the case in vehicle system because of higher DOFs and indicate that can explain the influence of all potential parameters perturbations on vehicle bifurcation.
TOPICS: Bifurcation, Rail vehicles, Vehicles, Dynamics (Mechanics), Numerical analysis, Springs, Wheelsets
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
Antonio Martinez, Hector Cifuentes and Fernando Medina
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4038819
This paper analyzes the dynamic soil-structure interaction (SSI) of a railway bridge under the load transmitted by high-speed trains using the finite element method (FEM). In this type of bridges, the correct analysis of SSI requires proper modeling of the soil; however, this task is one of the most difficult to achieve with the FEM method. In this study we explored the influence of SSI on the dynamic properties of the structure and the structure's response to high-speed train traffic using commercial finite element software with direct integration and modal superposition methods. High-speed trains are characterized by the High Speed Load Model (HSLM) in the Eurocode. We performed sensitive analyses of the influence of several parameters on the model, such as the size and stiffness of the discretized soil, mesh size and the influence of the dynamic behavior of the excitation. Based on the results, we make some important and reliable recommendations for building an efficient and simple model that includes SSI. We conducted a dynamic analysis of a full model of a general multi-span bridge including the piers, abutments and soil, and identified the impact factors that affected the design of the bridge. The analysis revealed that the methodology we propose allows for a more accurate determination of the dynamic effects of the passage of a train over the bridge, compared to the simpler and more widely used analysis of a directly supported isolated deck, which tends to overestimate the impact factors.
TOPICS: Finite element analysis, Bridges (Structures), Soil, High speed rail, Trains, Finite element methods, Stress, Stiffness, Traffic, Excitation, Piers (Structural), Design, Dynamic analysis, Modeling, Computer software, Railroads
Jinrong Yang, Chengjin Wu, Jianhua Yang and Houguang Liu
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4038778
In our former work [J. Comput. Nonlin. Dyn.,\textbf{12}(5) p.051011], we put forward the re-scaled vibrational resonance (VR) method in fractional Duffing oscillators to amplify a weak signal with arbitrary high frequency. In the present work, we propose another method named as twice sampling VR to achieve the same goal. Although physical processes of two discussed methods are different, the results obtained by them are identical completely. Besides the two external signals excitation case, the validity of the new proposed method are also verified in the system that excited by an amplitude modulated signal. Further, the dynamics of the system reveals that the resonance performance, i.e., the strength and the pattern, depends on the fractional-order closely.
TOPICS: Resonance, Signals, Excitation, Dynamics (Mechanics)
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
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
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
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
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.

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