Siyuan Xing and Albert C. J. Luo, Period-1 Motions to Twin Spiral Homoclinic Orbits in the Rössler System, J. Comput. Nonlinear Dynam. Aug 2023, 18(8): 081008. https://doi.org/10.1115/1.4062201

​The Rössler system was proposed as one of the simplest three-dimensional nonlinear systems in order to exhibit chaotic behaviors in 1976. Since then, extensive qualitative and quantitative research on such a system has been conducted to study the mathematical structures of periodic orbits in the vicinity of homoclinic orbits. Many advances in this field have been achieved through the linearized, approximate theory and numerical studies, but it is still far away to completely solve the problem. In this paper, the periodic motions of the Rössler system are predicted through an implicit mapping method, and the corresponding stability of periodic motions is determined by eigenvalue analysis. The semi-analytical bifurcation tree from periodic motions to two spiral homoclinic orbits is obtained. The unstable periodic motions with fast-slow movements are accurately predicted. Homoclinic orbits are identified through infinitely large eigenvalues. The approximate homoclinic orbits with different periods are presented for a better understanding of the spiral homoclinic orbits spiraling out from the saddle-focus equilibriums.  

Bianca Lento, Yannick Aoustin, and Teresa Zielinska, "Feasibility Study of Upper Limb Control Method Based on EMG-Angle Relation," ASME J. Comput. Nonlinear Dynam. Jun 2023, 18(6): 064501.  https://doi.org/10.1115/1.4056918

Qing Wu, Xiaohua Ge, Esteban Bernal, and Pengfei Liu, "A Real-Time Fluid Dynamic Air Brake Model for Long Heavy Haul Trains," ASME J. Comput. Nonlinear Dynam. Mar 2023, 18(3): 034502 ​https://doi.org/10.1115/1.4056849

Practical real-time fluid dynamic air brake models for long heavy haul trains have not been reported in open literature. Based on a previous work titled ‘Railway Air Brake Model and Parallel Computing Scheme’ in the same journal, this paper proposed upgrades to the previous model and achieved the real-time feature. The real-time contributing factors included a new brake cylinder model, a new scheme for updating characteristics, and the application of parallel computing. Results show that, for a 150-wagon train emergency brake simulation, the computing speed was improved from 5.26 times slower than real-time to 8.6 times faster than real-time. The three contributions improved the computing speed by 8.8, 1.8 and 2.9 times faster than the baseline models, respectively.

Wu, Q., Spiryagin, M., and Cole, C. (September 16, 2022). "Block–Wheel–Rail Temperature Assessments Via Longitudinal Train Dynamics Simulations." ASME. J. Comput. Nonlinear Dynam. November 2022; 17(11): 111007. https://doi.org/10.1115/1.4055431
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​Two research gaps were identified in block-wheel-rail temperature assessment. First, current studies are not combined with train dynamics which are better descriptions of the block-wheel-rail working environment. Second, current studies cannot simulate long rail sections. This paper developed a block-wheel-rail temperature assessment model by following the Finite Element idea. Models were validated by comparing with ANSYS Finite Element models and measured data. Case studies were carried out by combining the temperature model with a Longitudinal Train Dynamics model. A full-service and an emergency brake simulation were carried out for a 150-wagon heavy haul train on a 5,680 m long rail section. The results show that, due to brake force differences at different wagon positions, the maximum block and wheel temperature differences among individual wagons in the full-service brake simulation were 117.01 and 117.91 °C respectively. This highlighted the contribution of introducing train dynamics into block-wheel-rail temperature assessment. Rail temperature increases caused by wheel-rail temperature differences and frictional heating were about 10.60 and 2.65°C, respectively.

​Redundant manipulators provide versatility and enhance performance potential by using a greater number of inputs than outputs to be controlled. This flexibility enables obstacle avoidance and performance optimization, in addition to achieving specified outputs. However, this requires new analytical and computational tools that enable control strategies that select from an infinite number of admissible inputs that yield the specified output, while realizing enhanced manipulator performance. Topological attributes of Euclidean space, in which manipulators function, are employed to create a differentiable manifold structure that provides explicit parameterization of the infinite number of inputs associated with a desired output. This representation is employed to demonstrate achievement of output specifications, while avoiding obstacles in the manipulator’s workspace by switching between nominal input trajectories far from obstacles to self-motions that prevent collisions otherwise. It is also applied for mapping the self-motion manifold of a seven degree of freedom robot arm that is impossible to analyze using existing methods. A time domain implementation of the parameterization is presented that provides velocity and acceleration information required for control of manipulator dynamics. Computational methods are presented that enable real-time implementation of results derived on modern high-speed microprocessors, for use in computer-based manipulator control systems.

Thomas Breunung and Balakumar Balachandran, Computationally Efficient Simulations of Stochastically Perturbed Nonlinear Dynamical Systems, J. Comput. Nonlinear Dynam. Sep 2022, 17(9): 091008, https://doi.org/10.1115/1.4054932

Dynamical system models can be used to describe natural and engineering systems that evolve in time. Furthermore, most natural processes are inherently nonlinear and face uncertainties stemming from, for example, parameter variations or unknown environmental conditions. Models used to describe such systems can be grouped under stochastic, nonlinear dynamical systems. Here, the authors build on numerical integration routines meant for deterministic systems and present an algorithm to compute responses of stochastic nonlinear systems. With this approach, the well-developed deterministic tools can be used in stochastic system simulations. The algorithm’s performance is demonstrated by using numerical examples, including a system with two-hundred dimensions. This algorithm can be used to compute sample paths of stochastic dynamical systems about two orders of magnitude faster compared to established numerical stochastic integration routines. In addition, a deduced Gaussian kernel enables computations of the time-varying probability density function. With this approach, one can reduce the sample size significantly and thus enable computational investigations of higher dimensional systems that are infeasible with currently available methods. The algorithm discussed here can be used as a basis for computationally efficient investigations into stochastic dynamical systems over long time spans.

Yutong Xia, Narayanan Kidambi, Evgueni Filipov, K. W. Wang, "Deployment Dynamics of Miura Origami Sheets" ASME. J. Comput. Nonlinear Dynam. Jul 2022, 17(7): 071005. https://doi.org/10.1115/1.4054109

Origami is an ancient paper-folding art that can transform a two-dimensional (2-D) sheet into a complex 3-D structure. It has emerged as a promising tool for the design of mechanical structures with various functionalities. Because origami principles are scale independent, they can be adopted for the designs from large-scale space structures such as origami-based inflatable boom and antenna, to mesoscale origami robots, and to micro-scale medical devices. The foldability property allows for easy fabrication, compact storage, and easy transportation because origami can be compactly folded into small volumes and then unfolded to become large systems. Most studies have focused on static or kinematic deployment process of origami structures, while it is important to understand the deployment dynamics to achieve desired performances and mitigate safety concerns. In this research, we construct a dynamic model of a Miura origami sheet that captures the combined panel inertial and flexibility effects, which are otherwise ignored in rigid folding kinematic models but are critical in describing the dynamics of origami deployment. Results show that by considering these effects, the dynamic deployment behavior would substantially deviate from a nominal kinematic unfolding path. Additionally, the pattern geometries influence the effective structural stiffness, and it is shown that subtle changes can result in qualitatively different dynamic deployment behaviors. These differences are due to the multistability of the Miura origami sheet, where the structure may snap between its stable equilibria during the transient deployment process. Lastly, we show that varying the deployment rate can affect the dynamic deployment configuration. These observations are original and these phenomena have not and cannot be derived using traditional approaches. The tools and outcomes developed from this research enable a deeper understanding of the physics behind origami deployment that will pave the way for better designs of origami-based deployable structures, as well as extend our fundamental knowledge and expand our comfort zone beyond current practice.

Ships navigating heavy seas are susceptible to various types of wave excitation, which may lead to dynamic instabilities and, in the worst case, capsizing. Compared to the pitch and yaw motions, the roll motion of a ship has the least amount of damping. We study a harmonically excited, single-degree-of-freedom time-delay system with cubic and quintic nonlinearities. This system describes the direct resonance of a ship with an actively controlled anti-roll tank (ART) that is subjected to beam waves, or waves that are approximately perpendicular to the ship’s heading. A proportional–derivative (PD) controller with a constant time delay is assumed to operate the pump in the active ART system. A key result is obtained by deriving the stability boundary of the system, in the parametric space of the control gain and the delay, from the characteristic equation of the linearized system. As shown here, a smaller controller delay is not always better since, in some cases, reducing the delay will reduce the maximum controller gain for which the system is stable. We conduct further analyses using the spectral Tau method, the method of multiple scales, the method of harmonic balance, continuation techniques, and direct numerical simulation.
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Albert Peiret, Francisco González, József Kövecses​, and Marek Teichmann (February 24, 2020). "Co-Simulation of Multibody Systems With Contact Using Reduced Interface Models." ASME. J. Comput. Nonlinear Dynam. April 2020; 15(4): 041001. https://doi.org/10.1115/1.4046052

Co-simulation techniques enable the coupling of models of physically diverse subsystems in an efficient and modular way. Communication between subsystems takes place at discrete time points and is limited to a given set of coupling variables, while the internal details of the subsystems remain undisclosed, and are generally not accessible to the rest of the simulation environment. This can lead to the instability in non-iterative co-simulation that is commonly used  in real-time applications. The stability of the simulation in these cases can be enhanced using reduced, effective models of one or more subsystems. These reduced models provide physically  meaningful information to the other subsystems between communication points.  This work describes such interface models and their application in co-simulation for nonsmooth mechanical systems subjected to unilateral contact and friction. The performance of the proposed approach is shown in some challenging examples of non-iterative, multirate co-simulation interfacing mechanical and hydraulic subsystems. The use of an interface model improves stability and allows for larger integration step-sizes, thus resulting in more efficient simulation. 

Mohammad Bukhari and Oumar Barry (November 11, 2019). "Exact Nonlinear Dynamic Analysis of a Beam With a Nonlinear Vibration Absorber and With Various Boundary Conditions." ASME. J. Comput. Nonlinear Dynam. January 2020; 15(1): 011003. https://doi.org/10.1115/1.4045287

Beams are the basic component of many engineering applications. They are used in bridges, overhead transmission lines, pipelines, sensors, aircraft structures, and many others. To ensure safety and proper function, vibrations of beams need to be investigated for better prediction of the system dynamical response. When the vibration amplitude is small, linear theory can predict the response accurately. However, when the vibration amplitude becomes larger, nonlinearity must be considered to avoid erroneous results. This work investigates the nonlinear vibration of a beam with attached Nonlinear Vibration Absorber (NVA) consisting of a spring-mass system). The considered nonlinearity stems from mid-plane stretching due to immovable boundary conditions and from the nonlinear stiffness in the NVA. In addition, different types of immovable boundary are investigated. For weak nonlinearity, an approximate analytical solution is derived using the method of multiple scales. These analytical results are validated using direct numerical integration. Parametric studies demonstrate that the performance of the NVA does not only depend on its key design variables and location, but also on the beam boundary conditions, midplane stretching of the beam, and NVA configuration (i.e., grounded versus ungrounded). Our analysis also indicates that the common approach of employing approximate modes in estimating the nonlinear response of a loaded beam produces significant error, up to 1200% in some cases. These findings could contribute to the design improvement of NVAs, microelectromechanical systems (MEMS), energy harvesters, and metastructures. 

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T. Meyer, J. Kraft,  and B. Schweizer (February 24, 2021). "Co-Simulation: Error Estimation and Macro-Step Size Control." ASME. J. Comput. Nonlinear Dynam. April 2021; 16(4): 041002. https://doi.org/10.1115/1.4048944

Co-simulation techniques are commonly used to analyze multidisciplinary and multiphysical systems as well as to parallelize dynamical simulation models. Therefore, the overall system is decomposed into a certain number of subsystems. To define the coupling between the subsystems, coupling equations and appropriate coupling variables have to be specified. Moreover, a communication-time grid has to be introduced by defining macro-time points . The subsystems are integrated independently between the communication-time points; coupling variables are only exchanged at the macro-time points. The crucial point in connection with equidistant communication-time grids, which are frequently used in practical applications, is the appropriate choice of the macro-step size. Efficiency and accuracy of a co-simulation may, however, considerably be increased by using a variable communication-time grid. Therefore, an error estimator for controlling the macro-step size is required. Here, different error estimators for explicit and implicit co-simulation schemes are derived and incorporated into the macro-step size control algorithm. Numerical studies clearly demonstrate that the main problems associated with equidistant macro-grids – namely a trade-off between stability/accuracy and efficiency – disappear, if variable communication-time grids are used. The manuscript focuses on mechanical co-simulation models. The basic results may, however, also be applied to arbitrary, non-mechanical co-simulation models.

Shimmy is a self-excited vibration which can appear in various wheeled mechanisms such as trailers, motorcycles, bicycles, cars, landing gears of aircrafts, and even baby strollers or supermarket trolleys. Shimmy of cars is also known as vehicle shimmy or death wobble. The cause of shimmy is related to the dynamic characteristics of the tire-road contact and the overall system structure. It increases tire wear, deteriorates vehicle handling, and causes further instability problems of the whole vehicle.

In this paper, a 3 degree-of-freedom model of vehicle front wheels with dependent suspension is studied from the viewpoint of possible appearance of shimmy, and two tire models are compared. The two tire models have essentially different assumptions: Pacejka’s magic formula uses linearization in space along the tire-ground contact line where the tire points stick to the ground, while the delayed tire model uses linearization in time by considering small (but spatially nonlinear) lateral deformations of the tire in the contact region. The theoretical results show that the delayed tire model presents additional instabilities (i.e., shimmy) at low speeds, and especially at low damping values.

The investigation of this model is motivated by the occurrence of shimmy on some heavy vehicles and jeeps with worn front wheel suspension system, and the conclusions might be useful in the future study of shimmy in systems with independent suspensions of some electric vehicles.

​Edward J. Haug (February 24, 2021). "Multibody Dynamics on Differentiable Manifolds." ASME. J. Comput. Nonlinear Dynam. April 2021; 16(4): 041003. https://doi.org/10.1115/1.4049995
 

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​Topological and vector space attributes of Euclidean space are consolidated from the mathematical literature and employed to create a differentiable manifold structure for multibody kinematics and dynamics. A kinematic configuration space representation of admissible motion of a mechanical system provides the foundation for the development. Using vector space properties of Euclidean space and multivariable calculus, a tangent space kinematic parameterization is presented that establishes the regular configuration space of a multibody system as a differentiable manifold. Topological properties of Euclidean space show that this manifold is naturally partitioned into maximal, singularity free components of kinematic and dynamic functionality. A dynamic parameterization of the d’Alembert variational equation of multibody dynamics yields singularity free ordinary differential equations of system dynamics on these components, without introducing Lagrange multipliers. Solutions of the differential equations satisfy configuration, velocity, and acceleration constraint equations and the variational equations of dynamics; i.e., multibody kinematics and dynamics are embedded in these ordinary differential equations. Two examples, one planar and one spatial, are treated using the formulation presented. Solutions obtained are shown to satisfy all three forms of kinematic constraint to within specified error tolerances, using fourth order Runge-Kutta numerical integration methods.