Jean M. Souza, Luciana Loureiro S. Monteiro, Marcelo A. Savi
J. Comput. Nonlinear Dynam. December 2024, 19(12): 121005.
https://doi.org/10.1115/1.4066469

​Magnetic shape memory alloys (MSMAs) constitute a class of smart materials capable of exhibiting large magnetic field induced strain (MFIS) when subjected to magnetomechanical loadings. Two distinct mechanisms are responsible for the induced strain: martensitic variant reorientation and phase transformation. The martensitic reorientation is the most explored mechanism presenting the advantage to potential provide high-frequency actuation since it does not rely on phase transformation cycles. Despite its capabilities and potential dynamical applications, the dynamical behavior of MSMAs is not extensively explored in the literature that is usually focused on quasi-static behavior. Thereby, the objective of this work is to analyze the nonlinear dynamics of MSMAs. In this regard, an MSMA nonlinear oscillator is investigated, exploiting the system response under different bias magnetic field levels and actuation frequencies. A phenomenological model is employed to describe the MSMA magnetomechanical behavior. Numerical simulations are carried out using the operator split technique together with an iterative process and the fourth-order Runge–Kutta method. Results show that the application of a bias magnetic field can reduce the mean displacement of the system, increasing the oscillation amplitude. Furthermore, the period of oscillation can be modified, even achieving complex behaviors, including chaos. The potential use of MSMAs to dynamical systems is explored showing the possibility to provide adaptive behaviors.

R. Ju, S. M. Yang, H. Ren, W. Fan, R. C. Ni, and P. Gu
J. Comput. Nonlinear Dynam. Dec 2024, 19(12): 121001
https://doi.org/10.1115/1.4066221

​Steady-state rotary periodic responses of mechanisms lead to stress cycling in flexible structures or connecting joints, which in turn can result in structural fatigue. A general approach is developed to study rotary periodic solutions of rigid and flexible mechanisms with large spatial rotations based on the incremental harmonic balance (IHB) method. The challenge in analyzing such dynamic systems emanates from the noncommutativity of the spatial rotation and the nonsuperposition nature of the rotational coordinates. The generally used rotational coordinates, such as Euler angles, cannot be expanded into Fourier series, which prevents direct usage of the IHB method. To overcome the problem, the natural coordinates method and absolute nodal coordinate formulation (ANCF) are used herein for the dynamic modeling of the rigid and flexible bodies, respectively. The absolute positions and gradients are used as generalized coordinates, and rotational coordinates are naturally avoided. Equations of motions of the system are differential-algebraic equations (DAEs), and they are solved by the IHB method to obtain the steady-state rotary periodic solutions. The effectiveness of the proposed approach is verified by the simulation of rigid and flexible examples with spatial rotations. The approach is general and robust, and it has the potential to be further extended for other extensive multibody dynamic systems.

Xu Dai, József Kövecses, and Marek Teichmann
J. Comput. Nonlinear Dynam. Nov 2024, 19(11): 111005 
https://doi.org/10.1115/1.4066329

​Contact simulation is essential in modeling mechanical systems. The contact models require accurate geometric information, which is determined through collision detection methods. When the mechanical system includes flexible bodies such as structural components, the dynamic formulation and collision detection can be more challenging, as the geometric boundaries of such components keep changing during the simulation. The floating frame of reference (FFR) formulation is suitable for flexible systems with small deformation. In this work, a stable and efficient dynamic simulation method is introduced for flexible systems with contact based on the FFR formulation. In addition, a curve-based collision detection method is proposed, which is more consistent with the dynamic formulation and more efficient than common existing collision detection methods. Case studies of flexible beams and multibody systems are employed to demonstrate the performance of the proposed dynamic simulation and collision detection methods.

Paolo Magri, Marco Gadola, Daniel Chindamo, and Giulia Sandrini
ASME. J. Comput. Nonlinear Dyn. Oct 2024, 19(10): 101006
https://doi.org/10.1115/1.4066092​

Suspension and steering design play a major role in ensuring the correct dynamic behaviour of road vehicles. Passenger cars are especially demanding from this point of view: NVH and ride comfort requirements often collide with active safety-related requirements such as road holding in steady-state conditions and stability in transients. Driving pleasure is also important for market success, therefore accurate steering feedback and predictable handling properties are additional priorities.
Since flexible bushings are used as interface between the suspension arms and the chassis, extra degrees of freedom make the design process a complex task. While the use of a multibody software is common practice in the industry, a dedicated computational tool can be more practical and straightforward, especially when undertaking the design of a new suspension concept ground-up.
The paper presents a computational methodology for the design of an independent suspension with the associated kinematic and compliance attributes. Typical elastokinematic properties like toe, camber, wheelbase, and track variations vs tyre forces and moments can be computed by means of a dedicated software tool. A sort of validation was performed either by means of a comparison with a MathWorks Simscape® Multibody based model. Finally, a sensitivity analysis is given as an example.
Computationally, the method proposed is intuitively based on the equilibrium equations. The nonlinear equations are then solved with Newton-Raphson algorithm. The method can be also optimized for computational efficiency and is thoroughly described so that the reader can easily replicate it in the desired programming environment.

Sankalp Tiwari, Junaidvali Shaik, and C. P. Vyasarayani
J. Comput. Nonlinear Dynam. Feb 2024, 19(2): 021002 
​https://doi.org/10.1115/1.4064251

​Delayed systems are those in which the present dynamics is governed by what happened in the past. They are encountered in manufacturing, biology, population dynamics, control systems, etc. Determining stability of such systems is an important and difficult problem. In the existing works, stability is determined by assuming the governing differential equation. However, the equation may not be known or difficult to obtain. Unlike existing works, our method determines the linear stability of a delayed system using its response to a few known inputs. In particular, our method does not require or assume the differential equation governing that system. The only system information we use is its largest delay time, and the only assumption we make about the underlying equation is that its coefficients are either constant or time-periodic. Our approach involves giving the first few functions of an orthonormal polynomial basis as input and measuring/computing the corresponding responses to generate a state transition matrix, whose largest eigenvalue determines the stability. We demonstrate our method's correctness, efficacy, and convergence by studying four candidate DDEs with differing features. Importantly, we show that our approach is robust to noise in measurement, thereby establishing its suitability for practical applications.

Tomoyuki Suzuki, Kenji Hirohata, Yasutaka Ito, Takehiro Hato, Akira Kano
J. Comput. Nonlinear Dynam. November 2023, 18(11): 111001. 
https://doi.org/10.1115/1.4063224

Eduardo Okabe, Victor Paiva, Luis Silva-Teixeira, Jaime Izuka
J. Comput. Nonlinear Dynam. Oct 2023, 18(10): 104501 
https://doi.org/10.1115/1.4063222

Junaidvali Shaik, Sankalp Tiwari, and C. P. Vyasarayani
J. Comput. Nonlinear Dynam. Sep 2023, 18(9): 091005, https://doi.org/10.1115/1.4062633​

Delayed systems are those in which the present dynamics is governed by what happened in the past. They are encountered in manufacturing, biology, population dynamics, control systems, etc. Determining linear stability of such systems is an important and difficult problem. In this work, we propose a new method to determine stability of time-periodic delay differential equations (DDEs). In the usual approaches, the DDE is converted into an approximate system of time-periodic ordinary differential equations (ODEs). Later, standard ODE techniques are employed. In this paper, we develop a method that is more direct and general. Our approach is analogous to the well-known Floquet theory for ODEs: we consider one polynomial basis function at a time as the input function and stack the coefficients of the corresponding DDE solutions to construct a matrix whose largest magnitude eigenvalue determines linear stability. We demonstrate the correctness, efficacy and convergence of our method by studying several candidate DDEs with time-periodic parameters and/or delays, and comparing the results with those obtained from other standard methods. Our approach has the following additional advantages: (a) it is parallelizable, (b) it converges quickly, and (c) it requires knowledge of only elementary linear algebra and numerical computation of DDE solutions. ​

Josh H. P. Henry and Jacqueline Bridge
ASME. J. Comput. Nonlinear Dynam. August 2023; 18(8): 081012.
https://doi.org/10.1115/1.4062660

​A major issue with advancing prosthetics and robotics technology is mimicking natural motion. Super-Coiled Polymer (SCP) actuators are an economical and high-yield alternative to traditional actuators. However, the challenge lies in identifying suitable applications due to their hysteresis. By comparing SCP actuators with varying thread sizes, this paper suggests potential directions for their utilization. The actuators were created using coiling and heat training, controlled by Arduino. MATLAB was used to analyze the recorded data, focusing on the motion to assess the hysteresis characteristics. The observed characteristics inform recommendations for diverse applications in sensitive and coarse control systems.

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
​

​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.