Muhammad Hassaan Ahmed, Utkarsh Srivastava, Ranjan Das, and Sachin Goyal
J. Comput. Nonlinear Dynam. Jul 2026, 21(7): 071005
https://doi.org/10.1115/1.4071926

This paper presents an interactive graphical user interface (GUI) for studying large-deformation bending of cantilever beams using a geometrically exact nonlinear rod model. The tool allows users to directly compare the predictions of classical small-deflection beam theory with nonlinear large-deformation behavior in real time. This makes it easier to see how geometric nonlinearities affect the structural response as the deformation increases. Most educational beam visualization tools are limited to linear theory, but the approach used in this work can efficiently handle large deformations through a two-step initial value formulation. Because of this, users can quickly explore different parameter values without relying on computationally expensive iterative boundary-value solution methods. To evaluate the accuracy of the framework, the results from the GUI were compared with analytical solutions, nonlinear finite element simulations, and an experimentally validated computational rod model. The comparisons showed good agreement across the different methods and confirmed the numerical stability of the implementation. The GUI was developed with both teaching and research applications in mind. Its interactive design provides an accessible way for students and researchers to explore nonlinear structural mechanics and better understand geometrically exact rod behavior.

Tingying Lu, M. R. B. Shahadat, Qilin Liu, Runlin He, Xiaoyu Jiang, amd Zheng Li
J. Comput. Nonlinear Dynam. Apr 2026, 21(4): 041006
https://doi.org/10.1115/1.4070545

​This study introduces Gradient-Driven Physics-Informed Neural Networks (GDPINNs) to improve the accuracy of heat transfer and incompressible fluid flow problems with sharp gradients. Traditional Physics-Informed Neural Networks (PINNs) often struggle to capture regions with sharp changes in temperature or velocity because their loss functions treat all spatial regions equally. To address this limitation, our approach incorporates gradient information directly into the loss function and strategically increases collocation points in high-gradient regions. These two enhancements enable the model to learn the underlying physics more efficiently and reconstruct sharp variations with higher accuracy.

Andrés Bellei-Pardo and Balakumar Balachandran
J. Comput. Nonlinear Dynam. Mar 2026, 21(3): 031003
https://doi.org/10.1115/1.4070543

The growing demand for self-powered remote sensors and small electronics has spurred interest in energy harvesters that can operate in low-speed wind environments for which conventional turbines are not best suited. Energy harvesters based on vortex-induced vibrations offer a promising, sustainable alternative. However, modeling and optimization of these systems is challenging as high-fidelity simulations are often prohibitively expensive, while simplified lumped-parameter models fail to capture complex geometries or boundary conditions. Here, the authors address this challenge by presenting a reduced-order modeling framework in which a nonlinear wake oscillator is integrated with a finite-element structural formulation. With this approach, the fidelity required to capture complex mode shapes of the structure is retained while maintaining the computational efficiency of lower-order models. Validation is conducted by using data from three independent experiments. The integrated framework is found to capture the critical lock-in region, wherein vortex shedding and structural frequencies synchronize, which is essential for maximizing power extraction. By accurately predicting key metrics such as voltage output and vibration amplitude without the cost of full fluid dynamics simulations, this model can serve as a useful tool for efficient design and optimization of sustainable energy harvesters.

Erhan Ferhatoglu and Johann Gross
J. Comput. Nonlinear Dynam. Feb 2026, 21(2): 021003
https://doi.org/10.1115/1.4070197

This study advances the prediction of vibration response variability arising from the nonuniqueness of static friction forces (residual traction uncertainty) in turbine blades coupled by frictional interfaces. Utilizing a nonlinear mode-based method, uncertainty is first quantified on amplitude-dependent modal parameters and then forward propagated to the vibration response to obtain frequency response bounds via interval analysis. For the first time, the uncertainty quantification is systematically demonstrated on a state-of-the-art model with a newly developed optimization-based framework. To address the computational demands of the optimization problem, two variants are proposed: (1) performing three optimizations that are independent from the forcing pattern and response location, or (2) conducting six optimizations that enable a full characterization but are valid only for a specific forcing pattern and response location. The former yields a slightly more conservative upper bound of frequency responses, but is limited to the backbone curve computation, significantly reducing the overall computational effort. The effectiveness of the proposed approach is demonstrated using a high-fidelity model of turbine blades coupled by an asymmetric underplatform damper. During the uncertainty quantification phase, the bounds of amplitude-dependent modal parameters, systematically determined through optimization, are validated by comparison with results from multiple Harmonic Balance simulations using manually assigned residual tractions. In the uncertainty propagation phase, the frequency response bounds are shown to successfully capture the full range of vibration response variability, up to the onset of 1:1 internal resonance between the first two modes at higher amplitudes.

Alireza Ahmadi and Neda Maghsoodi
J. Comput. Nonlinear Dynam. Feb 2026, 21(2): 021004
https://doi.org/10.1115/1.4070198

​This paper investigates the effect of intrinsic (built-in) bending curvature on the dynamics, energetics, and stability of photomechanical fibers, which deform in response to illumination. We develop a multiphysics dynamic model based on the nonlinear Kirchhoff’s rod theory to capture the coupled photomechanical response of the curved fibers. Using two canonical examples—the bending of a clamped-free strip and the periodic flapping of a clamped-clamped strip—we demonstrate how intrinsic curvature fundamentally affects the spatiotemporal deformation of the strips subject to steady illumination. Our findings reveal that the dynamic behavior of intrinsically curved photomechanical fibers differs both qualitatively and quantitatively from their intrinsically flat counterparts, underscoring the importance of initial geometry in the design and control of photomechanical systems. In particular, in the case of the clamped- clamped strips, although both the pre-stressed strip and stress-free curved strip exhibit self-sustained periodic flapping motions when subject to steady illumination, the stress-free curved strip requires higher input energy (i.e., greater light intensity), oscillates at a lower frequency, and exhibits a largely asymmetric deformation pathway per cycle. Moreover, the range of illumination angles that can trigger self-sustained oscillations in stress-free curved strips is narrower compared to the pre-stressed case.

Bassam J. Alshaer and Hamid M. Lankarani
J. Comput. Nonlinear Dynam. Dec 2025, 20(12): 121008
https://doi.org/10.1115/1.4069962

This research introduces a new analytical framework for modeling finite-length lubricated journal bearings in multibody systems, striking a balance between the simplicity of traditional infinite-length models and the precision of detailed finite-length solutions. Although infinite-length approximations are computationally and implementationally efficient, they ignore axial leakage and 3D pressure effects, leading to inaccuracies in real-world scenarios. On the other hand, existing exact finite-length models provide high accuracy but are mathematically complex, apply domain transformations and implementation inefficient, and hindering widespread use. The proposed method employs a separation of variables approach to the Reynolds equation, deriving closed-form expressions for hydrodynamic pressure and forces that incorporate side leakage while remaining implementing efficient for system-level simulations. Implemented within a dynamic multibody framework using an augmented Lagrangian formulation, the model allows physical lubricated bearings to replace idealized revolute joints. Validation against numerical benchmarks confirms the accuracy of the analytical solutions. Case studies - including a loaded journal-bearing system and a high-speed crank-slider mechanism—demonstrate the model's ability to capture finite-length effects, such as elevated eccentricity ratios and dynamic force overshoots caused by axial leakage, without sacrificing simplicity. The findings underscore the substantial influence of finite-length corrections on dynamic behavior, including journal orbit stability, force distribution, and torque variations. This study provides a scientifically rigorous yet practical approach for integrating realistic lubrication effects into multibody dynamics, enhancing simulation accuracy for engineering systems with lubricated clearance joints.

He Ma, Zijun Yang, Suo Wang, Haitao Xu, and Shengxi Zhou
J. Comput. Nonlinear Dynam. Jan 2026, 21(1): 011002
https://doi.org/10.1115/1.4069824

​Bistable vibration energy harvesters have been comprehensively and thoroughly studied for their outstanding energy harvesting capabilities. The lever mechanism offers a straightforward and effective solution for realizing bistable systems. Neglecting dynamical characterization of such harvesters would lead to unanticipated nonlinear behaviors that impair performance. Thus, this paper proposes a nonlinear lever-type vibration energy harvester with a series-connected RLC circuit. First, a bistable energy harvester is designed by introducing negative stiffness. The theoretical model has been established and is validated by numerical and experimental results. Second, the relationship between the equivalent stiffness and the magnet space is studied, based on which dynamic responses under different magnet spaces are then analyzed by the bifurcation diagram. According to the Poincaré map, chaos can be perceived. The cause of the chaos is figured out as a period-doubling bifurcation through the phase trajectory. Third, potential energy with various lever pivot positions is compared, indicating that a higher potential energy well leads to interwell oscillations, and chaos is highly related to the pivot position. Finally, the power generated is discussed by altering the RLC circuit's resonant frequency and resistance value. The average power is capable of achieving 3.22 mW. Overall, this paper establishes the theoretical foundation for investigating the dynamic characteristics of lever-based bistable energy harvesters, as well as the influence of RLC circuit loading on power output performance.

Jie Wang, Qi Jiang, Zehou Zhang, and Na Li
J. Comput. Nonlinear Dynam. Nov 2025, 20(11): 111006
https://doi.org/10.1115/1.4069327

​Tendon-driven continuum robots are widely used in medical and industrial applications due to their slender and nimble characteristics. It is helpful to control tendon-driven continuum robots more accurately to study the mechanism and laws of generating friction loss and the hysteresis phenomenon in tendon–sheath transmission systems (TSTS). This paper deduces a theoretical model of tension transmission and hysteresis in the TSTS. A dynamic model of the TSTS containing arbitrary Lagrange–Euler (ALE) nodes is proposed using the absolute nodal coordinate formulation (ANCF) to obtain the system configuration, total deformation angle, and to accurately compute the friction and hysteresis in conjunction with the theoretical model. A friction calculation method based on Hertzian contact theory is developed, and a nonfixed TSTS was used as the experimental object to verify the accuracy of the dynamic model of the TSTS. A feedforward compensation control strategy based on the model is constructed and experimentally validated. The root-mean-square error (RMSE) of the friction compared to the theoretical value obtained using the numerical calculation method was minimized to 0.097 N. The friction of the tendon system was compensated using a feedforward control strategy, and the RMSE of the output relative to the desired value was obtained as 0.363 N. The results show that the dynamic model of the TSTS can accurately calculate the configurations and can be effectively combined with the theoretical model to realize model-predictive compensatory control.

Ioannis Polyzos and Athanasios Chasalevris
J. Comput. Nonlinear Dynam. Sep 2025, 20(9): 091003
https://doi.org/10.1115/1.4068698

In rotating systems where a shaft is mounted on journal bearings, chaotic dynamic response may occur under specific design and operating conditions. Although chaos does not necessarily prevent the operation of rotating machines, it may result in higher frictional power loss and temperature rise in the bearings, compared to operation with periodic or quasi-periodic responses; it is also likely to compromise the integrity of the system when whirling orbits evolve to a large extent. A rotor-bearing system consisting of a rigid rotor mounted on two journal bearings is used to produce chaotic dynamics, which are detected and verified using numerical tools. This study uses sliding bearings with active geometry, that serves as the control input, and implements the Ott-Grebogi-Yorke (OGY) discrete-time control method, to convert chaotic oscillations to periodic. It is found that the OGY method can control the chaotic response and produce periodic motions of desired periodicity with minimal control effort. This method proves robust to measurement errors and noise, actuation errors as well as model uncertainties in oil viscosity and bearing radial clearance. Performance was further enhanced with the use of a Model Predictive Control (MPC) assisted OGY strategy. The results create potential for smooth periodic motions in high-speed rotating systems.

Junaid Ali, Gregory Shaver, and Anil K. Bajaj
J. Comput. Nonlinear Dynam. Sep 2025, 20(9): 091007
https://doi.org/10.1115/1.4068930

This study presents an extended investigation into the dynamic behavior of a multidegree-of-freedom (DOF) driveline interconnected by a series of universal joints (U-joints). While previous studies have focused on the effects of rotational-type clearance within a single U-joint in a 2DOF shaft system—revealing bifurcation phenomena such as period-doubling routes to chaos and various crisis bifurcations—this work extends the analysis to a 3DOF driveline coupled with two U-joints arranged in a Z-type configuration, with a π/2 rad phase difference, which is previously not explored. The presence of multiple U-joints introduces additional holonomic constraints and nonsmooth nonlinearities, resulting in more complex dynamical behavior. This study highlights the significant influence of U-joint phasing on the dynamics of multijointed drivelines, particularly in the context of clearance-induced nonlinearities. Numerical bifurcation diagrams are constructed for driveline output states as functions of system parameters, and Poincaré mapping is used to characterize the presence of periodic and coexisting attractors, as well as strange chaotic attractors exhibiting fractal-like properties. The boundaries between periodic and chaotic regions are identified through the computation of basins of attraction for coexisting attractors and 2D parameter space. Furthermore, the study demonstrates that the driveline exhibits greater sensitivity to mechanical clearances in the downstream U-joint compared to the upstream joint, highlighting the critical role of U-joint phasing in torsional instability mitigation. These findings provide new insights into the nonlinear dynamics of driveline systems with multiple U-joints and clearances, paving the way for more accurate modeling and the development of robust design strategies.

Haitao Xu and Shengxi Zhou
J. Comput. Nonlinear Dynam. September 2025, 20(9): 091008
https://doi.org/10.1115/1.4068931

A vibration energy harvester, an electromechanical system, can capture energy from ambient vibration and convert it into electricity for low-powered sensors. It is inevitable that the random noise would have a considerable effect on the output power of the harvester. Therefore, this paper theoretically and numerically analyzes the performance of the “V” to “U” typed (the potential function shape can be adjusted as letter V and U) monostable energy harvester (V-U-MEH) that is injected with Gaussian white noise. First, the determined frequency is derived according to the energy balance method, taking into account the strong linearity under random excitation. Second, the stationary probability density function, which indicates the statistics of the harvester's output, is derived based on the generalized stochastic averaging method. Finally, the mean square voltage and averaging power are theoretically analyzed, which is examined through Monte Carlo simulation, and the results are in accordance with theoretical findings.

Thomas Breunung and Balakumar Balachandran
J. Comput. Nonlinear Dynam. Aug 2025, 20(8): 081007
https://doi.org/10.1115/1.4067983
​
​​Engineering systems naturally vibrate, and the reduction of the associated oscillations is crucial to increase lifespan, energy efficiency, and performance. To that end, many vibration attenuation strategies have been proposed and implemented in, for example , buildings, automotive systems, and aerospace applications. Most existing vibration attenuation schemes are based on well-developed linear systems theory. However, these schemes are not applicable to systems that exhibit nonlinear behavior. Furthermore, with linear approaches, one fails to leverage the potential of nonlinearities, which are invariably present in many applications. In this article, a beneficial interplay between nonlinearity and noise is utilized to reduce vibration amplitudes. More specifically, the sensitivity of high-amplitude nonlinear responses is leveraged. Through noise addition, the response is steered away from high-amplitude vibrations to low-amplitude vibrations. Hence, the vibration amplitudes associated with a resonance are effectively reduced. Experiments and simulations confirm the efficiency and universality of the proposed strategy. It is shown that the observed vibration attenuation is robust with respect to parameter changes, responses associated with multiple resonances can be affected with one, single scheme, and one can utilize various noise sources in this scheme. Overall, the maximal amplitude is reduced by about 50%.

Andrea Arena and Marco Lepidi
J. Comput. Nonlinear Dynam. August 2025, 20(8): 081011
https://doi.org/10.1115/1.4067702

A parametric lattice model is formulated to describe the dispersion properties of harmonic elastic waves propagating in two-dimensional textile metamaterials. Within a weak nonlinear regime, the free undamped motion of the textile metamaterial, starting from a spatially periodic prestressed configuration, is governed by nonlinear differential difference equations, where nonlinearities arise from the elastic contact between plain woven yarns. Within the linear field, the linear dispersion properties characterizing the regime of small oscillation amplitudes are obtained, by applying the Bloch's theorem. Parametric analyses are carried out to study the influence of the mechanical parameters on wavefrequencies, waveforms and group velocities. As major outcome, the dispersion spectrum is found to possess two distinct passbands, covering the low- and the high-frequency ranges, respectively, while a complete mid-frequency bandgap exists for large parameter regions. Within the nonlinear field, the nonlinear wavefrequencies and the multi-harmonic non-resonant response in the time domain are described, by means of perturbation techniques. As interesting finding, the free wave are shown to propagate with a systematic softening behavior. The wave polarization exalts the nonlinear effects in the high-frequency passband.

Thomas Kordik, Hubert Gattringer, and Andreas Müller
J. Comput. Nonlinear Dynam. Aug 2025, 20(8): 081008
​https://doi.org/10.1115/1.4068321

A major field of industrial robot applications deals with repetitive tasks that alternate between operating points. For these so-called pick-and-place operations, parallel kinematic manipulators (PKM) are frequently employed. These tasks tend to automatically run for a long period of time and therefore minimizing energy consumption is always of interest. As recent research addresses the use of elastic elements, this paper explores the possibilities of minimizing energy consumption of pick-and-place task performing PKM that are driven by series elastic actuators (SEA). The basic idea is to excite eigenmotions that result from the actuator springs and exploit their oscillating characteristics. To this end, a prescribed cyclic pick-and-place operation is analyzed and a dynamic model of SEA driven PKM is derived. Subsequently, an energy minimizing optimal control problem is formulated where operating trajectories as well as SEA stiffnesses are optimized simultaneously. Here, optimizing the actuator stiffness does not account for variable stiffness actuators. It serves as a tool for the design and dimensioning process. The hypothesis on energy reduction is tested on two (parallel) robot applications where redundant actuation is also addressed. The results confirm the validity of this approach.

Nami Mogharabin and Amin Ghadami
J. Comput. Nonlinear Dynam. Feb 2025, 20(2): 021006
https://doi.org/10.1115/1.4067297

​Characterizing the nonlinear behavior of dynamical systems near the stability boundary is a critical step toward understanding, designing, and controlling systems prone to stability concerns. Traditional methods for bifurcation analysis in both experimental systems and large-dimensional models are often hindered either by the absence of an accurate model or by the analytical complexity involved. This paper presents a novel approach that combines the theoretical frameworks of nonlinear reduced-order modeling and stability analysis with advanced machine learning techniques to perform bifurcation analysis in dynamical systems. By focusing on a low-dimensional nonlinear invariant manifold, this work proposes a data-driven methodology that simplifies the process of bifurcation analysis in dynamical systems. The core of our approach lies in utilizing carefully designed neural networks to identify nonlinear transformations that map observation space into reduced manifold coordinates in its normal form where bifurcation analysis can be performed. The unique integration of analytical and data-driven approaches in the proposed method enables the learning of these transformations and the performance of bifurcation analysis with a limited number of trajectories. Therefore, this approach improves bifurcation analysis in model-less experimental systems and cost-sensitive high-fidelity simulations. The effectiveness of this approach is demonstrated across several examples.