Nonlinear Dynamics最新文献

{"title":"Fluid-structure dynamics of a vibro-impact capsule robot in multiphase intestinal environments.","authors":"Zepeng Wang, Jiyuan Tian, Yang Liu, Ana Neves, Shyam Prasad","doi":"10.1007/s11071-025-12175-z","DOIUrl":"10.1007/s11071-025-12175-z","url":null,"abstract":"<p><p>The gastrointestinal tract contains complex fluids, such as mucus, chyme, and water, that can significantly influence capsule robot locomotion by reducing friction or introducing hydrodynamic drag. This study presents a bidirectional fluid-structure interaction model that captures the dynamics of a vibro-impact capsule self-propelling through a fluid-filled small intestine. The model couples the motion of the magnetically actuated capsule, the viscoelastic deformation of the intestinal wall, and a gas-liquid two-phase flow field. Numerical predictions were systematically validated against experimental measurements under controlled laboratory conditions. The results show that an increased liquid volume fraction generates stronger resistance to capsule motion, more so than fluid viscosity alone, by causing fluid accumulation and vortex formation, thereby elevating hydrodynamic pressure and drag. Moreover, capsule performance is improved with higher excitation frequencies and duty cycles, enhancing both propulsion and motion robustness. This work provides a validated numerical platform for designing and optimising magnetically driven capsule robots, advancing their potential for diagnostic and therapeutic applications in the gastrointestinal tract.</p>","PeriodicalId":19723,"journal":{"name":"Nonlinear Dynamics","volume":"114 4","pages":"294"},"PeriodicalIF":5.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12945900/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147327023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"MIMO Volterra kernel recovery in the frequency domain using neural networks.","authors":"O H L Preston, T J Rogers, K Worden","doi":"10.1007/s11071-026-12672-9","DOIUrl":"10.1007/s11071-026-12672-9","url":null,"abstract":"<p><p>This paper presents a detailed analysis of a process for recovering multi-degree-of-freedom Volterra kernels using neural network weights, addressing the fact that such Higher-order Frequency Response Functions (HFRFs) have not previously been directly recovered from data. A novel method is proposed for HFRF recovery of Volterra kernels up to third order, and its effectiveness is demonstrated on a variety of systems using simulated data for validation. The harmonic-probing algorithms are derived from a general multi-input-multi-output NARX neural network model. These algorithms recover Volterra kernels for time-invariant systems with up to <i>n</i> degrees of freedom. The results demonstrate the accuracy of the method and suggest a promising direction for HFRF recovery in nonlinear time-invariant systems.</p>","PeriodicalId":19723,"journal":{"name":"Nonlinear Dynamics","volume":"114 13","pages":"871"},"PeriodicalIF":5.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13331911/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148391169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A unified necessary condition for dynamic bow snap-through with prestress tuning in electrostatically actuated bistable microbeams.","authors":"Sagi Tal, Lior Medina","doi":"10.1007/s11071-026-12816-x","DOIUrl":"10.1007/s11071-026-12816-x","url":null,"abstract":"<p><p>A curved bistable microbeam, subjected to electrostatic loading from an electrode facing its concave side, may exhibit bow snap-through (<i>BST</i>) at nearly half the voltage ( <math><mrow><mo>≈</mo> <mn>54</mn> <mo>%</mo></mrow> </math> ) when compared to actuation from the convex side. Previously, it was shown that introducing prestress can enable <i>BST</i> where it is otherwise unattainable. The current work extends the <i>BST</i> condition to include dynamic actuation, thus establishing dynamic bow snap-through (<i>DBST</i>) as a viable and sustainable form of actuation, since it can reduce actuation by <math><mo>≈</mo></math>  10 to 16%. To enable analytical derivation while retaining generality across various loading scenarios, the analysis employs an undamped single-degree-of-freedom reduced-order model obtained via Galerkin's decomposition. The resulting formulation yields a necessary condition for <i>DBST</i>, expressed in terms of beam geometry, prestress, and initial conditions, forming a unified condition. Subsequent analysis shows that suddenly applied actuations, combined with prestress, can enable <i>BST</i> over a wider range of parameters, whereas excessive kinetic energy and/or prestress can suppress <i>DBST</i>. The proposed condition provides practical design guideline for energy-efficient, low-voltage and non-volatile bistable devices.</p>","PeriodicalId":19723,"journal":{"name":"Nonlinear Dynamics","volume":"114 14","pages":"915"},"PeriodicalIF":5.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13372859/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148471958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A magneto-elastic model for soft magnetic concentric tube robots.","authors":"Peter Lloyd, Joshua Davy, Yael L May, Jurgen E Schneider, Pietro Valdastri","doi":"10.1007/s11071-026-12856-3","DOIUrl":"10.1007/s11071-026-12856-3","url":null,"abstract":"<p><p>This paper presents a numerical solution to a reduced-order analytical energy formulation of a soft, magnetically actuated concentric tube continuum robot. Unlike conventional concentric tube robots, which rely on pre-curved elastic energy storage and suffer from material stiffness constraints and snap through instability, our design uses softly magnetic rings adhered to braided sleeves to generate deformation directly from a strong, stationary background field. While high-field MRI systems provide a convenient actuation environment, the proposed design principle is broadly applicable to any application featuring a sufficiently strong background magnetic field (B <math><mo>≳</mo></math> 1T). We derive a complete magneto-elastic formulation that couples easy-plane magnetic torque with sleeve curvature to determine stable catheter configurations. The model captures mechanical hysteresis, bistability, and the nonlinear relationship between base rotation and tip pose. Experimental validation in the background field of a 7<i>T</i> pre-clinical MRI scanner demonstrates strong agreement with simulated deformation, with an overall RMS error of <math><mrow><mn>4</mn> <mo>.</mo> <msup><mn>4</mn> <mo>∘</mo></msup> </mrow> </math> . This framework provides a foundation for closed-loop control, systematic design optimization, and self-sensing capabilities in magnetically actuated soft continuum robots, enabling new classes of highly compliant robotic systems for constrained and sensitive environments.</p><p><strong>Supplementary information: </strong>The online version contains supplementary material available at 10.1007/s11071-026-12856-3.</p>","PeriodicalId":19723,"journal":{"name":"Nonlinear Dynamics","volume":"114 15","pages":"986"},"PeriodicalIF":5.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13424712/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148654166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical convergence of the scalar auxiliary variable method applied to nonlinear stiff string models.","authors":"Riccardo Russo, Michele Ducceschi, Stefan Bilbao","doi":"10.1007/s11071-026-12708-0","DOIUrl":"10.1007/s11071-026-12708-0","url":null,"abstract":"<p><p>This work is concerned with the Scalar Auxiliary Variable (SAV) method applied to geometrically nonlinear string models, focusing on the analysis of numerical convergence across various model formulations. An ODE system with a potential akin to that of the geometrically exact string is first analysed, providing both mathematical and numerical insight. Then, three nonlinear stiff string models are considered: geometrically exact (in two formulations), cubic, and Kirchhoff-Carrier models, each incorporating a stiffness term based on the Euler-Bernoulli formulation. A unified mathematical description is introduced in the continuous domain, using both quadratically split and non-split forms. Spatial and temporal discretisation is performed using Finite-Difference Time-Domain (FDTD) methods. Convergence is assessed by comparing SAV solutions with benchmark results obtained from convergent reference integrators at high sample rates, considering the transverse displacement, longitudinal displacement (when present), and the auxiliary variable. Results show that the non-split SAV converges for all three models, but only when the spatial step remains above the stability threshold of the corresponding split version, despite the scheme being unconditionally stable; furthermore, the global error is further strongly dependent on a potential shift constant. The split formulation converges reliably only when the potential decomposition reflects a natural separation between linear and nonlinear dynamics, as in the cubic and Kirchhoff-Carrier models, and in one particular form of the geometrically exact string.</p>","PeriodicalId":19723,"journal":{"name":"Nonlinear Dynamics","volume":"114 13","pages":"857"},"PeriodicalIF":5.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13315311/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148361985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamic response and parameter identification of an impact oscillator with a one-sided elastic constraint.","authors":"Bo Tian, Yang Liu, Julián Londoño Monsalve","doi":"10.1007/s11071-026-12946-2","DOIUrl":"10.1007/s11071-026-12946-2","url":null,"abstract":"<p><p>Impact systems are common in engineering and exhibit inherently nonlinear and nonsmooth dynamics due to intermittent contact and elastic deformation. This study investigates the dynamic response and parameter identification of an impact oscillator with a one-sided elastic constraint. A custom experimental rig was developed to generate controlled vibro-impact responses, and a piecewise-smooth mathematical model was formulated to capture the unilateral contact dynamics. Two complementary parameter identification strategies, a genetic-algorithm-based optimisation and a backbone-curve fitting method derived from harmonic balance principles, were employed to estimate key system parameters, including impact stiffness, damping, and gap, using both displacement-frequency and time-domain data. The identified parameters agreed consistently with theoretical predictions across repeated experimental trials, demonstrating the repeatability of the proposed identification framework for the stable periodic responses observed under the forward stepped-sine excitation tests. Overall, the study provides an experimentally supported framework for identifying nonlinear characteristics of impact oscillators, with potential applications in structural dynamics, vibration mitigation, and biomedical diagnostics.</p>","PeriodicalId":19723,"journal":{"name":"Nonlinear Dynamics","volume":"114 17","pages":"1115"},"PeriodicalIF":5.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13541849/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148897646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hysteresis in cavitation emissions during a ramped-then-deramped amplitude sonication: A theoretical and experimental investigation.","authors":"Yikai Zhang, Shida Li, Paul Prentice, Andrea Cammarano","doi":"10.1007/s11071-026-12462-3","DOIUrl":"10.1007/s11071-026-12462-3","url":null,"abstract":"<p><p>Dynamic hysteresis in cavitation emissions is investigated experimentally and numerically using a continuous ramped-then-deramped acoustic excitation. Hydrophone spectrograms reveal clear asymmetries between the ramped and deramped phases at identical excitation amplitudes, including differences in harmonic, subharmonic, and broadband components. These observations show that the acoustic state of the bubble population depends on the excitation history. A fully coupled 12-bubble model, incorporating spatially resolved interaction forces, reproduces all salient experimental features, including the subharmonic route to chaos, broadband emission, and broadband clearing. Poincaré mapping and continuation analysis reveal multiple coexisting attractors, distinguished by oscillation amplitude and period, delimited by saddle-node and period-doubling bifurcations. The hysteresis observed under continuous excitation arises from history-dependent convergence to these attractors. Basin-of-attraction computations demonstrate that attractor selection depends jointly on initial conditions and bubble-bubble interaction, enabling different bubbles to converge to distinct attractors under identical excitation amplitudes. Together, these results establish a physically interpretable nonlinear-dynamical mechanism underlying hysteresis in cavitation emission.</p><p><strong>Supplementary information: </strong>The online version contains supplementary material available at 10.1007/s11071-026-12462-3.</p>","PeriodicalId":19723,"journal":{"name":"Nonlinear Dynamics","volume":"114 8","pages":"591"},"PeriodicalIF":5.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13100018/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147778017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"From deterministic to stochastic: limits of extracting bifurcation diagrams for noisy bistable oscillators with the control-based continuation method.","authors":"Henrik T Sykora, Sandor Beregi","doi":"10.1007/s11071-024-10522-0","DOIUrl":"10.1007/s11071-024-10522-0","url":null,"abstract":"<p><p>Noise limits the information that can be experimentally extracted from dynamical systems. In this study, we review the Control-based Continuation (CBC) approach, which is commonly used for experimental characterisation of nonlinear systems with coexisting stable and unstable steady states. The CBC technique, however, uses a deterministic framework, whereas in practice, almost all measurements are subject to some level of random perturbation, and the underlying dynamical system is inherently noisy. In order to discover what the CBC is capable of extracting from inherently noisy experiments, we study the Hopf normal form with quintic terms with additive noise. The bifurcation diagram of the deterministic core of this system is well-known, therefore the discrepancies introduced by noise can be easily assessed. First, we utilise the Step-Matrix Multiplication based Path Integral (SMM-PI) method to approximate the system's steady state probability density function (PDF) for different intensity noise perturbations. We associate the local extrema of the resulting PDFs with limit cycles, and compare the resulting bifurcation diagram to those captured by CBC. We show that CBC estimates the bifurcation diagram of the noisy system well for noise intensities varying from small to moderate, and in practice, the amplitudes provided by CBC may be accepted as a 'best guess' proxy for the vibration amplitudes characteristic to the near periodic solutions in a wide range of experiments.</p>","PeriodicalId":19723,"journal":{"name":"Nonlinear Dynamics","volume":"113 8","pages":"8249-8263"},"PeriodicalIF":5.2,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11919953/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143670558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Computation of simple invariant solutions in fluid turbulence with the aid of deep learning.","authors":"Jacob Page","doi":"10.1007/s11071-025-11773-1","DOIUrl":"10.1007/s11071-025-11773-1","url":null,"abstract":"<p><p>The dynamical systems view of a turbulent fluid flow provides a tantalizing connection between the self-sustaining nonlinear mechanics of turbulence and its more well-known statistical properties, and promises to open up new avenues in our ability to understand, predict and control complex fluid motion. However, successful application of these ideas to a high Reynolds number (<i>Re</i>) problem requires the discovery and convergence of an expansive library of simple invariant solutions (e.g. equilibria, periodic orbits). The key challenge for the field has been that algorithms to compute dynamically relevant structures struggle for a variety of reasons outside of the weakly turbulent regime. It is here that ideas from deep learning have started to show promise, and this review describes how various techniques from the machine learning community have accelerated progress. First, the use of autoencoders - neural networks which perform a nonlinear analogue to PCA - will be described. There is compelling evidence that the low-order representations of the flow learned by these models are closely connected to the unstable simple invariant solutions embedded in the turbulent attractor. As such, these representations can be used to measure shadowing of periodic solutions, to parameterize reduced order models and to estimate manifold dimension. The other key technique adapted from deep learning reviewed here is the advance in high-dimensional, gradient-based optimization that has been driven by the requirements of neural network training. To exploit these tools, the search for simple invariant solutions is converted to a hunt for minima of a scalar loss function, and gradient computation is performed efficiently within a fully differentiable flow solver. Using forced, two-dimensional turbulence as a test case, these new methods reveal an order of magnitude more solutions than has been possible using earlier approaches and converge periodic orbits where previous methods have been ineffective. An assessment will be made as to what the large set of new exact solutions says about the 'dynamical systems' exercise in general and the prospects for application at high <i>Re</i>.</p>","PeriodicalId":19723,"journal":{"name":"Nonlinear Dynamics","volume":"113 23","pages":"31895-31915"},"PeriodicalIF":5.2,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12559166/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145401582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bifurcation-based dynamics and internal resonance in micro ring resonators for MEMS applications.","authors":"Saber Azizi, Hamed Haddad Khodaparast, Hadi Madinei, Mohammad I Younis, Ghader Rezazadeh","doi":"10.1007/s11071-025-11379-7","DOIUrl":"10.1007/s11071-025-11379-7","url":null,"abstract":"<p><p>This paper presents a novel investigation into the dynamics of a micro ring structure subjected to harmonic base excitation, designed as a highly sensitive MEMS mass sensor or bifurcation-based switch. Leveraging the in-plane nature of the motion, the system exhibits an exceptionally low damping ratio, making it ideal for detecting subtle changes in dynamic behaviour. The governing nonlinear differential equations, incorporating the geometric nonlinearities of the support beams, were derived and simplified into a reduced-order model consisting of coupled nonlinear Duffing-type equations. A key innovation of this study lies in the tunability of the system's frequency ratios, enabling the activation of a 1:3 internal resonance. By varying the length of the support beams while keeping the central ring geometry fixed, the first two natural frequencies were carefully examined, revealing a significant influence on the dynamic response. Frequency response curves confirmed the presence of 1:3 internal resonance near the primary resonance of the first mode, highlighting the potential for efficient energy transfer between modes. Furthermore, a detailed bifurcation analysis uncovered a range of complex nonlinear phenomena, including nonlinear modal interactions, torus bifurcations, quasi-periodic motion, and cyclic fold bifurcations. These bifurcations not only provide deeper insight into the system's dynamics but also offer additional operational mechanisms for switching applications. The findings demonstrate the system's capability to exploit nonlinear dynamics for enhanced sensitivity and robustness, paving the way for the development of next-generation MEMS sensors and bifurcation-based devices.</p>","PeriodicalId":19723,"journal":{"name":"Nonlinear Dynamics","volume":"113 18","pages":"24329-24342"},"PeriodicalIF":5.2,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12423269/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145065318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}