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Recent advancements of nonlinear dynamics in mode coupled microresonators:a review

Applied Mathematics and Mechanics(English Edition) 2025年第2期46卷 209-232页

作者： Xuefeng WANG Zhan SHI Qiqi YANG Yuzhi CHEN Xueyong WEI Ronghua HUAN Department of Engineering Mechanics MIIT Key Laboratory of Dynamics and Control of Complex SystemsNorthwestern Polytechnical UniversityXi’an 710129China Department of Mechanics Key Laboratory of Soft Machines and Smart Devices of Zhejiang ProvinceZhejiang UniversityHangzhou 310027China State Key Laboratory for Manufacturing Systems Engineering Xi’an Jiaotong UniversityXi’an 710054China

Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential *** review focuses on mode-coupled micromechanical resonators,highlighting the latest advancements in four key areas:internal resonance,synchronization,frequency combs,and mode *** origin,development,and potential applications of each of these dynamic phenomena within mode-coupled micromechanical systems are investigated,with the goal of inspiring new ideas and directions for researchers in this field.

关键词： mode coupling micro-electro-mechanical system(MEMS)resonator nonlinear dynamics

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Mechanical and Geometric Properties of Nanosprings Based on Carbon Nanotubes with Dislocation Dipoles

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ACS Applied Nano Materials 2025年第18期8卷 9192-9200页

作者： Lei, Xiao-Wen Koyane, Jumpei Lu, Tong Matsuzaki, Kenichiro Yan, Yi Shi, Jin-Xing Fujii, Toshiyuki School of Materials and Chemical Technology Institute of Science Tokyo 2-12-1 Ookayama Meguro-ku Tokyo152-8550 Japan Department of Engineering Mechanics MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710072 China Department of Production Systems Engineering and Sciences Komatsu University Nu 1-3 Shicyomachi Ishikawa Komatsu923-8511 Japan

Carbon nanotubes (CNTs) are lightweight materials with excellent mechanical, electrical, and thermal conductivity, which make helical CNTs promising candidates for applications in mechanical components such as nanosprings. In this study, based on the continuous dislocation theory, we introduce dislocation dipoles into CNT with discrete crystal structures to design nanosprings, propose a method that integrates mechanics and geometry, and analyze the mechanical and geometric properties of nanosprings. In detail, this study investigated the feasibility of designing helical CNTs through spontaneous deformation induced by dislocation dipoles separated from Stone-Wales defects. Analytical models were constructed by systematically introducing dislocation dipoles into (4,4) CNTs of varying lengths. We combined mechanical and geometric methods, performed molecular dynamics simulations to obtain the stable structure of CNTs with dislocation dipoles, and employed differential geometry to investigate the Willmore energy of helically shaped CNTs. The results showed that when dislocation dipoles were introduced into straight CNTs, energy relaxation calculations demonstrated spontaneous deformation, leading to the formation of a spring-shaped CNT. The CNT length and dislocation type significantly affected the spring constant. Longer CNTs exhibited lower spring constants, and an increase in dislocation density led to a higher average potential energy. This study provides unique insights into the control of the CNT shape and mechanical and geometrical properties, contributing to the design of functional materials such as nanosprings. © 2025 The Authors. Published by American Chemical Society.

关键词： Geometry

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Nonlinear Dynamic Modeling and Analysis of Rigid-Flexible Coupling Spacecrafts with Time-Varying Temperature Distribution

SSRN

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SSRN 2025年

作者： Zhao, Bingxin Gu, Xudong Hu, Rongchun Wu, Sihan Deng, Zichen Department of Engineering Mechanics Northwestern Polytechnical University Xi’an China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an China

When establishing the dynamic model of a rigid-coupled spacecraft, the traditional linear method requires the flexible structure to satisfy the small deformation assumption. However, the wide range of motion of the large spacecraft may lead to nonlinear deformation of the flexible structure. In this paper, the nonlinear dynamic model of the rigid-flexible coupling spacecraft is established during in-orbit operation. Firstly, the kinetic energy of the rigid-flexible spacecraft is derived by incorporating the nonlinear deformations with second-order coupling terms. Secondly, the time-varying temperature distribution along the thickness direction of the flexible structure is derived by using a one-dimensional thermal conduction equation. Then, the nonlinear time-varying coupled dynamics equations of the rigid-flexible coupling spacecraft are obtained by the Hamilton’s variational principle. The discrete equations are derived by using the assumed modal method (AMM). Finally, the results obtained through numerical calculations indicate that the nonlinear model accurately predicts the dynamical stiffening phenomenon as the attitude rotational velocity of the rigid hub increases. At the same time, the effects of the temperature, the orbital radius and structure size on the response amplitude of the spacecraft are obtained. © 2025, The Authors. All rights reserved.

关键词： Kinetics

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Expand the synchronization range of MEMS linear oscillators based on mode coupling and phase control

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Sensors and Actuators A: Physical 2025年 389卷

作者： Dai, Hongsheng Wang, Xuefeng Shi, Zhan Yang, Qiqi Xiao, Zunhao Liu, Zhiqiang Wei, Xueyong Huan, Ronghua Department of Mechanics Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province Zhejiang University Hangzhou China Department of Engineering Mechanics MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an China State Key Laboratory for Manufacturing Systems Engineering Xi'an Jiaotong University Xi'an China School of Instrument Science and Technology Xi'an Jiaotong University Xi'an China Huanjiang Laboratory Shaoxing China

Synchronization is a widespread phenomenon observed in both natural and societal systems. The advancement of MEMS technology has facilitated the study and application of synchronization, significantly enhancing the performance of MEMS sensors. However, the limited synchronization range of linear systems has restricted its broader application in sensor technologies. In this article, we propose a method to expand the synchronization range based on mode coupling and phase control. Theoretical derivations and experimental validations were conducted to demonstrate the effectiveness of the proposed approach. Experimental results reveal that the method achieves a synchronization range expansion of more than 50 times for both downward and upward frequency sweeps. Furthermore, the maintenance time of the synchronized state is significantly extended. This achievement is expected to provide a new solution for the application of synchronization-enhanced sensing in various fields, paving the way for improved sensor performance and broader applicability. © 2025 Elsevier B.V.

关键词： Synchronization

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Higher-order interactions induce stepwise explosive phase transitions

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Physical Review E 2025年第2期111卷 024303-024303页

作者： Xueqi Li Palash Kumar Pal Youming Lei Dibakar Ghosh Michael Small School of Mathematics and Statistics Northwestern Polytechnical University Xi'an 710072 China Physics and Applied Mathematics Unit Indian Statistical Institute 203B. T. Road Kolkata 700108 India Ministry of Industry and Information Technology Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an 710072 China Complex Systems Group Department of Mathematics and Statistics The University of Western Australia Crawley WA 6009 Australia Mineral Resources CSIRO Kensington WA 6151 Australia

In recent studies, it has been established that higher-order interactions in coupled oscillators can induce a process from continuous to explosive phase transition. In this study, we identify a phase transition, termed the stepwise explosive phase transition, characterized by the emergence of multiple critical phase plateaus in a globally frequency-weighted coupled pendulum model. This transition bridges the continuous and explosive phase transitions, arising from a delicate balance between attractive higher-order interactions and repulsive pairwise interactions. Specifically, the stepwise explosive phase transition occurs when the higher-order coupling is moderate, neither large nor small, while the pairwise interactions remain repulsive. Our analysis shows that stronger attractive higher-order interactions necessitate weaker repulsive pairwise interactions, leading to partial frequency locking among oscillators and triggering the stepwise transition. We construct an analytical framework using self-consistent equations to provide an approximation of the steady-state behavior. This study uncovers an alternative pathway to the desynchronization, and it provides additional insights into the phase transitions in coupled dynamical networks.

关键词： Pendulums

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Negative-pressure soft pneumatic actuators enabled by asymmetrically distributed bending units

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Extreme Mechanics Letters 2025年 77卷

作者： Fu, Zeyu Chen, Tianyu Zou, Haoran Zhu, Zhiwei Deng, Zichen Wang, Yifan School of Mechanics Civil Engineering and Architecture Northwestern Polytechnical University Xi'an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an710072 China School of Mechanical and Aerospace Engineering Nanyang Technological University Singapore 639798 Singapore State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures Shijiazhuang Tiedao University Shijiazhuang050043 China

Soft pneumatic actuators are highly flexible and can adapt to complex environments, attracting significant attention for their ability to operate in settings where rigid actuators cannot. Most existing soft pneumatic actuators are powered by positive pressure, which has the disadvantage of volume increase during operation and risk of exploding under large pressures. In this study, we designed a new type of soft actuator by inducing asymmetric bending deformation throughout a holey structure under negative pressure. Using finite element analysis and a theoretical model, we studied the effects of various geometric parameters on the structure's bending behavior. We found that the displacement of the circle's center from the central axis is a parameter with the most significant impact on the bending behavior of the structure. By designing circular holes with offset from the central axis, the structure can bend toward the offset direction during subsequent bending deformation. Based on this deformation mechanism, we designed a soft gripper that bends upon actuation and effectively picks up objects. We further designed a bi-directional gripper that bends towards both sides and a circular gripper that contracts towards the center upon evacuation to hold objects. These soft grippers’ grasping capabilities are validated by experimental tests. Finally, by arranging the holes in a wavy pattern within the structure, we created a crawling robot that moves forward through cyclic negative pressure actuation. These findings highlight the potential of leveraging bending behaviors in asymmetrically distributed holey structures for the development of negative-pressure driven soft actuators and robots. © 2025 Elsevier Ltd

关键词： Pneumatic actuators

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Dynamic analysis of rigid-flexible coupling spacecraft based on Euler parameters

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Scientific Reports 2025年第1期15卷 1-12页

作者： Ji, Yi Zhang, Huan School of Astronautics Harbin Institute of Technology Harbin 150001 China Frontier Science Center for Interaction between Space Environment and Matter Harbin 150001 China National Key Laboratory of Modeling and Simulation for Complex Systems Harbin 150001 China MOE Key Laboratory of Dynamics and Control of Flight Vehicle Beijing Institute of Technology Beijing 100081 China

With the development of aerospace technology, rigid-flexible coupling spacecraft with strong nonlinearity dominates, bringing huge challenges for numerical tools. This paper aims to accurately and quickly analyze the dynamic behavior of rigid-flexible coupling spacecraft. In our work, rigid body and flexible body are both described by Euler parameters for avoiding singular angles. Then, for this type of strong nonlinear dynamic system, the BN-stable method that is unconditionally stable for nonlinear initial value problems proposed by the first author is introduced to solve the transient responses. To keep the accuracy of the numerical rotation matrix, the relation between the angular velocity and Euler parameters, and the constraint in the level of velocity, are introduced to reformulate the original BN-stable method. Through the dynamic analysis for rigid satellite bodies and flexible solar wings, we find that the proposed strategy can effectively simulate the dynamic responses of spacecraft, and compared to the currently popular strategy, our strategy enjoys considerable advantages in accuracy, stability, and dissipation. © The Author(s) 2025.

关键词： BN-stability Dynamic analysis Euler parameters Rigid-flexible coupling Rotation matrix

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Reverse aperiodic resonance in low- to high-dimensional bistable systems: A complement to stochastic resonance studies in logic circuits

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Communications in Nonlinear Science and Numerical Simulation 2025年 149卷

作者： Shen, Mengen Yang, Jianhua Sanjuán, MiguelA.F. Chen, Huatao Wang, Zhongqiu Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment School of Mechanical and Electrical Engineering China University of Mining and Technology Jiangsu Xuzhou221116 China Nonlinear Dynamics Chaos and Complex Systems Group Departamento de Física Universidad Rey Juan Carlos Tulipán s/n Madrid Móstoles28933 Spain Division of Dynamics and Control School of Mathematics and Statistics Shandong University of Technology Zibo255000 China School of Computer Science and Technology China University of Mining and Technology Jiangsu Xuzhou221116 China

As circuits continue to shrink in size, noise has emerged as a critical challenge in achieving optimal performance. Stochastic resonance in logic circuits offers an innovative approach to harness noise constructively;however, current implementations are limited to basic logical functions such as OR, AND, NOR, and NAND, restricting broader applications. This paper introduces a three-dimensional (3D) coupling model to investigate the counterintuitive phenomena that arise in nonlinear systems under noise. Compared to the one-dimensional Langevin equation and the two-dimensional Duffing equation, the 3D coupling model features more adjustable parameters and coupling interactions, enhancing the system's dynamic behavior. The study demonstrates that increasing noise intensity triggers reverse aperiodic resonance, leading to signal phase reversal and amplitude amplification. This phenomenon is attributed to the motion of Brownian particles in a bistable potential well. Additionally, reverse aperiodic resonance addresses the lack of logical negation in traditional stochastic resonance systems by introducing noise-driven phase reversal, providing a novel alternative to conventional inverters. © 2025 Elsevier B.V.

关键词： Sequential circuits

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Analysis of the optimal target node to reduce seizure-like discharge in networks

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Chinese Physics B 2024年第5期33卷 712-720页

作者：闫璐瑶张红慧孙中奎 School of Mathematics and Statistics Northwestern Polytechnical UniversityXi'an 710129China MIIT Key Laboratory of Dynamics and Control of Complex Systems Xi'an 710129China

Network approaches have been widely accepted to guide surgical strategy and predict outcome for epilepsy *** study starts with a single oscillator to explore brain activity,using a phenomenological model capable of describing healthy and epileptic *** ictal number of seizures decreases or remains unchanged with increasing the speed of oscillator excitability and in each seizure,there is an increasing tendency for ictal duration with respect to the *** underlying reason is that the strong excitability speed is conducive to reduce transition behaviors between two attractor ***,the selection of the optimal removal node is estimated by an indicator proposed in this *** show that when the indicator is less than the threshold,removing the driving node is more possible to reduce seizures significantly,while the indicator exceeds the threshold,the epileptic node could be the removal ***,the driving node is such a potential target that stimulating it is obviously effective in suppressing seizure-like activity compared to other nodes,and the propensity of seizures can be reduced 60%with the increased stimulus *** results could provide new therapeutic ideas for epilepsy surgery and neuromodulation.

关键词： epilepsy driving node epileptic node seizure regulation

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Topological edge state analysis of hexagonal phononic crystals

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Acta Mechanica Sinica 2022年第3期38卷 78-85,I0002页

作者： Kai Zhang Fang Hong Je Luo Zichen Deng School of Mechanics Civil Engineering and ArchitectureNorthwestern Polytechnical UniversityXi'an 710072China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical UniversityXi'an 710072China

In this study,we propose valley phononic crystals that consist of a hexagonal aluminum plate with six chiral arrangements of *** phononic crystals were introduced into a topological insulator(TI)system to produce topologically protected edge waves(TPEW s)along the topological *** implementation of chiral topological edge states is different from the implementation of topological edge states of systems with *** the conventional breaking of mirror symmetry,a new complete band with topological edge modes gap was opened up at the Dirac point by tuning the difference in lengths of the ligaments in the chiral unit *** investigated the dispersion properties in chiral systems and applied the dispersion properties to waveguides on the interfaces to achieve designable route ***,we simulated the robust propagation of TPEWs in different routes and demonstrated their immunity to backscattering at ***,the existence of the valley Hall effect in chiral systems was *** study findings may lead to the further study of the topological states of chiral materials.

关键词： Phononic crystals Topologically protected edge waves Chiral unit cells Topological insulator

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