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Synchronous oscillations in networks of time-delay coupled inert systems

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IFAC-PapersOnLine 2015年第18期48卷 31-36页

作者： E. Steur C. van Leeuwen A. Pogromsky KU Leuven Laboratory for Perceptual Dynamics Eindhoven University of Technology Department of Mechanical Engineering and Saint-Petersburg National Research University of Information Technologies Mechanics and Optics Department of Control Systems and Informatics Eindhoven University of Technology Institute for Complex Molecular Systems and Department of Mechanical Engineering

We discuss the emergence of oscillations in networks of inert single-input-single-output systems which interact via linear, time-delay coupling functions. We present conditions for 1. the solutions of the time-delay coupled systems to be bounded, 2. the network equilibrium to be unique, and 3. the network equilibrium to be unstable. If these conditions are all satisfied the network of time-delay coupled inert systems has a non-trivial oscillatory solution. In addition, we show that a necessary and sufficient condition for the emerge of oscillations in such networks is that the considered systems are at least second order. Moreover, using recent results on the existence of partial synchronization manifolds, we identify the patterns of oscillation that may emerge.

关键词： Coupling Instability Networks Oscillation Synchronization Time-delay

Elastic Wave Propagation in Nonlinear Two-dimensional Acoustic Metamaterials

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Research Square

Research Square 2021年

作者： Zhao, Cheng Zhang, Kai Zhao, Pengcheng Deng, Zichen 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

This study describes the wave propagation in a periodic lattice which is formed by a spring-mass two-dimensional structure with local Duffing nonlinear resonators. The wave propagation characteristics of the system is evaluated by using the perturbation method and Floquet-Bloch theorem to determine the dispersion relationships and wave propagation characteristics in the nonlinear two-dimensional acoustic metamaterials (2D AM). A quantitative study of wave amplitude is carried out to reveal the limits of the proposed method. In particular, the harmonic balance method is introduced to investigate the frequency response and effective mass of the nonlinear systems. We find that the dispersion relations, group velocity, negative effective mass of unit-cell are related to wave amplitude. Furthermore, the dual wave vector, bifurcation of periodic solutions and chaotic band are observed in the nonlinear systems. The results can be used to tune wave propagation in the nonlinear acoustic metamaterials and provide some ideas for the study of nonlinear metamaterials. © 2021, CC BY.

关键词： Frequency response

Broadband Vibration Reduction of Cylindrical Shell Structures with Circumferential Taper Resonators

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SSRN 2024年

作者： Zhang, Sen Ding, Liangzhu Wu, Xinwei Ma, Yongbin Deng, Zichen 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

In this study, a resonator with circumferential taper was proposed to achieve broadband vibration reduction of the circular cylindrical shell. The structural damping characteristics and vibration response of the circular cylindrical shell structure with circumferential taper resonators were conducted by an analytical wave propagation model developed based on the symplectic method. The taper resonator was segmented uniformly by using the Gaussian discretization method based on power law, which can accurately and efficiently handle the non-uniform characteristics of the taper resonator and the amplitude of each uniform segment was evaluated by using the analytical wave propagation model. In numerical examples, the accuracy and effectiveness of the homogenization approximation of the analytical model were validated by the finite element method. Meanwhile, the forced vibration response and damping properties of the circular cylindrical shell structure with uniform and taper resonators and with various boundary conditions were also investigated. The results showed that compared with uniform resonator, the taper resonator provided much larger damping, which its special damping capacity can even reach about 6 times of the uniform resonator. Therefore, even if the length of the taper resonator was relatively small, significant broadband vibration suppression in the primary circular cylindrical shell can also be achieved. In addition, under any boundary condition, the same parameters taper resonator can achieve broadband vibration reduction effects on circular cylindrical shell, and the distance between the excitation source and the position of the resonator can affect the vibration attenuation effect of the circular cylindrical shell. © 2024, The Authors. All rights reserved.

关键词： Resonators

Vibration and Acoustic Radiation Suppression of Multi-Layer Composite Sandwich Plates with Imperfect Acoustic Black Hole

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SSRN 2024年

作者： Zhang, Sen Wu, Xinwei Ding, Liangzhu Ma, Yongbin Deng, Zichen 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

Acoustic black holes (ABHs) had been recently revealed as an effective vibration control technology. However, due to inherent defects such as weakened stiffness, structural discontinuity and manufacturing difficulties, the practical application of ABH had been limited. Therefore, a multi-layer composite sandwich plate with filled imperfect-ABH (F-IABH) was proposed in this study to attenuate the vibration and sound radiation of the multi-layer sandwich plate, and could also enhance the bearing capacity of the structure and maintain its topological continuity. The structural damping characteristics and vibroacoustic response of the F-IABH were conducted by a semi-analytical wave propagation model developed based on the symplectic method and acoustic radiation mode method. In numerical examples, the accuracy and effectiveness of the analytical model were validated by the finite element method. The results showed that F-IABH can achieve broadband vibration attenuation and noise reduction effects. Especially at low frequencies, its vibration and noise reduction effect were significantly better than ABH structures. Meanwhile, the wave damping characteristics of uniform plate, ABH plate, and F-IABH plate were analyzed. The results showed that the wave damping of F-IABH was much higher than those of uniform plate, and they can generate more propagative waves to dissipate energy. In addition, the wave damping characteristics of F-IABH and ABH plate had very similar trends. However, at lower frequencies, due to the large variation range of wave mode damping characteristics of F-IABH, its control effect on structural vibration and acoustic radiation was more significant than that of ABH plate. © 2024, The Authors. All rights reserved.

关键词： Acoustic wave propagation

Symplectic Space Wave Propagation Method for Forced Vibration of Acoustic Black Hole Assemblies

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SSRN 2023年

作者： Zhang, Sen Ma, Yongbin Yan, Meng Deng, Zichen 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

A symplectic space wave propagation method is proposed for the forced vibration of the Acoustic Black Hole (ABH) assemblies. The governing differential equations for vibration of the ABH beam is first converted into Hamiltonian canonical equations. A symplectic eigenvalue problem is then formed, and the wave propagation parameters and wave shapes are obtained analytically. Secondly, A Gaussian point scheme is subsequently used to discrete the ABH beam, while the presented method is used to evaluate the wave amplitude at each point. Various coupling forms are considered for the ABH assemblies, in which the ABH beams are coupled directly or through a joint. The wave propagation method based on symplectic analysis is used to describe the vibration of ABH beams and the finite element method is used to describe the vibration of the joint. By using the displacement continuity and equilibrium of force at the connection interface, the dynamic coupling between the ABH beam and the joint is established. Since the presented method utilizes symplectic analytical solutions of wave modes, the computational efficiency and precision are high that are verified by several numerical examples. © 2023, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Towards a modeling, optimization and predictive control framework for fed-batch metabolic cybergenetics

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arXiv

arXiv 2023年

作者： Espinel-Ríos, Sebastián Morabito, Bruno Pohlodek, Johannes Bettenbrock, Katja Klamt, Steffen Findeisen, Rolf Analysis and Redesign of Biological Networks Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany Yokogawa Insilico Biotechnology GmbH Stuttgart Germany Control and Cyber-Physical Systems Laboratory Technical University of Darmstadt Darmstadt Germany

Biotechnology offers many opportunities for the sustainable manufacturing of valuable products. The toolbox to optimize bioprocesses includes extracellular process elements such as the bioreactor design and mode of operation, medium formulation, culture conditions, feeding rates, etc. However, these elements are frequently insufficient for achieving optimal process performance or precise product composition. One can use metabolic and genetic engineering methods for optimization at the intracellular level. Nevertheless, those are often of static nature, failing when applied to dynamic processes or if disturbances occur. Furthermore, many bioprocesses are optimized empirically and implemented with little-to-no feedback control to counteract disturbances. The concept of cybergenetics has opened new possibilities to optimize bioprocesses by enabling online modulation of the gene expression of metabolism-relevant proteins via external inputs (e.g., light intensity in optogenetics). Here, we fuse cybergenetics with model-based optimization and predictive control for optimizing dynamic bioprocesses. To do so, we propose to use dynamic constraint-based models that integrate the dynamics of metabolic reactions, resource allocation, and inducible gene expression. We formulate a model-based optimal control problem to find the optimal process inputs. Furthermore, we propose using model predictive control to address uncertainties via online feedback. We focus on fed-batch processes, where the substrate feeding rate is an additional optimization variable. As a simulation example, we show the optogenetic control of the ATPase enzyme complex for dynamic modulation of enforced ATP wasting to adjust product yield and productivity. © 2023, CC BY.

关键词： Model predictive control

Entropic stochastic resonance of finite-size particles in confined Brownian transport

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Physical Review E 2024年第5期109卷 054110-054110页

作者： Hai-Wei Hu Lin Du Ai-Li Fan Zi-Chen Deng Celso Grebogi School of Mathematics and Statistics Northwestern Polytechnical University Xi'an 710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an 710072 China School of Aeronautics Northwestern Polytechnical University Xi'an 710072 China Institute for Complex Systems and Mathematical Biology Kingdom College University of Aberdeen Aberdeen AB24 3UE United Kingdom

We demonstrate the existence of entropic stochastic resonance (ESR) of passive Brownian particles with finite size in a double- or triple-circular confined cavity, and compare the similarities and differences of ESR in the double-circular cavity and triple-circular cavity. When the diffusion of Brownian particles is constrained to the double- or triple-circular cavity, the presence of irregular boundaries leads to entropic barriers. The interplay between the entropic barriers, a periodic input signal, the gravity of particles, and intrinsic thermal noise may give rise to a peak in the spectral amplification factor and therefore to the appearance of the ESR phenomenon. It is shown that ESR can occur in both a double-circular cavity and a triple-circular cavity, and by adjusting some parameters of the system, the response of the system can be optimized. The differences are that the spectral amplification factor in a triple-circular cavity is significantly larger than that in a double-circular cavity, and compared with the ESR in a double-circular cavity, the ESR effect in a triple-circular cavity occurs within a wider range of external force parameters. In addition, the strength of ESR also depends on the particle radius, and smaller particles can induce more obvious ESR, indicating that the size effect cannot be safely neglected. The ESR phenomenon usually occurs in small-scale systems where confinement and noise play an important role. Therefore, the mechanism that is found could be used to manipulate and control nanodevices and biomolecules.

关键词： Brownian motion Stochastic dynamical systems Brownian dynamics Fokker–Planck equation Langevin equation

Chaos and fracture of a stiff thin film on a finite-thickness bi-layer substrate under an axial periodic load

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Chaos and fracture of a stiff thin film on a finite-thicknes...

第八届国际振动工程会议

作者： Haohao Bi Bo Wang Bohan Zhang Chao Xu Zichen Deng Department of Applied Mathematics Northwestern Polytechnical University Department of Engineering Mechanics Northwestern Polytechnical University Ministry of Industry and Information Technology Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University

To improve the robustness of the film-substrate type's stretchable electronics, an intermediate layer is introduced. However, due to the introducing of the intermediate layer between the film layer and the soft substrate layer to form tri-layer structure, the dynamic behaviour of this structure would be influenced. In this paper, the chaos and fracture of the tri-layer structure under an axial periodic load are investigated. Firstly, taking the shear stress between the film and the intermediate layer, and the deformation of the intermediate layer and the substrate layer into account, a more accurate analytical model has been established. Based on the Lagrange equation, the governing equation of the tri-layer structure has been derived. Then, the symplectic Runge-Kutta method is used to solve the corresponding equation. Numerical examples are performed to discuss the influences of the Young's modulus and thickness of the intermediate layer on the chaos and fracture of the tri-layer structure. These obtained results would be helpful for the design of higher reliability of the film/substrate-type stretchable electronics.

关键词： Chaos and fracture of a stiff thin film on a finite-thickness bi-layer substrate under an axial periodic load

Sub-Preferential Rotational Wave Beaming in Structurally Rhombus Re-Entrant Honeycombs

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SSRN 2023年

作者： Zhu, Zhiwei Deng, Zichen State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures Shijiazhuang Tiedao University Shijiazhuang050043 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'An710072 China

Rotational waves frequently manifest in micro-structured materials and are often coupled with classical shear or longitudinal wave modes. In this study, a distinctive isolated optical branch, exhibiting very high polarization index related to joint rotation motion, is found in dispersion diagram of elastic wave propagation in structurally rhombus re-entrant honeycomb (SSRH). Through an analysis of group velocity, we further explore the wave beaming of the rotational wave propagation within the SRRH, and intriguingly, observe the emergence of sub-preferential wave beaming occurring along the short diagonal directions. This dynamic anisotropic phenomenon stems from the intricate interplay between wave frequency and structural topology. To elucidate the underlying dynamic anisotropy of rotational waves, we propose a simple rigid-spring model and derive an anisotropic coefficient that precisely captures the intricate frequency-structure coupling behavior. The obtained anisotropic coefficient unveils the formation of sub-preferential directions of the rotational wave within the SRRH. Our findings transcend the elucidation of dynamic anisotropy in lattice materials, extending to practical implications encompassing the manipulation of elastic wave propagation and the design of waveguides. © 2023, The Authors. All rights reserved.

关键词： Anisotropy