Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coup...Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coupled micromechanical resonators,highlighting the latest advancements in four key areas:internal resonance,synchronization,frequency combs,and mode localization.The 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.展开更多
In recent years,scholars around the world have shown increasing interest in elastic support structures,leading to significant progress in dynamic modeling techniques for pipeline systems.Although multiple analytical a...In recent years,scholars around the world have shown increasing interest in elastic support structures,leading to significant progress in dynamic modeling techniques for pipeline systems.Although multiple analytical approaches exist,engineers increasingly prioritize computationally efficient,precise low-order models for practical implementation.In order to address this need,this study develops an innovative nonlinear dynamic formulation for pipelines accounting for both foundation and boundary nonlinearities.The proposed solution methodology initiates with global mode extraction using the global mode technique,followed by a detailed implementation procedure.Model validation is conducted through a cantilever pipeline case study featuring nonlinear support conditions,where strong agreement between the proposed model's predictions and finiteelement benchmark solutions demonstrates its reliability.Subsequently,a comprehensive parametric study investigates the combined effects of foundation stiffness,boundary constraints,excitation intensity,and nonlinear interaction terms on the vibrational response of the cantilever pipe.This systematic approach yields critical insights for practical engineering designs and applications.展开更多
The distribution-free P-box process serves as an effective quantification model for timevarying uncertainties in dynamical systems when only imprecise probabilistic information is available.However,its application to ...The distribution-free P-box process serves as an effective quantification model for timevarying uncertainties in dynamical systems when only imprecise probabilistic information is available.However,its application to nonlinear systems remains limited due to excessive computation.This work develops an efficient method for propagating distribution-free P-box processes in nonlinear dynamics.First,using the Covariance Analysis Describing Equation Technique(CADET),the dynamic problems with P-box processes are transformed into interval Ordinary Differential Equations(ODEs).These equations provide the Mean-and-Covariance(MAC)bounds of the system responses in relation to the MAC bounds of P-box-process excitations.They also separate the previously coupled P-box analysis and nonlinear-dynamic simulations into two sequential steps,including the MAC bound analysis of excitations and the MAC bounds calculation of responses by solving the interval ODEs.Afterward,a Gaussian assumption of the CADET is extended to the P-box form,i.e.,the responses are approximate parametric Gaussian P-box processes.As a result,the probability bounds of the responses are approximated by using the solutions of the interval ODEs.Moreover,the Chebyshev method is introduced and modified to efficiently solve the interval ODEs.The proposed method is validated based on test cases,including a duffing oscillator,a vehicle ride,and an engineering black-box problem of launch vehicle trajectory.Compared to the reference solutions based on the Monte Carlo method,with relative errors of less than 3%,the proposed method requires less than 0.2% calculation time.The proposed method also possesses the ability to handle complex black-box problems.展开更多
This paper tackles the robust leaderless Time-Varying Formation(TVF)control problem for the Unmanned Aerial Vehicle(UAV)swarm system with Lipschitz nonlinear dynamics,external disturbances and directed switching topol...This paper tackles the robust leaderless Time-Varying Formation(TVF)control problem for the Unmanned Aerial Vehicle(UAV)swarm system with Lipschitz nonlinear dynamics,external disturbances and directed switching topologies.In comparison with the previous achievements on formation control problems,the UAV swarm system with Lipschitz nonlinear dynamics can accomplish the pre-designed TVF while tracking a pre-given trajectory which is produced by a virtual leader UAV in the presence of external disturbances.Firstly,by applying the consensus theory,a TVF controller is developed with the local neighborhood status information,the errors of real time status of all UAVs,the expected formation configuration and the pre-given trajectory under directed switching topologies.Secondly,through a certain matrix variable substitution,the UAV swarm system formation control issue is transformed into a lower dimensional asymptotically stable control issue.Thirdly,by introducing the minimum dwell time,the design steps of formation control algorithm are further acquired.In the meantime,the stability of the UAV swarm system is analyzed through the construction of a piecewise continuous Lyapunov functional and via the Linear Matrix Inequalities(LMIs)method.Finally,the comparison results of a numerical simulation are elaborated to verify the validity of the proposed approach.展开更多
The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital ...The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital eccentricity. The flexible tether is modeled as a series of lumped masses and viscoelastic dampers so that a finite multi- degree-of-freedom nonlinear system is obtained. The stability of equilibrium positions of the nonlinear system is then analyzed via a simplified two-degree-freedom model in an orbital reference frame. In-plane motions of the tethered satellite system are studied numerically, taking the space environments into account. A large number of numerical simulations show that the flexible tethered satellite system displays nonlinear dynamic characteristics, such as bifurcations, quasi-periodic oscillations, and chaotic motions.展开更多
Because of significantly changed load and complex and variable driving road conditions of commercial vehicles,pneumatic suspension with lower natural frequencies is widely used in commercial vehicle suspension system....Because of significantly changed load and complex and variable driving road conditions of commercial vehicles,pneumatic suspension with lower natural frequencies is widely used in commercial vehicle suspension system.How ever,traditional pneumatic suspension system is hardly to respond the greatly changed load of commercial vehicles To address this issue,a new Gas-Interconnected Quasi-Zero Stiffness Pneumatic Suspension(GIQZSPS)is presented in this paper to improve the vibration isolation performance of commercial vehicle suspension systems under frequent load changes.This new structure adds negative stiffness air chambers on traditional pneumatic suspension to reduce the natural frequency of the suspension.It can adapt to different loads and road conditions by adjusting the solenoid valves between the negative stiffness air chambers.Firstly,a nonlinear mechanical model including the dimensionless stiffness characteristic and interconnected pipeline model is derived for GIQZSPS system.By the nonlinear mechanical model of GIQZSPS system,the force transmissibility rate is chosen as the evaluation index to analyze characteristics.Furthermore,a testing bench simulating 1/4 GIQZSPS system is designed,and the testing analysis of the model validation and isolating performance is carried out.The results show that compared to traditional pneumatic suspension,the GIQZSPS designed in the article has a lower natural frequency.And the system can achieve better vibration isolation performance under different load states by switching the solenoid valves between air chambers.展开更多
Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid...Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.展开更多
An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this pa...An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this paper,the stochastic dynamics of the nonlinear predator-prey system considering random environmental mutations is investigated, and a feedback control strategy is proposed to reshape the response of the predator-prey system against random abrupt environmental mutations. A delayed Markov jump system(MJS) is established to model such a predator-prey system. A novel first integral is constructed which leads to better approximation solutions of the ecosystem. Then, by applying the stochastic averaging method based on this novel first integral, the stochastic response of the predator-prey system is investigated, and an analytical feedback control is designed to reshape the response of the ecosystem from the disturbed state back to the undisturbed one.Numerical simulations finally illustrate the accuracy and effectiveness of the proposed procedure.展开更多
In many engineering networks, only a part of target state variables are required to be estimated.On the other hand,multi-layer complex network exists widely in practical situations.In this paper, the state estimation ...In many engineering networks, only a part of target state variables are required to be estimated.On the other hand,multi-layer complex network exists widely in practical situations.In this paper, the state estimation of target state variables in multi-layer complex dynamical networks with nonlinear node dynamics is studied.A suitable functional state observer is constructed with the limited measurement.The parameters of the designed functional observer are obtained from the algebraic method and the stability of the functional observer is proven by the Lyapunov theorem.Some necessary conditions that need to be satisfied for the design of the functional state observer are obtained.Different from previous studies, in the multi-layer complex dynamical network with nonlinear node dynamics, the proposed method can estimate the state of target variables on some layers directly instead of estimating all the individual states.Thus, it can greatly reduce the placement of observers and computational cost.Numerical simulations with the three-layer complex dynamical network composed of three-dimensional nonlinear dynamical nodes are developed to verify the effectiveness of the method.展开更多
This paper presents a mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and ordered rate constitutive theories in Lagrangian description derived using entropy ...This paper presents a mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and ordered rate constitutive theories in Lagrangian description derived using entropy inequality and the representation theorem for thermoviscoelastic solids (TVES) with rheology. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics and are based on contravariant deviatoric second Piola-Kirchhoff stress tensor and its work conjugate covariant Green’s strain tensor and their material derivatives of up to order m and n respectively. All published works on nonlinear dynamics of TVES with rheology are mostly based on phenomenological mathematical models. In rare instances, some aspects of CBL are used but are incorrectly altered to obtain mass, stiffness and damping matrices using space-time decoupled approaches. In the work presented in this paper, we show that this is not possible using CBL of CCM for TVES with rheology. Thus, the mathematical models used currently in the published works are not the correct description of the physics of nonlinear dynamics of TVES with rheology. The mathematical model used in the present work is strictly based on the CBL of CCM and is thermodynamically and mathematically consistent and the space-time coupled finite element methodology used in this work is unconditionally stable and provides solutions with desired accuracy and is ideally suited for nonlinear dynamics of TVES with memory. The work in this paper is the first presentation of a mathematical model strictly based on CBL of CCM and the solution of the mathematical model is obtained using unconditionally stable space-time coupled computational methodology that provides control over the errors in the evolution. Both space-time coupled and space-time decoupled finite element formulations are considered for obtaining solutions of the IVPs described by the mathematical model and are presented in the paper. Factors or the physics influencing dynamic response and dynamic bifurcation for TVES with rheology are identified and are also demonstrated through model problem studies. A simple model problem consisting of a rod (1D) of TVES material with memory fixed at one end and subjected to harmonic excitation at the other end is considered to study nonlinear dynamics of TVES with rheology, frequency response as well as dynamic bifurcation phenomenon.展开更多
Internal effects of the dynamic behaviors and nonlinear characteristics of a coupled fractional order hydropower generation system(HGS) are analyzed. A mathematical model of hydro-turbine governing system(HTGS) with r...Internal effects of the dynamic behaviors and nonlinear characteristics of a coupled fractional order hydropower generation system(HGS) are analyzed. A mathematical model of hydro-turbine governing system(HTGS) with rigid water hammer and hydro-turbine generator unit(HTGU) with fractional order damping forces are proposed. Based on Lagrange equations, a coupled fractional order HGS is established. Considering the dynamic transfer coefficient eis variational during the operation, introduced e as a periodic excitation into the HGS. The internal relationship of the dynamic behaviors between HTGS and HTGU is analyzed under different parameter values and fractional order. The results show obvious fast–slow dynamic behaviors in the HGS, causing corresponding vibration of the system, and some remarkable evolution phenomena take place with the changing of the periodic excitation parameter values.展开更多
In this paper, we have demonstrated an Er-doped ultrafast laser with a single mode fiber-gradient index multimode fiber-single mode fiber(SMF-GIMF-SMF, SMS) structure as saturable absorber(SA), which can generate not ...In this paper, we have demonstrated an Er-doped ultrafast laser with a single mode fiber-gradient index multimode fiber-single mode fiber(SMF-GIMF-SMF, SMS) structure as saturable absorber(SA), which can generate not only stable single-pulse state, but also special mode-locked pulses with the characteristics of high energy and noisy behaviors at proper pump power and cavity polarization state. In addition, we have deeply investigated the real-time spectral evolutions of the mode-locked pulses through the dispersive Fourier transformation(DFT) technique. It can be found that the pulse regime can actually consist of a lot of small noise pulses with randomly varying intensities. We believe that these results will further enrich the nonlinear dynamical processes in the ultrafast lasers.展开更多
Molecular dynamics(MD)is a powerful method widely used in materials science and solid-state physics.The accuracy of MD simulations depends on the quality of the interatomic potentials.In this work,a special class of e...Molecular dynamics(MD)is a powerful method widely used in materials science and solid-state physics.The accuracy of MD simulations depends on the quality of the interatomic potentials.In this work,a special class of exact solutions to the equations of motion of atoms in a body-centered cubic(bcc)lattice is analyzed.These solutions take the form of delocalized nonlinear vibrational modes(DNVMs)and can serve as an excellent test of the accuracy of the interatomic potentials used in MD modeling for bcc crystals.The accuracy of the potentials can be checked by comparing the frequency response of DNVMs calculated using this or that interatomic potential with that calculated using the more accurate ab initio approach.DNVMs can also be used to train new,more accurate machine learning potentials for bcc metals.To address the above issues,it is important to analyze the properties of DNVMs,which is the main goal of this work.Considering only the point symmetry groups of the bcc lattice,34 DNVMs are found.Since interatomic potentials are not used in finding DNVMs,they are exact solutions for any type of potential.Here,the simplest interatomic potentials with cubic anharmonicity are used to simplify the analysis and to obtain some analytical results.For example,the dispersion relations for small-amplitude phonon modes are derived,taking into account interactions between up to the fourth nearest neighbor.The frequency response of the DNVMs is calculated numerically,and for some DNVMs examples of analytical analysis are given.The energy stored by the interatomic bonds of different lengths is calculated,which is important for testing interatomic potentials.The pros and cons of using DNVMs to test and improve interatomic potentials for metals are discussed.Since DNVMs are the natural vibrational modes of bcc crystals,any reliable interatomic potential must reproduce their properties with reasonable accuracy.展开更多
In recent years,the increased application of inverter-based resources in power grids,along with the gradual replacement of synchronous generators,has made the grid support capability of inverters essential for maintai...In recent years,the increased application of inverter-based resources in power grids,along with the gradual replacement of synchronous generators,has made the grid support capability of inverters essential for maintaining system stability under large disturbances.Critical clearing time provides a quantitative measure of fault severity and system stability,and its sensitivity can help guide parameter adjustments to enhance the grid support capability of inverters.Building on previous researches,this paper proposes a method for calculating critical clearing time sensitivity in power systems with a high proportion of power electronic devices,accounting for the new dynamic characteristics introduced by these devices.The current limit and switching control of inverterbased resources are considered,and the critical clearing time sensitivity under controlling periodic orbits is derived.The proposed critical clearing time sensitivity calculation method is then validated using a double generator single load system and a modified 39-bus system.展开更多
Recent advances in statistical physics highlight the significant potential of machine learning for phase transition recognition.This study introduces a deep learning framework based on graph neural network to investig...Recent advances in statistical physics highlight the significant potential of machine learning for phase transition recognition.This study introduces a deep learning framework based on graph neural network to investigate non-equilibrium phase transitions,specifically focusing on the directed percolation process.By converting lattices with varying dimensions and connectivity schemes into graph structures and embedding the temporal evolution of the percolation process into node features,our approach enables unified analysis across diverse systems.The framework utilizes a multi-layer graph attention mechanism combined with global pooling to autonomously extract critical features from local dynamics to global phase transition signatures.The model successfully predicts percolation thresholds without relying on lattice geometry,demonstrating its robustness and versatility.Our approach not only offers new insights into phase transition studies but also provides a powerful tool for analyzing complex dynamical systems across various domains.展开更多
The feasibility of using a problem-dependent method to solve systems of second order ODEs is corroborated by an eigen-based theory and a methodology to develop such a numerical method is constructed.The key steps of t...The feasibility of using a problem-dependent method to solve systems of second order ODEs is corroborated by an eigen-based theory and a methodology to develop such a numerical method is constructed.The key steps of this methodology are to decouple a system of ODEs of second order into a set of uncoupled ODEs of second order;next,an eigen-dependent method is proposed to approximate the solution of each uncoupled ODE of second order.It is vital to transform all eigen-dependent methods to a problem-dependent method to bypass an Eigen analysis.The development of an eigen-dependent method plays a key role in this methodology so that slow eigenmodes can be accurately integrated while there is no instability or excessive amplitude growth in fast eigenmodes.This can explain why a problem-dependent method can simultaneously combine the explicitness of each step and A-stability.Consequently,huge computational efforts can be saved for solving nonlinear stiff problems.A new family of problem-dependent methods is developed in this work so that the feasibility of the proposed methodology can be affirmed.It has almost the same performance as that of the HHT-αmethod.However,it can save more than 99.5%of CPU demand in approximating a solution for a system of 1000 nonlinear second order ODEs.展开更多
One-dimensional(1D)nonlinear lattices that conserve momentum exhibit anomalous heat conduction,except for the specific case of the 1D coupled rotator lattice.Unlike classical interacting 1D nonlinear lattices such as ...One-dimensional(1D)nonlinear lattices that conserve momentum exhibit anomalous heat conduction,except for the specific case of the 1D coupled rotator lattice.Unlike classical interacting 1D nonlinear lattices such as the Fermi-Pasta-Ulamβ(FPU-β)lattice,the 1D coupled rotator lattice has a bounded interaction potential energy.Recently,the 1D coupled rotator lattice with additional bounded kinetic energy has also been found to exhibit normal heat conduction.Here,we study energy diffusion in the 1D momentum-conserving lattice with bounded kinetic energy only.We find that this lattice exhibits normal energy diffusion as well as normal stretch diffusion.This work indicates that bounded energy,whether kinetic or potential,is crucial for normal energy diffusion and heat conduction in 1D momentum-conserving nonlinear lattices.展开更多
This study describes a new solution for resolving nonlinear dynamics. Surpri<span>singly, it has been resolved and completed by non-physicists on behalf of</span> phy<span>sicists in 2021. It is a re...This study describes a new solution for resolving nonlinear dynamics. Surpri<span>singly, it has been resolved and completed by non-physicists on behalf of</span> phy<span>sicists in 2021. It is a revolutionary solution like the Copernican Theory,</span> which is perfectly different from the existing chaos theory. In the past, nonlinear <span>dynamics has been analyzed using logical solutions, such as chaos theory,</span> based on logical thinking. However, it is not perfect systematic solution, hence;the new solution has been analyzed and resolved by systematic analytical tool in other sciences. Then, the result is more perfect and precise than the old chaos theory. Regrettably, most physicists do not welcome this advancement, because they have primitive solutions such as chaos theory. If the new solution <span>is true, it is very disadvantageous to them like Galileo’s heliocentric theory. Therefore, they do not welcome it and deny and reject it. Hence, they wish it to fail;moreover, they want to remain in safe zone. Unfortunately, they became outsiders because they have no ability to review new solutions. Unfortunately, we have no obligation to follow physicists. If so, non-physicists, bypassing physicists, must study independently nonlinear dynamics based on systems thinking, and have to share the findings</span></span><span style="font-family:""> </span><span style="font-family:"">other</span><span style="font-family:""> </span><span style="font-family:"">scientists. It means that</span><span style="font-family:""> <span>the new solution would be replaced the chaos theory in traditional physics;moreover, it would be resolved many unsolved nonlinear dynamics in the fu</span>ture.展开更多
Nonlinear amphibious vehicle rolling under regular waves and wind load is analyzed by a single degree of freedom system.Considering nonlinear damping and restoring moments,a nonlinear rolling dynamical equation of amp...Nonlinear amphibious vehicle rolling under regular waves and wind load is analyzed by a single degree of freedom system.Considering nonlinear damping and restoring moments,a nonlinear rolling dynamical equation of amphibious vehicle is established.The Hamiltonian function of the nonlinear rolling dynamical equation of amphibious vehicle indicate when subjected to joint action of periodic wave excitation and crosswind,the nonlinear rolling system degenerates into being asymmetric.The threshold value of excited moment of wave and wind is analyzed by the Melnikov method.Finally,the nonlinear rolling motion response and phase portrait were simulated by four order Runge-Kutta method at different excited moment parameters.展开更多
This investigation focuses on the nonlinear dynamic behaviors in the trans- verse vibration of an axiMly accelerating viscoelastic Timoshenko beam with the external harmonic excitation. The parametric excitation is ca...This investigation focuses on the nonlinear dynamic behaviors in the trans- verse vibration of an axiMly accelerating viscoelastic Timoshenko beam with the external harmonic excitation. The parametric excitation is caused by the harmonic fluctuations of the axial moving speed. An integro-partial-differential equation governing the transverse vibration of the Timoshenko beam is established. Many factors are considered, such as viscoelasticity, the finite axial support rigidity, and the longitudinally varying tension due to the axial acceleration. With the Galerkin truncation method, a set of nonlinear ordinary differential equations are derived by discretizing the governing equation. Based on the numerical solutions, the bifurcation diagrams are presented to study the effect of the external transverse excitation. Moreover, the frequencies of the two excitations are assumed to be multiple. Further, five different tools, including the time history, the Poincaré map, and the sensitivity to initial conditions, are used to identify the motion form of the nonlinear vibration. Numerical results also show the characteristics of the quasiperiodic motion of the translating Timoshenko beam under an incommensurable re- lationship between the dual-frequency excitations.展开更多
基金supported by the National Key Research and Development Program of China(No.2022YFB3203600)the National Natural Science Foundation of China(Nos.12202355,12132013,and 12172323)the Zhejiang Provincial Natural Science Foundation of China(No.LZ22A020003)。
文摘Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coupled micromechanical resonators,highlighting the latest advancements in four key areas:internal resonance,synchronization,frequency combs,and mode localization.The 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.
基金supported by the National Natural Science Foundation of China(Nos.52401342 and 12572025)the Fundamental Research Funds for the Central Universities of China(Nos.D5000240076 and G2025KY05171)+1 种基金the Natural Science Basic Research Program of Shaanxi Province(No.2025JCYBMS-026)the Basic Research Programs of Taicang(No.TC2024JC36)。
文摘In recent years,scholars around the world have shown increasing interest in elastic support structures,leading to significant progress in dynamic modeling techniques for pipeline systems.Although multiple analytical approaches exist,engineers increasingly prioritize computationally efficient,precise low-order models for practical implementation.In order to address this need,this study develops an innovative nonlinear dynamic formulation for pipelines accounting for both foundation and boundary nonlinearities.The proposed solution methodology initiates with global mode extraction using the global mode technique,followed by a detailed implementation procedure.Model validation is conducted through a cantilever pipeline case study featuring nonlinear support conditions,where strong agreement between the proposed model's predictions and finiteelement benchmark solutions demonstrates its reliability.Subsequently,a comprehensive parametric study investigates the combined effects of foundation stiffness,boundary constraints,excitation intensity,and nonlinear interaction terms on the vibrational response of the cantilever pipe.This systematic approach yields critical insights for practical engineering designs and applications.
基金supported by the major advanced research project of Civil Aerospace from State Administration of Science,Technology and Industry of China.
文摘The distribution-free P-box process serves as an effective quantification model for timevarying uncertainties in dynamical systems when only imprecise probabilistic information is available.However,its application to nonlinear systems remains limited due to excessive computation.This work develops an efficient method for propagating distribution-free P-box processes in nonlinear dynamics.First,using the Covariance Analysis Describing Equation Technique(CADET),the dynamic problems with P-box processes are transformed into interval Ordinary Differential Equations(ODEs).These equations provide the Mean-and-Covariance(MAC)bounds of the system responses in relation to the MAC bounds of P-box-process excitations.They also separate the previously coupled P-box analysis and nonlinear-dynamic simulations into two sequential steps,including the MAC bound analysis of excitations and the MAC bounds calculation of responses by solving the interval ODEs.Afterward,a Gaussian assumption of the CADET is extended to the P-box form,i.e.,the responses are approximate parametric Gaussian P-box processes.As a result,the probability bounds of the responses are approximated by using the solutions of the interval ODEs.Moreover,the Chebyshev method is introduced and modified to efficiently solve the interval ODEs.The proposed method is validated based on test cases,including a duffing oscillator,a vehicle ride,and an engineering black-box problem of launch vehicle trajectory.Compared to the reference solutions based on the Monte Carlo method,with relative errors of less than 3%,the proposed method requires less than 0.2% calculation time.The proposed method also possesses the ability to handle complex black-box problems.
基金co-supported by the Key-area Research and Development Program of Guangdong ProvinceChina(No.2019B090915001)+2 种基金National Key R&D Program of China(No.2018YFB1308000),National Natural Science Funds of China(Nos.61772508,U1913202,U1813205,U1713213)CAS Key Technology Talent Program,Shenzhen Technology ProjectChina(Nos.JCYJ20180507182610734,JSGG20191129094012321).
文摘This paper tackles the robust leaderless Time-Varying Formation(TVF)control problem for the Unmanned Aerial Vehicle(UAV)swarm system with Lipschitz nonlinear dynamics,external disturbances and directed switching topologies.In comparison with the previous achievements on formation control problems,the UAV swarm system with Lipschitz nonlinear dynamics can accomplish the pre-designed TVF while tracking a pre-given trajectory which is produced by a virtual leader UAV in the presence of external disturbances.Firstly,by applying the consensus theory,a TVF controller is developed with the local neighborhood status information,the errors of real time status of all UAVs,the expected formation configuration and the pre-given trajectory under directed switching topologies.Secondly,through a certain matrix variable substitution,the UAV swarm system formation control issue is transformed into a lower dimensional asymptotically stable control issue.Thirdly,by introducing the minimum dwell time,the design steps of formation control algorithm are further acquired.In the meantime,the stability of the UAV swarm system is analyzed through the construction of a piecewise continuous Lyapunov functional and via the Linear Matrix Inequalities(LMIs)method.Finally,the comparison results of a numerical simulation are elaborated to verify the validity of the proposed approach.
基金supported by the National Natural Science Foundation of China(Nos.11002068 and11202094)the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures(No.0113Y01)the Priority Academic Program of Jiangsu Higher Education Institutions
文摘The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital eccentricity. The flexible tether is modeled as a series of lumped masses and viscoelastic dampers so that a finite multi- degree-of-freedom nonlinear system is obtained. The stability of equilibrium positions of the nonlinear system is then analyzed via a simplified two-degree-freedom model in an orbital reference frame. In-plane motions of the tethered satellite system are studied numerically, taking the space environments into account. A large number of numerical simulations show that the flexible tethered satellite system displays nonlinear dynamic characteristics, such as bifurcations, quasi-periodic oscillations, and chaotic motions.
基金Supported by National Natural Science Foundation of China (Grant No.51875256)Open Platform Fund of Human Institute of Technology (Grant No.KFA22009)。
文摘Because of significantly changed load and complex and variable driving road conditions of commercial vehicles,pneumatic suspension with lower natural frequencies is widely used in commercial vehicle suspension system.How ever,traditional pneumatic suspension system is hardly to respond the greatly changed load of commercial vehicles To address this issue,a new Gas-Interconnected Quasi-Zero Stiffness Pneumatic Suspension(GIQZSPS)is presented in this paper to improve the vibration isolation performance of commercial vehicle suspension systems under frequent load changes.This new structure adds negative stiffness air chambers on traditional pneumatic suspension to reduce the natural frequency of the suspension.It can adapt to different loads and road conditions by adjusting the solenoid valves between the negative stiffness air chambers.Firstly,a nonlinear mechanical model including the dimensionless stiffness characteristic and interconnected pipeline model is derived for GIQZSPS system.By the nonlinear mechanical model of GIQZSPS system,the force transmissibility rate is chosen as the evaluation index to analyze characteristics.Furthermore,a testing bench simulating 1/4 GIQZSPS system is designed,and the testing analysis of the model validation and isolating performance is carried out.The results show that compared to traditional pneumatic suspension,the GIQZSPS designed in the article has a lower natural frequency.And the system can achieve better vibration isolation performance under different load states by switching the solenoid valves between air chambers.
基金Project supported by the National Natural Science Foundation of China (Nos.12072119,12325201,and 52205594)the China National Postdoctoral Program for Innovative Talents (No.BX20220118)。
文摘Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.
基金the National Natural Science Foundation of China(Nos.11772293 and12072312)Zhejiang Science and Technology Project(No.2019C03129)。
文摘An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this paper,the stochastic dynamics of the nonlinear predator-prey system considering random environmental mutations is investigated, and a feedback control strategy is proposed to reshape the response of the predator-prey system against random abrupt environmental mutations. A delayed Markov jump system(MJS) is established to model such a predator-prey system. A novel first integral is constructed which leads to better approximation solutions of the ecosystem. Then, by applying the stochastic averaging method based on this novel first integral, the stochastic response of the predator-prey system is investigated, and an analytical feedback control is designed to reshape the response of the ecosystem from the disturbed state back to the undisturbed one.Numerical simulations finally illustrate the accuracy and effectiveness of the proposed procedure.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.62373197 and 61873326)。
文摘In many engineering networks, only a part of target state variables are required to be estimated.On the other hand,multi-layer complex network exists widely in practical situations.In this paper, the state estimation of target state variables in multi-layer complex dynamical networks with nonlinear node dynamics is studied.A suitable functional state observer is constructed with the limited measurement.The parameters of the designed functional observer are obtained from the algebraic method and the stability of the functional observer is proven by the Lyapunov theorem.Some necessary conditions that need to be satisfied for the design of the functional state observer are obtained.Different from previous studies, in the multi-layer complex dynamical network with nonlinear node dynamics, the proposed method can estimate the state of target variables on some layers directly instead of estimating all the individual states.Thus, it can greatly reduce the placement of observers and computational cost.Numerical simulations with the three-layer complex dynamical network composed of three-dimensional nonlinear dynamical nodes are developed to verify the effectiveness of the method.
文摘This paper presents a mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and ordered rate constitutive theories in Lagrangian description derived using entropy inequality and the representation theorem for thermoviscoelastic solids (TVES) with rheology. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics and are based on contravariant deviatoric second Piola-Kirchhoff stress tensor and its work conjugate covariant Green’s strain tensor and their material derivatives of up to order m and n respectively. All published works on nonlinear dynamics of TVES with rheology are mostly based on phenomenological mathematical models. In rare instances, some aspects of CBL are used but are incorrectly altered to obtain mass, stiffness and damping matrices using space-time decoupled approaches. In the work presented in this paper, we show that this is not possible using CBL of CCM for TVES with rheology. Thus, the mathematical models used currently in the published works are not the correct description of the physics of nonlinear dynamics of TVES with rheology. The mathematical model used in the present work is strictly based on the CBL of CCM and is thermodynamically and mathematically consistent and the space-time coupled finite element methodology used in this work is unconditionally stable and provides solutions with desired accuracy and is ideally suited for nonlinear dynamics of TVES with memory. The work in this paper is the first presentation of a mathematical model strictly based on CBL of CCM and the solution of the mathematical model is obtained using unconditionally stable space-time coupled computational methodology that provides control over the errors in the evolution. Both space-time coupled and space-time decoupled finite element formulations are considered for obtaining solutions of the IVPs described by the mathematical model and are presented in the paper. Factors or the physics influencing dynamic response and dynamic bifurcation for TVES with rheology are identified and are also demonstrated through model problem studies. A simple model problem consisting of a rod (1D) of TVES material with memory fixed at one end and subjected to harmonic excitation at the other end is considered to study nonlinear dynamics of TVES with rheology, frequency response as well as dynamic bifurcation phenomenon.
基金Project supported by the National Natural Science Foundation of China for Outstanding Youth(Grant No.51622906)the National Natural Science Foundation of China(Grant No.51479173)+2 种基金the Fundamental Research Funds for the Central Universities(Grant No.201304030577)the Scientific Research Funds of Northwest A&F University(Grant No.2013BSJJ095)the Science Fund for Excellent Young Scholars from Northwest A&F University and Shaanxi Nova Program,China(Grant No.2016KJXX-55)
文摘Internal effects of the dynamic behaviors and nonlinear characteristics of a coupled fractional order hydropower generation system(HGS) are analyzed. A mathematical model of hydro-turbine governing system(HTGS) with rigid water hammer and hydro-turbine generator unit(HTGU) with fractional order damping forces are proposed. Based on Lagrange equations, a coupled fractional order HGS is established. Considering the dynamic transfer coefficient eis variational during the operation, introduced e as a periodic excitation into the HGS. The internal relationship of the dynamic behaviors between HTGS and HTGU is analyzed under different parameter values and fractional order. The results show obvious fast–slow dynamic behaviors in the HGS, causing corresponding vibration of the system, and some remarkable evolution phenomena take place with the changing of the periodic excitation parameter values.
基金supported by the Guangdong Basic and Applied Basic Research Foundation (No.2023A1515010093)the Shenzhen Fundamental Research Program (Stable Support Plan Program)(Nos.JCYJ20220809170611004, 20231121110828001 and 20231121113641002)the National Taipei University of Technology-Shenzhen University Joint Research Program (No.2024001)。
文摘In this paper, we have demonstrated an Er-doped ultrafast laser with a single mode fiber-gradient index multimode fiber-single mode fiber(SMF-GIMF-SMF, SMS) structure as saturable absorber(SA), which can generate not only stable single-pulse state, but also special mode-locked pulses with the characteristics of high energy and noisy behaviors at proper pump power and cavity polarization state. In addition, we have deeply investigated the real-time spectral evolutions of the mode-locked pulses through the dispersive Fourier transformation(DFT) technique. It can be found that the pulse regime can actually consist of a lot of small noise pulses with randomly varying intensities. We believe that these results will further enrich the nonlinear dynamical processes in the ultrafast lasers.
基金support of the RSF Grant No.24-11-00139(analytics,numerical results,manuscript writing)Daxing Xiong acknowledges the support of the NNSF Grant No.12275116,the NSF Grant No.2021J02051,and the startup fund Grant No.MJY21035For Aleksey A.Kudreyko,this work was supported by the Bashkir StateMedicalUniversity StrategicAcademic Leadership Program(PRIORITY-2030)(analytics).
文摘Molecular dynamics(MD)is a powerful method widely used in materials science and solid-state physics.The accuracy of MD simulations depends on the quality of the interatomic potentials.In this work,a special class of exact solutions to the equations of motion of atoms in a body-centered cubic(bcc)lattice is analyzed.These solutions take the form of delocalized nonlinear vibrational modes(DNVMs)and can serve as an excellent test of the accuracy of the interatomic potentials used in MD modeling for bcc crystals.The accuracy of the potentials can be checked by comparing the frequency response of DNVMs calculated using this or that interatomic potential with that calculated using the more accurate ab initio approach.DNVMs can also be used to train new,more accurate machine learning potentials for bcc metals.To address the above issues,it is important to analyze the properties of DNVMs,which is the main goal of this work.Considering only the point symmetry groups of the bcc lattice,34 DNVMs are found.Since interatomic potentials are not used in finding DNVMs,they are exact solutions for any type of potential.Here,the simplest interatomic potentials with cubic anharmonicity are used to simplify the analysis and to obtain some analytical results.For example,the dispersion relations for small-amplitude phonon modes are derived,taking into account interactions between up to the fourth nearest neighbor.The frequency response of the DNVMs is calculated numerically,and for some DNVMs examples of analytical analysis are given.The energy stored by the interatomic bonds of different lengths is calculated,which is important for testing interatomic potentials.The pros and cons of using DNVMs to test and improve interatomic potentials for metals are discussed.Since DNVMs are the natural vibrational modes of bcc crystals,any reliable interatomic potential must reproduce their properties with reasonable accuracy.
文摘In recent years,the increased application of inverter-based resources in power grids,along with the gradual replacement of synchronous generators,has made the grid support capability of inverters essential for maintaining system stability under large disturbances.Critical clearing time provides a quantitative measure of fault severity and system stability,and its sensitivity can help guide parameter adjustments to enhance the grid support capability of inverters.Building on previous researches,this paper proposes a method for calculating critical clearing time sensitivity in power systems with a high proportion of power electronic devices,accounting for the new dynamic characteristics introduced by these devices.The current limit and switching control of inverterbased resources are considered,and the critical clearing time sensitivity under controlling periodic orbits is derived.The proposed critical clearing time sensitivity calculation method is then validated using a double generator single load system and a modified 39-bus system.
基金supported by the Fund from the Science and Technology Department of Henan Province,China(Grant Nos.222102210233 and 232102210064)the National Natural Science Foundation of China(Grant Nos.62373169 and 72474086)+5 种基金the Young and Midcareer Academic Leader of Jiangsu Province,China(Grant No.Qinglan Project in 2024)the National Statistical Science Research Project(Grant No.2022LZ03)Shaanxi Provincial Soft Science Project(Grant No.2022KRM111)Shaanxi Provincial Social Science Foundation(Grant No.2022R016)the Special Project for Philosophical and Social Sciences Research in Shaanxi Province,China(Grant No.2024QN018)the Fund from the Henan Office of Philosophy and Social Science(Grant No.2023CJJ112).
文摘Recent advances in statistical physics highlight the significant potential of machine learning for phase transition recognition.This study introduces a deep learning framework based on graph neural network to investigate non-equilibrium phase transitions,specifically focusing on the directed percolation process.By converting lattices with varying dimensions and connectivity schemes into graph structures and embedding the temporal evolution of the percolation process into node features,our approach enables unified analysis across diverse systems.The framework utilizes a multi-layer graph attention mechanism combined with global pooling to autonomously extract critical features from local dynamics to global phase transition signatures.The model successfully predicts percolation thresholds without relying on lattice geometry,demonstrating its robustness and versatility.Our approach not only offers new insights into phase transition studies but also provides a powerful tool for analyzing complex dynamical systems across various domains.
文摘The feasibility of using a problem-dependent method to solve systems of second order ODEs is corroborated by an eigen-based theory and a methodology to develop such a numerical method is constructed.The key steps of this methodology are to decouple a system of ODEs of second order into a set of uncoupled ODEs of second order;next,an eigen-dependent method is proposed to approximate the solution of each uncoupled ODE of second order.It is vital to transform all eigen-dependent methods to a problem-dependent method to bypass an Eigen analysis.The development of an eigen-dependent method plays a key role in this methodology so that slow eigenmodes can be accurately integrated while there is no instability or excessive amplitude growth in fast eigenmodes.This can explain why a problem-dependent method can simultaneously combine the explicitness of each step and A-stability.Consequently,huge computational efforts can be saved for solving nonlinear stiff problems.A new family of problem-dependent methods is developed in this work so that the feasibility of the proposed methodology can be affirmed.It has almost the same performance as that of the HHT-αmethod.However,it can save more than 99.5%of CPU demand in approximating a solution for a system of 1000 nonlinear second order ODEs.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12175074 and 12475037)the Science and Technology Commission of Shanghai Municipality(Grant No.24520711200)supported by the Shuguang Program of Shanghai Education Development Foundation and the Shanghai Municipal Education Commission(Grant No.23SG18)。
文摘One-dimensional(1D)nonlinear lattices that conserve momentum exhibit anomalous heat conduction,except for the specific case of the 1D coupled rotator lattice.Unlike classical interacting 1D nonlinear lattices such as the Fermi-Pasta-Ulamβ(FPU-β)lattice,the 1D coupled rotator lattice has a bounded interaction potential energy.Recently,the 1D coupled rotator lattice with additional bounded kinetic energy has also been found to exhibit normal heat conduction.Here,we study energy diffusion in the 1D momentum-conserving lattice with bounded kinetic energy only.We find that this lattice exhibits normal energy diffusion as well as normal stretch diffusion.This work indicates that bounded energy,whether kinetic or potential,is crucial for normal energy diffusion and heat conduction in 1D momentum-conserving nonlinear lattices.
文摘This study describes a new solution for resolving nonlinear dynamics. Surpri<span>singly, it has been resolved and completed by non-physicists on behalf of</span> phy<span>sicists in 2021. It is a revolutionary solution like the Copernican Theory,</span> which is perfectly different from the existing chaos theory. In the past, nonlinear <span>dynamics has been analyzed using logical solutions, such as chaos theory,</span> based on logical thinking. However, it is not perfect systematic solution, hence;the new solution has been analyzed and resolved by systematic analytical tool in other sciences. Then, the result is more perfect and precise than the old chaos theory. Regrettably, most physicists do not welcome this advancement, because they have primitive solutions such as chaos theory. If the new solution <span>is true, it is very disadvantageous to them like Galileo’s heliocentric theory. Therefore, they do not welcome it and deny and reject it. Hence, they wish it to fail;moreover, they want to remain in safe zone. Unfortunately, they became outsiders because they have no ability to review new solutions. Unfortunately, we have no obligation to follow physicists. If so, non-physicists, bypassing physicists, must study independently nonlinear dynamics based on systems thinking, and have to share the findings</span></span><span style="font-family:""> </span><span style="font-family:"">other</span><span style="font-family:""> </span><span style="font-family:"">scientists. It means that</span><span style="font-family:""> <span>the new solution would be replaced the chaos theory in traditional physics;moreover, it would be resolved many unsolved nonlinear dynamics in the fu</span>ture.
基金The Pre-research Project of the General Armament DepartmentThe Science Fund of North University of China(No.20130105)
文摘Nonlinear amphibious vehicle rolling under regular waves and wind load is analyzed by a single degree of freedom system.Considering nonlinear damping and restoring moments,a nonlinear rolling dynamical equation of amphibious vehicle is established.The Hamiltonian function of the nonlinear rolling dynamical equation of amphibious vehicle indicate when subjected to joint action of periodic wave excitation and crosswind,the nonlinear rolling system degenerates into being asymmetric.The threshold value of excited moment of wave and wind is analyzed by the Melnikov method.Finally,the nonlinear rolling motion response and phase portrait were simulated by four order Runge-Kutta method at different excited moment parameters.
基金Project supported by the State Key Program of National Natural Science Foundation of China(No.11232009)the National Natural Science Foundation of China(Nos.11372171 and 11422214)
文摘This investigation focuses on the nonlinear dynamic behaviors in the trans- verse vibration of an axiMly accelerating viscoelastic Timoshenko beam with the external harmonic excitation. The parametric excitation is caused by the harmonic fluctuations of the axial moving speed. An integro-partial-differential equation governing the transverse vibration of the Timoshenko beam is established. Many factors are considered, such as viscoelasticity, the finite axial support rigidity, and the longitudinally varying tension due to the axial acceleration. With the Galerkin truncation method, a set of nonlinear ordinary differential equations are derived by discretizing the governing equation. Based on the numerical solutions, the bifurcation diagrams are presented to study the effect of the external transverse excitation. Moreover, the frequencies of the two excitations are assumed to be multiple. Further, five different tools, including the time history, the Poincaré map, and the sensitivity to initial conditions, are used to identify the motion form of the nonlinear vibration. Numerical results also show the characteristics of the quasiperiodic motion of the translating Timoshenko beam under an incommensurable re- lationship between the dual-frequency excitations.
