The crucial effect of compressibility of rods on their instability is novelly demonstrated via singularity theory. It is shown that the critical load of compressible rod is always greater than the one of the Euler rod...The crucial effect of compressibility of rods on their instability is novelly demonstrated via singularity theory. It is shown that the critical load of compressible rod is always greater than the one of the Euler rod, and a subcritical pitchfork bifurcation, which cannot occur for the Euler rod, may occur for a compressible rod. A whole bifurcation diagram of compressible rods is as follows ： when the original slenderness ratio of a compressible rod, $o is smaller than （1 ＋ v/3 √3π/2,, the rod does not buckle; when So∈ [1＋ v/3）3√3π/2 ,（1＋v/5）5 5√5π/4）,the rod may undergo a subcritical pitchfork bifurcation and a collapse may occur; when So ∈ [1＋ v/5）5√5π/4 ＋ ∞）, the rod may undergo a supercritical pitchfork bifurcation. The deformation of cross section of rods causes a little shift of bifurcation points towards to the one corresponding to larger slenderness ratio.展开更多
Continental crust is the long-term achievements of Earth's evolution across billions of years.The continental rocks could have been modified by various types of geological processes,such as metamorphism,weathering...Continental crust is the long-term achievements of Earth's evolution across billions of years.The continental rocks could have been modified by various types of geological processes,such as metamorphism,weathering,and reworking.Therefore,physical or chemical properties of rocks through time record the composite effects of geological,biological,hydrological,and climatological processes.Temporal variations in these time series datasets could provide important clues for understanding the co-evolution of different layers on Earth.However,deciphering Earth's evolution in deep time is challenged by incompleteness,singularity,and intermittence of geological records associated with extreme geological events,hindering a rigorous assessment of the underlying coupling mechanisms.Here,we applied the recently developed local singularity analysis and wavelet analysis method to deep-time U-Pb age spectra and sedimentary abundance record across the past 3.5 Gyrs.Standard cross-correlation analysis suggests that the singularity records of marine sediment accumulations and magmatism intensity at continental margin are correlated negatively(R^(2)=0.8),with a delay of~100 Myr.Specifically,wavelet coherence analysis suggests a~500-800 Myr cycle of correlation between two records,implying a coupling between the major downward processes(subduction and recycling sediments)and upward processes(magmatic events)related to the aggregation and segregation of supercontinents.The results clearly reveal the long-term cyclic feedback mechanism between sediment accumulation and magmatism intensity through aggregation of supercontinents.展开更多
The Theory of General Singularity is presented, unifying quantum field theory, general relativity, and the standard model. This theory posits phonons as fundamental excitations in a quantum vacuum, modeled as a Bose-E...The Theory of General Singularity is presented, unifying quantum field theory, general relativity, and the standard model. This theory posits phonons as fundamental excitations in a quantum vacuum, modeled as a Bose-Einstein condensate. Through key equations, the role of phonons as intermediaries between matter, energy, and spacetime geometry is demonstrated. The theory expands Einsteins field equations to differentiate between visible and dark matter, and revises the standard model by incorporating phonons. It addresses dark matter, dark energy, gravity, and phase transitions, while making testable predictions. The theory proposes that singularities, the essence of particles and black holes, are quantum entities ubiquitous in nature, constituting the very essence of elementary particles, seen as micro black holes or quantum fractal structures of spacetime. As the theory is refined with increasing mathematical rigor, it builds upon the foundation of initial physical intuition, connecting the spacetime continuum of general relativity with the hydrodynamics of the quantum vacuum. Inspired by the insights of Tesla and Majorana, who believed that physical intuition justifies the infringement of mathematical rigor in the early stages of theory development, this work aims to advance the understanding of the fundamental laws of the universe and the perception of reality.展开更多
We have derived the first Noether theorem and Noether identities in canonical formalism for field theory with higher-order singular Lagrangian,which is a powerful tool toanalyse Dirac constraint for such system. A gau...We have derived the first Noether theorem and Noether identities in canonical formalism for field theory with higher-order singular Lagrangian,which is a powerful tool toanalyse Dirac constraint for such system. A gauge-variant system in canonical variables formalism must has Dirac constraint.For a system with first class constraint (FCC), we have developed an algorithm for construction of the gauge generator of such system. An application to the Podolsky generalized electromagnetic field was given.展开更多
The development of theories on human rights with Chinese characteristics and China’s engagement in global human rights governance cannot be separated from attention to contemporary Western human rights theory.The deb...The development of theories on human rights with Chinese characteristics and China’s engagement in global human rights governance cannot be separated from attention to contemporary Western human rights theory.The debate between naturalistic and political conceptions of human rights has a long history,but discussions on the basic criteria for evaluating human rights theories have been insufficient.This article,focusing on the criterion of fidelity to practice,attempts to identify the development trajectory and direction of human rights theory.The universal claims of naturalistic human rights perspectives and the human rights catalog they propose have been criticized for deviating from practice.On the other hand,political conceptions of human rights,while emphasizing domestic human rights practices,have been criticized for their occasional nature and perceived loss of criticality.The broad-way practice theory seeks a third way that goes beyond the divide between these two perspectives.On the one hand,the theory itself faces limitations and the need for reshaping,while on the other hand,the traditional singular practice theory is also undergoing self-renewal.It can be said that the“internal critique”of contemporary Western human rights theory is already underway and will continue.展开更多
In this paper,we focus on the dynamics of the modified Leslie Gower model with a weak Allee effect and fear effect on predators.Assuming that the inherent growth rate of prey is much faster than that of predators,this...In this paper,we focus on the dynamics of the modified Leslie Gower model with a weak Allee effect and fear effect on predators.Assuming that the inherent growth rate of prey is much faster than that of predators,this becomes a singular perturbation problem.Based on the geometric singular perturbation theory,we prove the existence of canard cycles and relaxation oscillation and provide an asymptotic expression of the relaxation oscillation period.Furthermore,it demonstrates that,under certain conditions,the degenerate transcritical bifurcation point is a global attractor using geometric singular perturbation theory,the center manifold theorem and the blow-up method.Numerical simulations verify the theoretical results.展开更多
In this article,a novel model-free coordinated optimal regulation design methodology is proposed for the rigidly connected dual permanent magnet synchronous motor(PMSM)system via adaptive dynamic programming(ADP).Firs...In this article,a novel model-free coordinated optimal regulation design methodology is proposed for the rigidly connected dual permanent magnet synchronous motor(PMSM)system via adaptive dynamic programming(ADP).First,we adopt the classical master-slave structure to maintain torque synchronization by virtue of field-oriented control.Then,a reducedorder model of the dual-PMSM system is established through the application of singular perturbation theory(SPT),which is of significance to decrease the learning time and computational complexity in the outer speed loop design.Afterwards,we design a coordinated adaptive optimal regulator in framework of ADP to drive the speed of girth gear asymptotic tracking the reference signal and accommodate the load torque disturbance,which is independent of the knowledge of model parameters of the system.According to SPT,we analyze the suboptimality,closed-loop stability,and robustness properties of the obtained controller under mild conditions.Finally,comprehensive experimental studies are provided to verify that the proposed control strategy can achieve the speed regulation and the torque synchronization,as well as ameliorate the transient response.展开更多
The modern definition of the wave concept,which is based on the functional connection between the parameters of the spatial structure of an instantaneous flow pattern and the characteristics of the temporal variabilit...The modern definition of the wave concept,which is based on the functional connection between the parameters of the spatial structure of an instantaneous flow pattern and the characteristics of the temporal variability at a given point,is discussed.The dispersion relation for 2D plane periodic perturbations on the surface of viscous stratified fluid is selected as the characteristic function defining the wave motion.Using the theory of singular perturbations,a method for calculating complete solutions to the dispersion relations of periodic flows,including regular wave and singular ligament solutions is presented.Properties of the complete exact solution of the dispersion relation containing regular and singular functions are compared with asymptotic solutions.In limiting cases,obtained dispersion relations are matched with well⁃known expressions for waves in homogeneous viscous and ideal liquids.展开更多
The dynamical equations of a thin rectangle plate subjected to the friction support boundary and its plane force are established in this paper. The local bifurcation of this system is investigated by using L S method...The dynamical equations of a thin rectangle plate subjected to the friction support boundary and its plane force are established in this paper. The local bifurcation of this system is investigated by using L S method and the singularity theory. The Z 2 bifurcation in non degenerate case is discussed. The local bifurcation diagrams of the unfolding parameters and the bifurcation response characters referred to the physical parameters of the system are obtained by numerical simulation. The results of the computer simulation are coincident with the theoretical analysis and experimental results.展开更多
A reduced model is proposed and analyzed for the simulation of vortexinduced vibrations （VIVs） for turbine blades. A rotating blade is modelled as a uniform cantilever beam, while a van der Pol oscillator is used to...A reduced model is proposed and analyzed for the simulation of vortexinduced vibrations （VIVs） for turbine blades. A rotating blade is modelled as a uniform cantilever beam, while a van der Pol oscillator is used to represent the time-varying characteristics of the vortex shedding, which interacts with the equations of motion for the blade to simulate the fluid-structure interaction. The action for the structural motion on the fluid is considered as a linear inertia coupling. The nonlinear characteristics for the dynamic responses are investigated with the multiple scale method, and the modulation equations are derived. The transition set consisting of the bifurcation set and the hystere- sis set is constructed by the singularity theory and the effects of the system parameters, such as the van der Pol damping. The coupling parameter on the equilibrium solutions is analyzed. The frequency-response curves are obtained, and the stabilities are determined by the Routh-Hurwitz criterion. The phenomena including the saddle-node and Hopf bifurcations are found to occur under certain parameter values. A direct numerical method is used to analyze the dynamic characteristics for the original system and verify the va- lidity of the multiple scale method. The results indicate that the new coupled model is useful in explaining the rich dynamic response characteristics such as possible bifurcation phenomena in the VIVs.展开更多
Bifurcations with constraints are open problems appeared in research on periodic bifurcations of nonlinear dynamical systems, but the present singularity theory doesn't contain any analytical methods and results a...Bifurcations with constraints are open problems appeared in research on periodic bifurcations of nonlinear dynamical systems, but the present singularity theory doesn't contain any analytical methods and results about it. As the complement to singularity theory and the first step to study on constrained bifurcations, here are given tire transition sets and persistent perturbed bifurcation diagrams of 10 elementary bifurcation of codimension no more than three.展开更多
The nonlinear normal modes (NNMs) associated with integrnal resonance can be classified into two kinds: uncoupled and coupled. The bifurcation problem of the coupled NNM of system with 1 : 2 : 5 dual internal resonanc...The nonlinear normal modes (NNMs) associated with integrnal resonance can be classified into two kinds: uncoupled and coupled. The bifurcation problem of the coupled NNM of system with 1 : 2 : 5 dual internal resonance is in two variables. The singular analysis of it is presented after separating the two variables by taking advantage of Maple algebra, and some new bifurcation patterns are found. Different from the NNMs of systems with single internal resonance, the number of the NNMs of systems with dual internal resonance may be more or less than the number of the degrees of freedom. At last, it is pointed out that bifurcation problems in two variables can be conveniently solved by separating variables as well as using coupling equations.展开更多
The static bifurcation of the parametrically excited strongly nonlinear oscillator is studied. We consider the averaged equations of a system subject to Duffing-van der Pol and quintic strong nonlinearity by introduci...The static bifurcation of the parametrically excited strongly nonlinear oscillator is studied. We consider the averaged equations of a system subject to Duffing-van der Pol and quintic strong nonlinearity by introducing the undetermined fundamental frequency into the computation in the complex normal form. To discuss the static bifurcation, the bifurcation problem is described as a 3-codimensional unfolding with Z2 symmetry on the basis of singularity theory. The transition set and bifurcation diagrams for the singularity are presented, while the stability of the zero solution is studied by using the eigenvalues in various parameter regions.展开更多
Bifurcations of one kind of reaction_diffusion equations, u″+μ(u-u k)=0(μ is a parameter,4≤k∈Z +), with boundary value condition u(0)=u(π)=0 are discussed. By means of singularity theory based on the method of...Bifurcations of one kind of reaction_diffusion equations, u″+μ(u-u k)=0(μ is a parameter,4≤k∈Z +), with boundary value condition u(0)=u(π)=0 are discussed. By means of singularity theory based on the method of Liapunov_Schmidt reduction, satisfactory results can be acquired.展开更多
Bifurcation of periodic solutions widely exists in nonlinear dynamical systems. In this paper, categories of bifurcations of systems with two state variables with different types of constraints are discussed, where so...Bifurcation of periodic solutions widely exists in nonlinear dynamical systems. In this paper, categories of bifurcations of systems with two state variables with different types of constraints are discussed, where some new types of transition sets are added. Additionally, the bifurcation properties of two-dimensionM systems without constraints are compared with the ones with constraints. The results obtained in this paper can be used by engineers for the choice of the structural parameters of the systems.展开更多
The method of averaging is applied in this paper to deal with primary resonance of a three circular plates torsion vibration system having cubic nonlinearities which is excited by a simple-harmonic excitation. Bifurca...The method of averaging is applied in this paper to deal with primary resonance of a three circular plates torsion vibration system having cubic nonlinearities which is excited by a simple-harmonic excitation. Bifurcation equation of the steady state response is obtained and its singularity analysis is given. The results of theoretical analysis are shown to be in good agreement with experimental ones.展开更多
A kinetic model of the piecewise-linear nonlinear suspension system that consists of a dominant spring and an assistant spring is established. Bifurcation of the resonance solution to a suspension system with two degr...A kinetic model of the piecewise-linear nonlinear suspension system that consists of a dominant spring and an assistant spring is established. Bifurcation of the resonance solution to a suspension system with two degrees of freedom is investigated with the singularity theory. Transition sets of the system and 40 groups of bifurcation diagrams are obtained. The local bifurcation is found, and shows the overall character- istics of bifurcation. Based on the. relationship between parameters and the topological bifurcation solutions, motion characteristics with different parameters are obtained. The results provides a theoretical basis for the optimal control of vehicle suspension system parameters.展开更多
The nonlinear equations of an elastic tank-liquid coupling system subjected to the external excitation are established.By means of the multi-scale method and the singularity theory,the bifurcation behaviors of the sys...The nonlinear equations of an elastic tank-liquid coupling system subjected to the external excitation are established.By means of the multi-scale method and the singularity theory,the bifurcation behaviors of the system are investigated and analyzed.The various nonlinear dynamical behaviors of the coupling system are obtained,which can further explain the relationship between the physical parameters and the bifurcation solutions.The results provide a theoretical basis to the realization of the parameter optimal control.展开更多
Biforations of an ordinary differential equation with two-point boundary value condition are investigated. Using the singularity theory based on the Liapunov-Schmidt reduction, we have obtained some characterization r...Biforations of an ordinary differential equation with two-point boundary value condition are investigated. Using the singularity theory based on the Liapunov-Schmidt reduction, we have obtained some characterization results.展开更多
An optimized damage identification method of beam combined wavelet with neural network is presented in an attempt to improve the calculation iterative speed and accuracy damage identification. The mathematical model i...An optimized damage identification method of beam combined wavelet with neural network is presented in an attempt to improve the calculation iterative speed and accuracy damage identification. The mathematical model is developed to identify the structure damage based on the theory of finite elements and rotation modal parameters. The model is integrated with BP neural network optimization approach which utilizes the Genetic algorithm optimization method. The structural rotation modal parameters are performed with the continuous wavelet transform through the Mexico hat wavelet. The location of structure damage is identified by the maximum of wavelet coefficients. Then, the multi-scale wavelet coefficients modulus maxima are used as the inputs of the BP neural network, and through training and updating the optimal weight and threshold value to obtain the ideal output which is used to describe the degree of structural damage. The obtained results demonstrate the effectiveness of the proposed approach in simultaneously improving the structural damage identification precision including the damage locating and severity.展开更多
基金Supported by National Natural Science Foundation of China(No. 10272079)joint grant from National Natural Science Foundation of Chinathe Royal Society of UK under their Joint Project Scheme
文摘The crucial effect of compressibility of rods on their instability is novelly demonstrated via singularity theory. It is shown that the critical load of compressible rod is always greater than the one of the Euler rod, and a subcritical pitchfork bifurcation, which cannot occur for the Euler rod, may occur for a compressible rod. A whole bifurcation diagram of compressible rods is as follows ： when the original slenderness ratio of a compressible rod, $o is smaller than （1 ＋ v/3 √3π/2,, the rod does not buckle; when So∈ [1＋ v/3）3√3π/2 ,（1＋v/5）5 5√5π/4）,the rod may undergo a subcritical pitchfork bifurcation and a collapse may occur; when So ∈ [1＋ v/5）5√5π/4 ＋ ∞）, the rod may undergo a supercritical pitchfork bifurcation. The deformation of cross section of rods causes a little shift of bifurcation points towards to the one corresponding to larger slenderness ratio.
基金supported by the National Natural Science Foundation of China(No.42050103)。
文摘Continental crust is the long-term achievements of Earth's evolution across billions of years.The continental rocks could have been modified by various types of geological processes,such as metamorphism,weathering,and reworking.Therefore,physical or chemical properties of rocks through time record the composite effects of geological,biological,hydrological,and climatological processes.Temporal variations in these time series datasets could provide important clues for understanding the co-evolution of different layers on Earth.However,deciphering Earth's evolution in deep time is challenged by incompleteness,singularity,and intermittence of geological records associated with extreme geological events,hindering a rigorous assessment of the underlying coupling mechanisms.Here,we applied the recently developed local singularity analysis and wavelet analysis method to deep-time U-Pb age spectra and sedimentary abundance record across the past 3.5 Gyrs.Standard cross-correlation analysis suggests that the singularity records of marine sediment accumulations and magmatism intensity at continental margin are correlated negatively(R^(2)=0.8),with a delay of~100 Myr.Specifically,wavelet coherence analysis suggests a~500-800 Myr cycle of correlation between two records,implying a coupling between the major downward processes(subduction and recycling sediments)and upward processes(magmatic events)related to the aggregation and segregation of supercontinents.The results clearly reveal the long-term cyclic feedback mechanism between sediment accumulation and magmatism intensity through aggregation of supercontinents.
文摘The Theory of General Singularity is presented, unifying quantum field theory, general relativity, and the standard model. This theory posits phonons as fundamental excitations in a quantum vacuum, modeled as a Bose-Einstein condensate. Through key equations, the role of phonons as intermediaries between matter, energy, and spacetime geometry is demonstrated. The theory expands Einsteins field equations to differentiate between visible and dark matter, and revises the standard model by incorporating phonons. It addresses dark matter, dark energy, gravity, and phase transitions, while making testable predictions. The theory proposes that singularities, the essence of particles and black holes, are quantum entities ubiquitous in nature, constituting the very essence of elementary particles, seen as micro black holes or quantum fractal structures of spacetime. As the theory is refined with increasing mathematical rigor, it builds upon the foundation of initial physical intuition, connecting the spacetime continuum of general relativity with the hydrodynamics of the quantum vacuum. Inspired by the insights of Tesla and Majorana, who believed that physical intuition justifies the infringement of mathematical rigor in the early stages of theory development, this work aims to advance the understanding of the fundamental laws of the universe and the perception of reality.
文摘We have derived the first Noether theorem and Noether identities in canonical formalism for field theory with higher-order singular Lagrangian,which is a powerful tool toanalyse Dirac constraint for such system. A gauge-variant system in canonical variables formalism must has Dirac constraint.For a system with first class constraint (FCC), we have developed an algorithm for construction of the gauge generator of such system. An application to the Podolsky generalized electromagnetic field was given.
基金a phased result of the research project“Study on Contemporary Chinese Human Rights Theory and Discourse”funded by the Scientific Research Fund of the Renmin University of China(Approval No.22XNA006)。
文摘The development of theories on human rights with Chinese characteristics and China’s engagement in global human rights governance cannot be separated from attention to contemporary Western human rights theory.The debate between naturalistic and political conceptions of human rights has a long history,but discussions on the basic criteria for evaluating human rights theories have been insufficient.This article,focusing on the criterion of fidelity to practice,attempts to identify the development trajectory and direction of human rights theory.The universal claims of naturalistic human rights perspectives and the human rights catalog they propose have been criticized for deviating from practice.On the other hand,political conceptions of human rights,while emphasizing domestic human rights practices,have been criticized for their occasional nature and perceived loss of criticality.The broad-way practice theory seeks a third way that goes beyond the divide between these two perspectives.On the one hand,the theory itself faces limitations and the need for reshaping,while on the other hand,the traditional singular practice theory is also undergoing self-renewal.It can be said that the“internal critique”of contemporary Western human rights theory is already underway and will continue.
基金supported by the National Natural Science Foundation of China(No.12371168)in part by the Science and Technology Commission of Shanghai Municipality(No.22DZ2229014)。
文摘In this paper,we focus on the dynamics of the modified Leslie Gower model with a weak Allee effect and fear effect on predators.Assuming that the inherent growth rate of prey is much faster than that of predators,this becomes a singular perturbation problem.Based on the geometric singular perturbation theory,we prove the existence of canard cycles and relaxation oscillation and provide an asymptotic expression of the relaxation oscillation period.Furthermore,it demonstrates that,under certain conditions,the degenerate transcritical bifurcation point is a global attractor using geometric singular perturbation theory,the center manifold theorem and the blow-up method.Numerical simulations verify the theoretical results.
基金supported by the National Natural Science Foundation of China(62073327,62403467,62373090,62273350,62521001)the Natural Science Foundation of Jiangsu Province(BK20241635)+2 种基金the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation(CPSF)(GZB20240827)Jiangsu Funding Program for Excellent Postdoctoral Talent(2024ZB604)the China Postdoctoral Science Foundation(2024M763545,2025T054ZGMK).
文摘In this article,a novel model-free coordinated optimal regulation design methodology is proposed for the rigidly connected dual permanent magnet synchronous motor(PMSM)system via adaptive dynamic programming(ADP).First,we adopt the classical master-slave structure to maintain torque synchronization by virtue of field-oriented control.Then,a reducedorder model of the dual-PMSM system is established through the application of singular perturbation theory(SPT),which is of significance to decrease the learning time and computational complexity in the outer speed loop design.Afterwards,we design a coordinated adaptive optimal regulator in framework of ADP to drive the speed of girth gear asymptotic tracking the reference signal and accommodate the load torque disturbance,which is independent of the knowledge of model parameters of the system.According to SPT,we analyze the suboptimality,closed-loop stability,and robustness properties of the obtained controller under mild conditions.Finally,comprehensive experimental studies are provided to verify that the proposed control strategy can achieve the speed regulation and the torque synchronization,as well as ameliorate the transient response.
基金Sponsored by Ministry of Science and Higher Education within the Framework of Russian State Assignment(Grant No.124012500442⁃3).
文摘The modern definition of the wave concept,which is based on the functional connection between the parameters of the spatial structure of an instantaneous flow pattern and the characteristics of the temporal variability at a given point,is discussed.The dispersion relation for 2D plane periodic perturbations on the surface of viscous stratified fluid is selected as the characteristic function defining the wave motion.Using the theory of singular perturbations,a method for calculating complete solutions to the dispersion relations of periodic flows,including regular wave and singular ligament solutions is presented.Properties of the complete exact solution of the dispersion relation containing regular and singular functions are compared with asymptotic solutions.In limiting cases,obtained dispersion relations are matched with well⁃known expressions for waves in homogeneous viscous and ideal liquids.
文摘The dynamical equations of a thin rectangle plate subjected to the friction support boundary and its plane force are established in this paper. The local bifurcation of this system is investigated by using L S method and the singularity theory. The Z 2 bifurcation in non degenerate case is discussed. The local bifurcation diagrams of the unfolding parameters and the bifurcation response characters referred to the physical parameters of the system are obtained by numerical simulation. The results of the computer simulation are coincident with the theoretical analysis and experimental results.
基金Project supported by the National Basic Research Program of China(973 Program)(No.2015CB057405)the National Natural Science Foundation of China(No.11372082)the State Scholarship Fund of China Scholarship Council(CSC)(2014)
文摘A reduced model is proposed and analyzed for the simulation of vortexinduced vibrations （VIVs） for turbine blades. A rotating blade is modelled as a uniform cantilever beam, while a van der Pol oscillator is used to represent the time-varying characteristics of the vortex shedding, which interacts with the equations of motion for the blade to simulate the fluid-structure interaction. The action for the structural motion on the fluid is considered as a linear inertia coupling. The nonlinear characteristics for the dynamic responses are investigated with the multiple scale method, and the modulation equations are derived. The transition set consisting of the bifurcation set and the hystere- sis set is constructed by the singularity theory and the effects of the system parameters, such as the van der Pol damping. The coupling parameter on the equilibrium solutions is analyzed. The frequency-response curves are obtained, and the stabilities are determined by the Routh-Hurwitz criterion. The phenomena including the saddle-node and Hopf bifurcations are found to occur under certain parameter values. A direct numerical method is used to analyze the dynamic characteristics for the original system and verify the va- lidity of the multiple scale method. The results indicate that the new coupled model is useful in explaining the rich dynamic response characteristics such as possible bifurcation phenomena in the VIVs.
文摘Bifurcations with constraints are open problems appeared in research on periodic bifurcations of nonlinear dynamical systems, but the present singularity theory doesn't contain any analytical methods and results about it. As the complement to singularity theory and the first step to study on constrained bifurcations, here are given tire transition sets and persistent perturbed bifurcation diagrams of 10 elementary bifurcation of codimension no more than three.
文摘The nonlinear normal modes (NNMs) associated with integrnal resonance can be classified into two kinds: uncoupled and coupled. The bifurcation problem of the coupled NNM of system with 1 : 2 : 5 dual internal resonance is in two variables. The singular analysis of it is presented after separating the two variables by taking advantage of Maple algebra, and some new bifurcation patterns are found. Different from the NNMs of systems with single internal resonance, the number of the NNMs of systems with dual internal resonance may be more or less than the number of the degrees of freedom. At last, it is pointed out that bifurcation problems in two variables can be conveniently solved by separating variables as well as using coupling equations.
基金Project supported by the National Natural Science Foundation of China (Grant No 10872141)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No 20060056005)
文摘The static bifurcation of the parametrically excited strongly nonlinear oscillator is studied. We consider the averaged equations of a system subject to Duffing-van der Pol and quintic strong nonlinearity by introducing the undetermined fundamental frequency into the computation in the complex normal form. To discuss the static bifurcation, the bifurcation problem is described as a 3-codimensional unfolding with Z2 symmetry on the basis of singularity theory. The transition set and bifurcation diagrams for the singularity are presented, while the stability of the zero solution is studied by using the eigenvalues in various parameter regions.
文摘Bifurcations of one kind of reaction_diffusion equations, u″+μ(u-u k)=0(μ is a parameter,4≤k∈Z +), with boundary value condition u(0)=u(π)=0 are discussed. By means of singularity theory based on the method of Liapunov_Schmidt reduction, satisfactory results can be acquired.
基金supported by the National Natural Science Foundation of China (No. 10632040)
文摘Bifurcation of periodic solutions widely exists in nonlinear dynamical systems. In this paper, categories of bifurcations of systems with two state variables with different types of constraints are discussed, where some new types of transition sets are added. Additionally, the bifurcation properties of two-dimensionM systems without constraints are compared with the ones with constraints. The results obtained in this paper can be used by engineers for the choice of the structural parameters of the systems.
文摘The method of averaging is applied in this paper to deal with primary resonance of a three circular plates torsion vibration system having cubic nonlinearities which is excited by a simple-harmonic excitation. Bifurcation equation of the steady state response is obtained and its singularity analysis is given. The results of theoretical analysis are shown to be in good agreement with experimental ones.
基金supported by the National Natural Science Foundation of China (No. 10632040)
文摘A kinetic model of the piecewise-linear nonlinear suspension system that consists of a dominant spring and an assistant spring is established. Bifurcation of the resonance solution to a suspension system with two degrees of freedom is investigated with the singularity theory. Transition sets of the system and 40 groups of bifurcation diagrams are obtained. The local bifurcation is found, and shows the overall character- istics of bifurcation. Based on the. relationship between parameters and the topological bifurcation solutions, motion characteristics with different parameters are obtained. The results provides a theoretical basis for the optimal control of vehicle suspension system parameters.
基金supported by the National Natural Science Foundation of China (No. 10632040)the Tianjin Natural Science Foundation (No. 09JCZDJC26800)
文摘The nonlinear equations of an elastic tank-liquid coupling system subjected to the external excitation are established.By means of the multi-scale method and the singularity theory,the bifurcation behaviors of the system are investigated and analyzed.The various nonlinear dynamical behaviors of the coupling system are obtained,which can further explain the relationship between the physical parameters and the bifurcation solutions.The results provide a theoretical basis to the realization of the parameter optimal control.
基金the National Natural Science Foundation of China(19971057) and the Youth Science Foundation of ShanghaiMunicipal Commission
文摘Biforations of an ordinary differential equation with two-point boundary value condition are investigated. Using the singularity theory based on the Liapunov-Schmidt reduction, we have obtained some characterization results.
文摘An optimized damage identification method of beam combined wavelet with neural network is presented in an attempt to improve the calculation iterative speed and accuracy damage identification. The mathematical model is developed to identify the structure damage based on the theory of finite elements and rotation modal parameters. The model is integrated with BP neural network optimization approach which utilizes the Genetic algorithm optimization method. The structural rotation modal parameters are performed with the continuous wavelet transform through the Mexico hat wavelet. The location of structure damage is identified by the maximum of wavelet coefficients. Then, the multi-scale wavelet coefficients modulus maxima are used as the inputs of the BP neural network, and through training and updating the optimal weight and threshold value to obtain the ideal output which is used to describe the degree of structural damage. The obtained results demonstrate the effectiveness of the proposed approach in simultaneously improving the structural damage identification precision including the damage locating and severity.
