Three dimensional dynamic stress intensity factors are analyzed for a curved crack with a second order perturbation method. The method is extended to obtain an approximate representation of a three dimensional dynamic...Three dimensional dynamic stress intensity factors are analyzed for a curved crack with a second order perturbation method. The method is extended to obtain an approximate representation of a three dimensional dynamic stress intensity factors at the tip of a curved crack. Due to three dimensional curved crack growth the dynamic energy release rate can be calculated by using the Irwin＇s formula. A three dimensional curved crack in materials with inhomogeneous fracture toughness are considered. Paths of a brittle three dimensional curved crack propagating along a welded joint are predicted via the present method, where the effects of dynamic applied stresses, residual stresses, and material deterioration due to welding are taken into considerations.展开更多
Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application. Two categories of the tension-dominant and curvaturedominant nonlinearities are analyzed. The dynamic non...Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application. Two categories of the tension-dominant and curvaturedominant nonlinearities are analyzed. The dynamic nonlinearity of four beam structures of nanomechanical resonator is quantitatively studied via a dimensional analysis approach. The dimensional analysis shows that for the nanomechanical resonator of tension-dominant nonlinearity, its dynamic nonlinearity decreases monotonically with increasing axial loading and increases monotonically with the increasing aspect ratio of length to thickness; the dynamic nonlinearity can only result in the hardening effects. However, for the nanomechanical resonator of the curvature-dominant nonlinearity, its dynamic nonlinearity is only dependent on axial loading. Compared with the tension-dominant nonlinearity, the curvature-dominant nonlinearity increases monotonically with increasing axial loading; its dynamic nonlinearity展开更多
A variable dimensional state space(VDSS) has been proposed to improve the re-planning time when the robotic systems operate in large unknown environments.VDSS is constructed by uniforming lattice state space and grid ...A variable dimensional state space(VDSS) has been proposed to improve the re-planning time when the robotic systems operate in large unknown environments.VDSS is constructed by uniforming lattice state space and grid state space.In VDSS,the lattice state space is only used to construct search space in the local area which is a small circle area near the robot,and grid state space elsewhere.We have tested VDSS with up to 80 indoor and outdoor maps in simulation and on segbot robot platform.Through the simulation and segbot robot experiments,it shows that exploring on VDSS is significantly faster than exploring on lattice state space by Anytime Dynamic A*(AD*) planner and VDSS is feasible to be used on robotic systems.展开更多
This paper is concentrated on a nonlinear Galerkin method with sm small- scale components for Kuramoto-Sivashmsky equation, in which convergence results and the analysis of error estimates are given, The conclusion sh...This paper is concentrated on a nonlinear Galerkin method with sm small- scale components for Kuramoto-Sivashmsky equation, in which convergence results and the analysis of error estimates are given, The conclusion shows that this choce of modes is efficient .for The method modifred.展开更多
Signal processing in phase space based on nonlinear dynamics theory is a new method for underwater acoustic signal processing. One key problem when analyzing actual acoustic signal in phase space is how to reduce the ...Signal processing in phase space based on nonlinear dynamics theory is a new method for underwater acoustic signal processing. One key problem when analyzing actual acoustic signal in phase space is how to reduce the noise and lower the embedding dimen- sion. In this paper, local-geometric-projection method is applied to obtain fow dimensional element from various target radiating noise and the derived phase portraits show obviously low dimensional attractors. Furthermore, attractor dimension and cross prediction error are used for classification. It concludes that combining these features representing the geometric and dynamical properties respectively shows effects in target classification.展开更多
The existence of approximate inertial manifold Using wavelet to Burgers' equation, and numerical solution under multiresolution analysis with the low modes were studied. It is shown that the Burgers' equation ...The existence of approximate inertial manifold Using wavelet to Burgers' equation, and numerical solution under multiresolution analysis with the low modes were studied. It is shown that the Burgers' equation has a good localization property of the numerical solution distinguishably.展开更多
In this paper foe Liapunov functionals has been constructed.the decay property of the high dimensional modes of the J-J equations in the Josephson junctions is obtained,and thus the approxtmate inertial manifolds are...In this paper foe Liapunov functionals has been constructed.the decay property of the high dimensional modes of the J-J equations in the Josephson junctions is obtained,and thus the approxtmate inertial manifolds are given.展开更多
Dynamic transient responses of rotating twisted plate under the air-blast loading and step loading respectively considering the geometric nonlinear relationships are investigated using classical shallow shell theory.B...Dynamic transient responses of rotating twisted plate under the air-blast loading and step loading respectively considering the geometric nonlinear relationships are investigated using classical shallow shell theory.By applying energy principle,a novel high dimensional nonlinear dynamic system of the rotating cantilever twisted plate is derived for the first time.The use of variable mode functions by polynomial functions according to the twist angles and geometric of the plate makes it more accurate to describe the dynamic system than that using the classic cantilever beam functions and the free-free beam functions.The comparison researches are carried out between the present results and other literatures to validate present model,formulation and computer process.Equations of motion describing the transient high dimensional nonlinear dynamic response are reduced to a four degree of freedom dynamic system which expressed by out-plane displacement.The effects of twisted angle,stagger angle,rotation speed,load intensity and viscous damping on nonlinear dynamic transient responses of the twisted plate have been investigated.It’s important to note that although the homogeneous and isotropic material is applied here,it might be helpful for laminated composite,functionally graded material as long as the equivalent material parameters are obtained.展开更多
In the present paper we study the maximum dissipative extension of Schrodingeroperator.introduce the generalized indefinite metvic space and get the representation ofmaximum dissipative extension of Schrodinger operat...In the present paper we study the maximum dissipative extension of Schrodingeroperator.introduce the generalized indefinite metvic space and get the representation ofmaximum dissipative extension of Schrodinger operator in natural boundary space.make preparation for the further study longtime chaotic behaxior of infinite dimensiondynamics system in nonlinear Schrodinger equation.展开更多
The complexity of multi-dimensional optical wave dynamics arises from the introduction of multiple degrees of freedom and their intricate interactions.In comparison to multimode spatiotemporal mode-locked solitons,exp...The complexity of multi-dimensional optical wave dynamics arises from the introduction of multiple degrees of freedom and their intricate interactions.In comparison to multimode spatiotemporal mode-locked solitons,expanding the wavelength dimension is also crucial for studying the dynamics of multi-dimensional solitons,with simpler characterization techniques。展开更多
This paper discusses the relation between the long-time dynamics of solutions of the two-dimensional （2D） incompressible non-Newtonian fluid system and the 2D Navier-Stokes system. We first show that the solutions o...This paper discusses the relation between the long-time dynamics of solutions of the two-dimensional （2D） incompressible non-Newtonian fluid system and the 2D Navier-Stokes system. We first show that the solutions of the non-Newtonian fluid system converge to the solutions of the Navier-Stokes system in the energy norm. Then we establish that the global attractors {.Aε^H}0〈≤1 of the non-Newtonian fluid system converge to the global attractor .A0H of the Navier-Stokes system as ε → 0. We also construct the minimal limit A^H min of the H global attractors {Aε^H}0〈ε≤ as ≤→ 0 and prove that A^Hmin iS a strictly invariant and connected set.展开更多
基金supported by National Natural Science Foundation of China(No.91016026)Henan Province Natural Science Foundation Subsidy Project(No.152300410003)
文摘Three dimensional dynamic stress intensity factors are analyzed for a curved crack with a second order perturbation method. The method is extended to obtain an approximate representation of a three dimensional dynamic stress intensity factors at the tip of a curved crack. Due to three dimensional curved crack growth the dynamic energy release rate can be calculated by using the Irwin＇s formula. A three dimensional curved crack in materials with inhomogeneous fracture toughness are considered. Paths of a brittle three dimensional curved crack propagating along a welded joint are predicted via the present method, where the effects of dynamic applied stresses, residual stresses, and material deterioration due to welding are taken into considerations.
基金supported by the National Natural Science Foundation of China (10721202 and 11023001)the Chinese Academy of Sciences (KJCX2-EW-L03)
文摘Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application. Two categories of the tension-dominant and curvaturedominant nonlinearities are analyzed. The dynamic nonlinearity of four beam structures of nanomechanical resonator is quantitatively studied via a dimensional analysis approach. The dimensional analysis shows that for the nanomechanical resonator of tension-dominant nonlinearity, its dynamic nonlinearity decreases monotonically with increasing axial loading and increases monotonically with the increasing aspect ratio of length to thickness; the dynamic nonlinearity can only result in the hardening effects. However, for the nanomechanical resonator of the curvature-dominant nonlinearity, its dynamic nonlinearity is only dependent on axial loading. Compared with the tension-dominant nonlinearity, the curvature-dominant nonlinearity increases monotonically with increasing axial loading; its dynamic nonlinearity
基金Supported by the National Natural Science Foundation of China(90920304)
文摘A variable dimensional state space(VDSS) has been proposed to improve the re-planning time when the robotic systems operate in large unknown environments.VDSS is constructed by uniforming lattice state space and grid state space.In VDSS,the lattice state space is only used to construct search space in the local area which is a small circle area near the robot,and grid state space elsewhere.We have tested VDSS with up to 80 indoor and outdoor maps in simulation and on segbot robot platform.Through the simulation and segbot robot experiments,it shows that exploring on VDSS is significantly faster than exploring on lattice state space by Anytime Dynamic A*(AD*) planner and VDSS is feasible to be used on robotic systems.
文摘This paper is concentrated on a nonlinear Galerkin method with sm small- scale components for Kuramoto-Sivashmsky equation, in which convergence results and the analysis of error estimates are given, The conclusion shows that this choce of modes is efficient .for The method modifred.
文摘Signal processing in phase space based on nonlinear dynamics theory is a new method for underwater acoustic signal processing. One key problem when analyzing actual acoustic signal in phase space is how to reduce the noise and lower the embedding dimen- sion. In this paper, local-geometric-projection method is applied to obtain fow dimensional element from various target radiating noise and the derived phase portraits show obviously low dimensional attractors. Furthermore, attractor dimension and cross prediction error are used for classification. It concludes that combining these features representing the geometric and dynamical properties respectively shows effects in target classification.
文摘The existence of approximate inertial manifold Using wavelet to Burgers' equation, and numerical solution under multiresolution analysis with the low modes were studied. It is shown that the Burgers' equation has a good localization property of the numerical solution distinguishably.
文摘In this paper foe Liapunov functionals has been constructed.the decay property of the high dimensional modes of the J-J equations in the Josephson junctions is obtained,and thus the approxtmate inertial manifolds are given.
基金support of National Natural Science Foundation of China through grant Nos.11872127,11832002 and 11732005,Fundamental Research Program of Shenzhen Municipality No.JCYJ20160608153749600 and the Project of Highlevel Innovative Team Building Plan for Beijing Municipal Colleges and Universities No.IDHT20180513 and the project of Qin Xin Talents Cultivation Program,Beijing Information Science&Technology University QXTCP A201901.
文摘Dynamic transient responses of rotating twisted plate under the air-blast loading and step loading respectively considering the geometric nonlinear relationships are investigated using classical shallow shell theory.By applying energy principle,a novel high dimensional nonlinear dynamic system of the rotating cantilever twisted plate is derived for the first time.The use of variable mode functions by polynomial functions according to the twist angles and geometric of the plate makes it more accurate to describe the dynamic system than that using the classic cantilever beam functions and the free-free beam functions.The comparison researches are carried out between the present results and other literatures to validate present model,formulation and computer process.Equations of motion describing the transient high dimensional nonlinear dynamic response are reduced to a four degree of freedom dynamic system which expressed by out-plane displacement.The effects of twisted angle,stagger angle,rotation speed,load intensity and viscous damping on nonlinear dynamic transient responses of the twisted plate have been investigated.It’s important to note that although the homogeneous and isotropic material is applied here,it might be helpful for laminated composite,functionally graded material as long as the equivalent material parameters are obtained.
文摘In the present paper we study the maximum dissipative extension of Schrodingeroperator.introduce the generalized indefinite metvic space and get the representation ofmaximum dissipative extension of Schrodinger operator in natural boundary space.make preparation for the further study longtime chaotic behaxior of infinite dimensiondynamics system in nonlinear Schrodinger equation.
基金National Natural Science Foundation of China(12274238, 62205159, 61835006)Special Project for Cooperation in Basic Research of Beijing,Tianjin and Hebei (21JCZXJC00010)
文摘The complexity of multi-dimensional optical wave dynamics arises from the introduction of multiple degrees of freedom and their intricate interactions.In comparison to multimode spatiotemporal mode-locked solitons,expanding the wavelength dimension is also crucial for studying the dynamics of multi-dimensional solitons,with simpler characterization techniques。
基金supported by National Natural Science Foundation of China(Grant Nos.10901121,11271290 and 11028102)National Basic Research Program of China(Grant No.2012CB426510)+4 种基金Natural Science Foundation of Zhejiang Province(Grant No.Y6080077)Natural Science Foundation of Wenzhou University(Grant No.2008YYLQ01)Zhejiang Youth Teacher Training ProjectWenzhou 551 Projectthe Fundamental Research Funds for the Central Universities(Grant No.2010ZD037)
文摘This paper discusses the relation between the long-time dynamics of solutions of the two-dimensional （2D） incompressible non-Newtonian fluid system and the 2D Navier-Stokes system. We first show that the solutions of the non-Newtonian fluid system converge to the solutions of the Navier-Stokes system in the energy norm. Then we establish that the global attractors {.Aε^H}0〈≤1 of the non-Newtonian fluid system converge to the global attractor .A0H of the Navier-Stokes system as ε → 0. We also construct the minimal limit A^H min of the H global attractors {Aε^H}0〈ε≤ as ≤→ 0 and prove that A^Hmin iS a strictly invariant and connected set.
