Mastering the influence laws of parameters on the solution structure of nonlinear systems is the basis of carrying out vibration isolation and control.Many researches on solution structure and bifurcation phenomenon i...Mastering the influence laws of parameters on the solution structure of nonlinear systems is the basis of carrying out vibration isolation and control.Many researches on solution structure and bifurcation phenomenon in parameter spaces are carried out broadly in many fields,and the research on nonlinear gear systems has attracted the attention of many scholars.But there is little study on the solution domain boundary of nonlinear gear systems.For a periodic non-autonomous nonlinear dynamic system with several control parameters,a solution domain boundary analysis method of nonlinear systems in parameter spaces is proposed,which combines the cell mapping method based on Poincaré point mapping in phase spaces with the domain decomposition technique of parameter spaces.The cell mapping is known as a global analysis method to analyze the global behavior of a nonlinear dynamic system with finite dimensions,and the basic idea of domain decomposition techniques is to divide and rule.The method is applied to analyze the solution domain boundaries in parameter spaces of a nonlinear gear system.The distribution of different period domains,chaos domain and the domain boundaries between different period domains and chaotic domain are obtained in control parameter spaces constituted by meshing damping ratio with excitation frequency,fluctuation coefficient of meshing stiffness and average exciting force respectively by calculation.The calculation results show that as the meshing damping increases,the responses of the system change towards a single motion,while the variations of the excitation frequency,meshing stiffness and exciting force make the solution domain presenting diversity.The proposed research contribution provides evidence for vibration control and parameter design of the gear system,and confirms the validity of the solution domain boundary analysis method.展开更多
The fast sweeping method is an efficient iterative method for hyperbolic problems. It combines Gauss-Seidel iterations with alternating sweeping orderings. In this paper several parallel implementations of the fast sw...The fast sweeping method is an efficient iterative method for hyperbolic problems. It combines Gauss-Seidel iterations with alternating sweeping orderings. In this paper several parallel implementations of the fast sweeping method are presented. These parallel algorithms are simple and efficient due to the causality of the underlying partial different equations. Numerical examples are used to verify our algorithms.展开更多
作者用 X 射线衍射仪法定量分析了 Al_2O_3-MgO·2T1O_2复合物系在烧结过程中的物相变化及烧结体的物相组成和晶格参数。探讨了(Al_(2(1-x))Mg_xTi_(1+x)O_5型固溶体的形成机制。通过扫描电镜和偏光显微镜观测烧结体的微观组织,结...作者用 X 射线衍射仪法定量分析了 Al_2O_3-MgO·2T1O_2复合物系在烧结过程中的物相变化及烧结体的物相组成和晶格参数。探讨了(Al_(2(1-x))Mg_xTi_(1+x)O_5型固溶体的形成机制。通过扫描电镜和偏光显微镜观测烧结体的微观组织,结合弯曲强度及热膨胀、收缩性能,讨论了烧结体组成、结构与性能之间的相互关系。展开更多
In this paper, we are concerned with the following class of elliptic problems:where 2 = 2N/（N-2） is the critical Sobolev exponent, 2 【 q 【 2 , 0≤μ 【 μˉ=（N-2）2<sub>4</sub> , a（x）, k（x） ∈ C（...In this paper, we are concerned with the following class of elliptic problems:where 2 = 2N/（N-2） is the critical Sobolev exponent, 2 【 q 【 2 , 0≤μ 【 μˉ=（N-2）2<sub>4</sub> , a（x）, k（x） ∈ C（RN ）. Through a compactness analysis of the functional corresponding to the problems , we obtain the existence of positive solutions for this problem under certain assumptions on a（x） and k（x）.展开更多
By constructing a special cone and using cone compression and expansion fixed point theorem, this paper presents some existence results of positive solutions of singular boundary value problem on unbounded domains for...By constructing a special cone and using cone compression and expansion fixed point theorem, this paper presents some existence results of positive solutions of singular boundary value problem on unbounded domains for a class of first order differential equation. As applications of the main results, two examples are given at the end of this paper.展开更多
For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional...For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional-order differential equations based on the definition of Grunwald-Letnikov is presented. The results of numerical solution by using the novel method and the frequency-domain method are compared, and the limitations of frequency-domain method are discussed.展开更多
Applying Krasnosel'skii fixed point theorem of cone expansion-compression type, the existence of positive radial solutions for some second-order nonlinear elliptic equations in annular domains, subject to Dirichle...Applying Krasnosel'skii fixed point theorem of cone expansion-compression type, the existence of positive radial solutions for some second-order nonlinear elliptic equations in annular domains, subject to Dirichlet boundary conditions, is investigated. By considering the properties of nonlinear term on boundary closed intervals, several existence results of positive radial solutions are established. The main results are independent of superlinear growth and sublinear growth of nonlinear term. If nonlinear term has extreme values and satisfies suitable conditions, the main results are very effective.展开更多
基金supported by National Hi-tech Research and Development Program of China (863 Program,Grant No.2009AA04Z404)
文摘Mastering the influence laws of parameters on the solution structure of nonlinear systems is the basis of carrying out vibration isolation and control.Many researches on solution structure and bifurcation phenomenon in parameter spaces are carried out broadly in many fields,and the research on nonlinear gear systems has attracted the attention of many scholars.But there is little study on the solution domain boundary of nonlinear gear systems.For a periodic non-autonomous nonlinear dynamic system with several control parameters,a solution domain boundary analysis method of nonlinear systems in parameter spaces is proposed,which combines the cell mapping method based on Poincaré point mapping in phase spaces with the domain decomposition technique of parameter spaces.The cell mapping is known as a global analysis method to analyze the global behavior of a nonlinear dynamic system with finite dimensions,and the basic idea of domain decomposition techniques is to divide and rule.The method is applied to analyze the solution domain boundaries in parameter spaces of a nonlinear gear system.The distribution of different period domains,chaos domain and the domain boundaries between different period domains and chaotic domain are obtained in control parameter spaces constituted by meshing damping ratio with excitation frequency,fluctuation coefficient of meshing stiffness and average exciting force respectively by calculation.The calculation results show that as the meshing damping increases,the responses of the system change towards a single motion,while the variations of the excitation frequency,meshing stiffness and exciting force make the solution domain presenting diversity.The proposed research contribution provides evidence for vibration control and parameter design of the gear system,and confirms the validity of the solution domain boundary analysis method.
基金This work is partially supported by Sloan FoundationNSF DMS0513073+1 种基金ONR grant N00014-02-1-0090DARPA grant N00014-02-1-0603
文摘The fast sweeping method is an efficient iterative method for hyperbolic problems. It combines Gauss-Seidel iterations with alternating sweeping orderings. In this paper several parallel implementations of the fast sweeping method are presented. These parallel algorithms are simple and efficient due to the causality of the underlying partial different equations. Numerical examples are used to verify our algorithms.
文摘作者用 X 射线衍射仪法定量分析了 Al_2O_3-MgO·2T1O_2复合物系在烧结过程中的物相变化及烧结体的物相组成和晶格参数。探讨了(Al_(2(1-x))Mg_xTi_(1+x)O_5型固溶体的形成机制。通过扫描电镜和偏光显微镜观测烧结体的微观组织,结合弯曲强度及热膨胀、收缩性能,讨论了烧结体组成、结构与性能之间的相互关系。
基金supported by National Natural Science Foundation of China (Grant Nos.10631030, 10871075)the PhD Specialized Grant of the Ministry of Education of China (Grant No. 20060511001)the Natural Science Foundation of Guangdong Province, China (Grant No. 9451064201003736)
文摘In this paper, we are concerned with the following class of elliptic problems:where 2 = 2N/（N-2） is the critical Sobolev exponent, 2 【 q 【 2 , 0≤μ 【 μˉ=（N-2）2<sub>4</sub> , a（x）, k（x） ∈ C（RN ）. Through a compactness analysis of the functional corresponding to the problems , we obtain the existence of positive solutions for this problem under certain assumptions on a（x） and k（x）.
基金Supported by the National Natural Science Foundation of China(No.10671167)the Natural Science Foundation of Liaocheng University(31805)
文摘By constructing a special cone and using cone compression and expansion fixed point theorem, this paper presents some existence results of positive solutions of singular boundary value problem on unbounded domains for a class of first order differential equation. As applications of the main results, two examples are given at the end of this paper.
基金the Natural Science Foundation of CQ CSTC under Grant No. 2007BB2161.
文摘For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional-order differential equations based on the definition of Grunwald-Letnikov is presented. The results of numerical solution by using the novel method and the frequency-domain method are compared, and the limitations of frequency-domain method are discussed.
文摘Applying Krasnosel'skii fixed point theorem of cone expansion-compression type, the existence of positive radial solutions for some second-order nonlinear elliptic equations in annular domains, subject to Dirichlet boundary conditions, is investigated. By considering the properties of nonlinear term on boundary closed intervals, several existence results of positive radial solutions are established. The main results are independent of superlinear growth and sublinear growth of nonlinear term. If nonlinear term has extreme values and satisfies suitable conditions, the main results are very effective.
