We give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain compact fiber bundles with non-trivial four dimensional fibers in the sense of cobordism, by virtue of the rigid...We give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain compact fiber bundles with non-trivial four dimensional fibers in the sense of cobordism, by virtue of the rigidity theorem of harmonic maps due to Schoen and Yau (Topology, 18, 1979, 361-380). As a corollary of this estimate, we compute the degree of symmetry and the semi-simple degree of symmetry of CP2×V, where V is a closed smooth manifold admitting a real analytic Riemannian metric of non-positive curvature. In addition, by the Albanese map, we obtain the sharp estimate of the degree of symmetry of a compact smooth manifold with some restrictions on its one dimensional cohomology.展开更多
Time-varying stiffness is one of the most important dynamic characteristics of rolling element bearings.The method of analyzing the elements in the bearing stiffness matrix is usually adopted to investigate the charac...Time-varying stiffness is one of the most important dynamic characteristics of rolling element bearings.The method of analyzing the elements in the bearing stiffness matrix is usually adopted to investigate the characteristics of bearing stiffness.Linear mapping structure of the bearing stiffness matrix is helpful to understand the varying compliance excitation and its influence on vibration transmission.In this study,a method to analyze the mapping structure of bearing stiffness matrix is proposed based on the singular value decomposition of block matrices in the stiffness matrix.Not only does this method have the advantages of coordinate transformation independence and unit independence,but also the analysis procedure involved is geometrically intuitive.The time-varying stiffness matrix of double-row tapered bearing is calculated and analyzed using the proposed method under two representative load cases.The principal stiffnesses and principal axes defined in the method together indicate the dominant and insignificant stiffness properties with the corresponding directions,and the vibration transmission properties are also revealed.Besides,the coupling behaviors between different shaft motions are found during the analysis of mapping structure.The mechanism of the generation of varying compliance excitation is also revealed.展开更多
基金Project supported by the Japanese Government Scholarshipthe Japan Society for the Promotion of Science Postdoctoral Fellowship for Foreign Researchers+2 种基金the Focused Research Group Postdoctoral Fellowshipthe Program of Visiting Scholars at Chern Institute of Mathematicsthe National Natural Science Foundation of China (No. 10601053).
文摘We give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain compact fiber bundles with non-trivial four dimensional fibers in the sense of cobordism, by virtue of the rigidity theorem of harmonic maps due to Schoen and Yau (Topology, 18, 1979, 361-380). As a corollary of this estimate, we compute the degree of symmetry and the semi-simple degree of symmetry of CP2×V, where V is a closed smooth manifold admitting a real analytic Riemannian metric of non-positive curvature. In addition, by the Albanese map, we obtain the sharp estimate of the degree of symmetry of a compact smooth manifold with some restrictions on its one dimensional cohomology.
基金the Joint Funds of the National Natural Science Foundation of China(Grant No.U1834202).
文摘Time-varying stiffness is one of the most important dynamic characteristics of rolling element bearings.The method of analyzing the elements in the bearing stiffness matrix is usually adopted to investigate the characteristics of bearing stiffness.Linear mapping structure of the bearing stiffness matrix is helpful to understand the varying compliance excitation and its influence on vibration transmission.In this study,a method to analyze the mapping structure of bearing stiffness matrix is proposed based on the singular value decomposition of block matrices in the stiffness matrix.Not only does this method have the advantages of coordinate transformation independence and unit independence,but also the analysis procedure involved is geometrically intuitive.The time-varying stiffness matrix of double-row tapered bearing is calculated and analyzed using the proposed method under two representative load cases.The principal stiffnesses and principal axes defined in the method together indicate the dominant and insignificant stiffness properties with the corresponding directions,and the vibration transmission properties are also revealed.Besides,the coupling behaviors between different shaft motions are found during the analysis of mapping structure.The mechanism of the generation of varying compliance excitation is also revealed.
