The vortex-induced vibration may lead to a premature failure of hydraulic mechanical systems,especially under the resonance condition in the torsional mode.To predict the structural fatigue life,a careful consideratio...The vortex-induced vibration may lead to a premature failure of hydraulic mechanical systems,especially under the resonance condition in the torsional mode.To predict the structural fatigue life,a careful consideration of the dynamic response to the hydraulic excitations is essential in the design phase.This study focuses on the numerical investigation of the relationship between the flow velocity,the added mass and the hydrodynamic damping,particularly,with respect to a Donaldson-type hydrofoil,vibrating in the first torsional mode.A two-way fluid-structure interaction(FSI)method is used to predict above two parameters.The flow velocity is in the range of 0 m/s-20m/s.To evaluate the hydrodynamic damping ratio,an identification method is proposed,based on a modified version of the logarithmic decay method.The relative deviations of the simulated natural frequencies and hydrodynamic damping ratios as compared with the experimental data for the first torsional modes,are within 8.1%and 16.6%,respectively.The analysis results show that the added mass coefficient for the first torsional mode is in the range of 1.59-1.86,and is around 44%of that for the first bending mode.The trends of the boundary layer thickness and the wake width against the reduced velocity are found to be opposite to that of the hydrodynamic damping ratio.The theoretical equation for predicting the hydrodynamic damping ratio is modified,which is shown to be more reliable due to its consideration of the velocity independent hydrodynamic damping phase.展开更多
Let （M, ω） be a closed symplectic 2n-dimensional manifold. Donaldson in his paper showed that there exist 2m-dimensional symplectie submanifolds （V^2m,ω） of （M,ω）, 1 ≤m ≤ n - 1, with （m - 1）-equivalent in...Let （M, ω） be a closed symplectic 2n-dimensional manifold. Donaldson in his paper showed that there exist 2m-dimensional symplectie submanifolds （V^2m,ω） of （M,ω）, 1 ≤m ≤ n - 1, with （m - 1）-equivalent inclusions. On the basis of this fact we obtain isomorphic relations between kernel of Lefschetz map of M and kernels of Lefschetz maps of Donaldson submanifolds V^2m, 2 ≤ m ≤ n - 1. Then, using this relation, we show that the flux group of M is discrete if the action of π1 （M） on π2（M） is trivial and there exists a retraction r ： M→ V, where V is a 4-dimensional Donaldson submanifold. And, in the symplectically aspherical case, we investigate the flux groups of the manifolds.展开更多
Abstract We define the motivic Milnor fiber of cyclic L∞-algebras of dimension three using the method of Denef and Loeser of motivic integration. It is proved by Nicaise and Sebag that the topo- logical Euler charact...Abstract We define the motivic Milnor fiber of cyclic L∞-algebras of dimension three using the method of Denef and Loeser of motivic integration. It is proved by Nicaise and Sebag that the topo- logical Euler characteristic of the motivic Milnor fiber is equal to the Euler characteristic of the étale cohomology of the analytic Milnor fiber. We prove that the value of Behrend function on the germ moduli space determined by a cyclic L∞-algebra L is equal to the Euler characteristic of the analytic Milnor fiber. Thus we prove that the Behrend function depends only on the formal neighborhood of the moduli space.展开更多
基金the National Natural Science Foundation of China(Grant Nos.51836010,51879266 and 51839001)the National Key Research and Development Program of China(Grant No.2017YFC0403206)+1 种基金the Beijing Municipal Science and Technology Project(Grant No.Z181100005518013)the Chinese Universities Scientific Fund(Grant No.2019TC040).
文摘The vortex-induced vibration may lead to a premature failure of hydraulic mechanical systems,especially under the resonance condition in the torsional mode.To predict the structural fatigue life,a careful consideration of the dynamic response to the hydraulic excitations is essential in the design phase.This study focuses on the numerical investigation of the relationship between the flow velocity,the added mass and the hydrodynamic damping,particularly,with respect to a Donaldson-type hydrofoil,vibrating in the first torsional mode.A two-way fluid-structure interaction(FSI)method is used to predict above two parameters.The flow velocity is in the range of 0 m/s-20m/s.To evaluate the hydrodynamic damping ratio,an identification method is proposed,based on a modified version of the logarithmic decay method.The relative deviations of the simulated natural frequencies and hydrodynamic damping ratios as compared with the experimental data for the first torsional modes,are within 8.1%and 16.6%,respectively.The analysis results show that the added mass coefficient for the first torsional mode is in the range of 1.59-1.86,and is around 44%of that for the first bending mode.The trends of the boundary layer thickness and the wake width against the reduced velocity are found to be opposite to that of the hydrodynamic damping ratio.The theoretical equation for predicting the hydrodynamic damping ratio is modified,which is shown to be more reliable due to its consideration of the velocity independent hydrodynamic damping phase.
文摘Let （M, ω） be a closed symplectic 2n-dimensional manifold. Donaldson in his paper showed that there exist 2m-dimensional symplectie submanifolds （V^2m,ω） of （M,ω）, 1 ≤m ≤ n - 1, with （m - 1）-equivalent inclusions. On the basis of this fact we obtain isomorphic relations between kernel of Lefschetz map of M and kernels of Lefschetz maps of Donaldson submanifolds V^2m, 2 ≤ m ≤ n - 1. Then, using this relation, we show that the flux group of M is discrete if the action of π1 （M） on π2（M） is trivial and there exists a retraction r ： M→ V, where V is a 4-dimensional Donaldson submanifold. And, in the symplectically aspherical case, we investigate the flux groups of the manifolds.
基金Supported by Simon Foundation Collaboration Grants(Grant No.311837)
文摘Abstract We define the motivic Milnor fiber of cyclic L∞-algebras of dimension three using the method of Denef and Loeser of motivic integration. It is proved by Nicaise and Sebag that the topo- logical Euler characteristic of the motivic Milnor fiber is equal to the Euler characteristic of the étale cohomology of the analytic Milnor fiber. We prove that the value of Behrend function on the germ moduli space determined by a cyclic L∞-algebra L is equal to the Euler characteristic of the analytic Milnor fiber. Thus we prove that the Behrend function depends only on the formal neighborhood of the moduli space.
