The mechanism of a retracting cantilevered beam has been investigated by the invariant and energy-based analysis. The time-varying parameter partial differential equation governing the transverse vibrations of a beam ...The mechanism of a retracting cantilevered beam has been investigated by the invariant and energy-based analysis. The time-varying parameter partial differential equation governing the transverse vibrations of a beam with retracting motion is derived based on the momentum theorem. The assumed-mode method is used to truncate the governing partial differential equation into a set of ordinary differential equations (ODEs) with time-dependent coefficients. It is found that if the order of truncation is not less than the order of the initial conditions, the assumed-mode method can yield accurate results. The energy transfers among assumed modes are discussed during retraction. The total energy varying with time has been investigated by numerical and analytical methods, and the results have good agreement with each other. For the transverse vibrations of the axially retracting beam, the adiabatic invariant is derived by both the averaging method and the Bessel function method. (C) 2016 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license.展开更多
Our aim in the present article is to introduce and study types of retraction of one dimensional manifold. New types of geodesics in one dimensional manifold are presented. The deformation retracts of one dimensional m...Our aim in the present article is to introduce and study types of retraction of one dimensional manifold. New types of geodesics in one dimensional manifold are presented. The deformation retracts of one dimensional manifold into itself and onto geodesics is deduced. Also, the isometric and topological folding in each case and the relation between the deformations retracts after and before folding has been obtained. New types of conditional folding are described.展开更多
In order to conduct effective reliability analysis of retracting actuator with multi-state(success state,safety failure state and action failure state), we redefine type-3 operator in goal oriented(GO) method to descr...In order to conduct effective reliability analysis of retracting actuator with multi-state(success state,safety failure state and action failure state), we redefine type-3 operator in goal oriented(GO) method to describe three states of main charge of retracting actuator and improve type-15 operator in GO method to describe the logic relations of multi-state output. The quantitative and qualitative reliability analyses of retracting actuator are made based on GO method in this paper. The system state probability of retracting actuator is obtained through quantitative analysis, and its weakness is found through qualitative analysis. The analysis results show that GO method is effective to improve the reliability of retracting actuator, and this method is also feasible for reliability analysis of other complicated initiating explosive systems.展开更多
The authors introduce a notion of a weak graph map homotopy(they call it M-homotopy),discuss its properties and applications.They prove that the weak graph map homotopy equivalence between graphs coincides with the gr...The authors introduce a notion of a weak graph map homotopy(they call it M-homotopy),discuss its properties and applications.They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001.The difference between them is that the weak graph map homotopy transformation is defined in terms of maps,while the graph homotopy transformation is defined by means of combinatorial operations.They discuss its advantages over the graph homotopy transformation.As its applications,they investigate the mapping class group of a graph and the 1-order M P-homotopy group of a pointed simple graph.Moreover,they show that the 1-order M P-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 11322214, 11172010, 11290152 and 11402007)supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada, the Canada Research Chair (CRC) Program+1 种基金the Bizkaia Talent Grant under the Basque Government through the BERC 2014–2017 ProgramSpanish Ministry of Economy and Competitiveness MINECO:BCAM Severo Ochoa excellence accreditation SEV-2013-0323
文摘The mechanism of a retracting cantilevered beam has been investigated by the invariant and energy-based analysis. The time-varying parameter partial differential equation governing the transverse vibrations of a beam with retracting motion is derived based on the momentum theorem. The assumed-mode method is used to truncate the governing partial differential equation into a set of ordinary differential equations (ODEs) with time-dependent coefficients. It is found that if the order of truncation is not less than the order of the initial conditions, the assumed-mode method can yield accurate results. The energy transfers among assumed modes are discussed during retraction. The total energy varying with time has been investigated by numerical and analytical methods, and the results have good agreement with each other. For the transverse vibrations of the axially retracting beam, the adiabatic invariant is derived by both the averaging method and the Bessel function method. (C) 2016 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license.
文摘Our aim in the present article is to introduce and study types of retraction of one dimensional manifold. New types of geodesics in one dimensional manifold are presented. The deformation retracts of one dimensional manifold into itself and onto geodesics is deduced. Also, the isometric and topological folding in each case and the relation between the deformations retracts after and before folding has been obtained. New types of conditional folding are described.
基金the Advanced Research Fund for National Defense Science and Technology Key Laboratory(No.9104C3705021003)
文摘In order to conduct effective reliability analysis of retracting actuator with multi-state(success state,safety failure state and action failure state), we redefine type-3 operator in goal oriented(GO) method to describe three states of main charge of retracting actuator and improve type-15 operator in GO method to describe the logic relations of multi-state output. The quantitative and qualitative reliability analyses of retracting actuator are made based on GO method in this paper. The system state probability of retracting actuator is obtained through quantitative analysis, and its weakness is found through qualitative analysis. The analysis results show that GO method is effective to improve the reliability of retracting actuator, and this method is also feasible for reliability analysis of other complicated initiating explosive systems.
基金supported by the National Natural Science Foundation of China(No.11771116)。
文摘The authors introduce a notion of a weak graph map homotopy(they call it M-homotopy),discuss its properties and applications.They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001.The difference between them is that the weak graph map homotopy transformation is defined in terms of maps,while the graph homotopy transformation is defined by means of combinatorial operations.They discuss its advantages over the graph homotopy transformation.As its applications,they investigate the mapping class group of a graph and the 1-order M P-homotopy group of a pointed simple graph.Moreover,they show that the 1-order M P-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.
