Due to the effects of samples and testing conditions on fibre-bundle tensile behaviour, it is necessary to investigate the relationships between experimental factors and tensile properties for the fibre-bundle tensile...Due to the effects of samples and testing conditions on fibre-bundle tensile behaviour, it is necessary to investigate the relationships between experimental factors and tensile properties for the fibre-bundle tensile tester (TENSOR). The effects of bundle sample preparation, fibre bundle mass and fibre alignment have been tested. The experimental results indicated that (1) the low damage in combing and no free-end fibres in the cut bundle are most important for the sample preparation; (2) the reasonable bundle mass is 400700 tex, but the tensile properties measured should be modified with the bundle mass because a small amount of bundle mass causes the scatter results, while the larger is the bundle mass, the more difficult to comb fibres parallel and to clamp fibre evenly; and (3) the fibre irregular arrangement forms a slack bundle resulting in interaction between fibres, which will affect the reproducibility and accuracy of the tensile testing.展开更多
The testing conditions of a fibre bundle tensile tester (TENSOR) are elongation speed (ES), gauge length (GL), pretension, jaw pressure, environmental temperature and relative humidity, instrument linearity and sensit...The testing conditions of a fibre bundle tensile tester (TENSOR) are elongation speed (ES), gauge length (GL), pretension, jaw pressure, environmental temperature and relative humidity, instrument linearity and sensitivity. The effects on fibre-bundle tensile properties at different GL and ES have been discussed in detail and compared with Peirce’s theories on the weaklinks and the breaking time effect. The experimental results indicate that the tensile properties of fibre bundles are strongly affected by GL and vary with different GL. The reasonable GL should be 5 15 mm rather than 3.2 mm for wool bundle measurements. The ES ranging from 20 mm/min to 40 mm/min is beneficial for obtaining comparatively stable and accurate tensile values, whereas 20 mm/min used in current testing for wool fibre bundles is at the lower limit of the suggested range. For bundle modulus measurement, the sampling interval must be selected appropriately. The new calculation of the sampling interval has been established.展开更多
Fibre bundle tensile curves can be used to characterise fibre processing properties and end-use performance directly and to predict single-fibre properties in theory. In this paper, the tensile behaviour of polyester ...Fibre bundle tensile curves can be used to characterise fibre processing properties and end-use performance directly and to predict single-fibre properties in theory. In this paper, the tensile behaviour of polyester fibre-bundles has been analysed in characteristic values and diagramming. The characteristic distributions which include the symmetry distribution on right part, SRBS′ (e), on left part, SLBS′(e) and the curve on base-line modification, MBS′ (e),based on the modulus distribution, BS′ (e), as well as the frequency density function of broken fibres, B′ (e), have been derived from the tail of bundle tensile curves. The theoretical and measured results show that the most important curves are MBS′ ( e ) and B′ ( e ) and can be used to estimate the breaking-extension distribution of single fibres. Especially for MBS′(e), the modulus distribution can accurately characterize single-fibre tensile properties and is no limitation as the calculation of B′(e) because the bundle specific stress Y(e) of no fibre breaking at extension e should be found at first.展开更多
There exists an Ehresmann connection on the fibred constrained sub-manifold defined by Pfaffian differential constraints. It is proved that curvature of the connection is closely related to the d-delta commutation rel...There exists an Ehresmann connection on the fibred constrained sub-manifold defined by Pfaffian differential constraints. It is proved that curvature of the connection is closely related to the d-delta commutation relation in the classical nonholonomic mechanics. It is also proved that conditions of complete integrability for Pfaffian systems in Frobenius sense are equivalent to the three requirements upon the conditional variations in the classical calculus of variations: (1) the variations belong to the constrained manifold, (2) variational operators commute with differential operators, (3) variations satisfy the Chetaev's conditions. Thus this theory verifies the conjecture or experience of researchers of mechanics on the integrability conditions in terms of variation calculus.展开更多
The definition of nonlinear control sysms on fibre bundles proposed by Brockett and Willems is incomplete from the mathematical view geometric framework is proposed and a minimal realization theory is developed for no...The definition of nonlinear control sysms on fibre bundles proposed by Brockett and Willems is incomplete from the mathematical view geometric framework is proposed and a minimal realization theory is developed for nonlinear control systems on fibre bundles which is elaborated as a natural generalization of Sussmann's theory and differs essentially from Van der Schaft's approach. Limitations of realization theory given by Van der Schaft are also discussed.展开更多
Ⅰ. INTRODUCTION Classifying all the possible smooth involutions on a given smooth dosed n-manifold, up to equivariant cobordism, is an interesting problem in the study of manifolds with involutions. But, very few con...Ⅰ. INTRODUCTION Classifying all the possible smooth involutions on a given smooth dosed n-manifold, up to equivariant cobordism, is an interesting problem in the study of manifolds with involutions. But, very few contributions have been seen in this subject except Ref. [1], just because there were hardly any effective methods to solve this problem. With a kind展开更多
Given a smooth unfree involution (M^n, T), where M^n is a smooth closed n-manifold, weshall associate (M^n, T) with a number sequence I(T), called the involution number sequenceassociated with (M^n, T). We shall prove...Given a smooth unfree involution (M^n, T), where M^n is a smooth closed n-manifold, weshall associate (M^n, T) with a number sequence I(T), called the involution number sequenceassociated with (M^n, T). We shall prove that I(T)is precisely the strictly increasing arrange-ment of all the possible integers n-k in which F^k is nonempty, F^k being the disjointunion of all the k-dimensional components in the fixed point set F of the involution (M^n,T). For application, we shall give a proof for the well-known fact that the fixed point set ofa smooth unfree involution on S^n must be a constant-dimensional smooth closed submanifoldof S^n.展开更多
文摘Due to the effects of samples and testing conditions on fibre-bundle tensile behaviour, it is necessary to investigate the relationships between experimental factors and tensile properties for the fibre-bundle tensile tester (TENSOR). The effects of bundle sample preparation, fibre bundle mass and fibre alignment have been tested. The experimental results indicated that (1) the low damage in combing and no free-end fibres in the cut bundle are most important for the sample preparation; (2) the reasonable bundle mass is 400700 tex, but the tensile properties measured should be modified with the bundle mass because a small amount of bundle mass causes the scatter results, while the larger is the bundle mass, the more difficult to comb fibres parallel and to clamp fibre evenly; and (3) the fibre irregular arrangement forms a slack bundle resulting in interaction between fibres, which will affect the reproducibility and accuracy of the tensile testing.
文摘The testing conditions of a fibre bundle tensile tester (TENSOR) are elongation speed (ES), gauge length (GL), pretension, jaw pressure, environmental temperature and relative humidity, instrument linearity and sensitivity. The effects on fibre-bundle tensile properties at different GL and ES have been discussed in detail and compared with Peirce’s theories on the weaklinks and the breaking time effect. The experimental results indicate that the tensile properties of fibre bundles are strongly affected by GL and vary with different GL. The reasonable GL should be 5 15 mm rather than 3.2 mm for wool bundle measurements. The ES ranging from 20 mm/min to 40 mm/min is beneficial for obtaining comparatively stable and accurate tensile values, whereas 20 mm/min used in current testing for wool fibre bundles is at the lower limit of the suggested range. For bundle modulus measurement, the sampling interval must be selected appropriately. The new calculation of the sampling interval has been established.
文摘Fibre bundle tensile curves can be used to characterise fibre processing properties and end-use performance directly and to predict single-fibre properties in theory. In this paper, the tensile behaviour of polyester fibre-bundles has been analysed in characteristic values and diagramming. The characteristic distributions which include the symmetry distribution on right part, SRBS′ (e), on left part, SLBS′(e) and the curve on base-line modification, MBS′ (e),based on the modulus distribution, BS′ (e), as well as the frequency density function of broken fibres, B′ (e), have been derived from the tail of bundle tensile curves. The theoretical and measured results show that the most important curves are MBS′ ( e ) and B′ ( e ) and can be used to estimate the breaking-extension distribution of single fibres. Especially for MBS′(e), the modulus distribution can accurately characterize single-fibre tensile properties and is no limitation as the calculation of B′(e) because the bundle specific stress Y(e) of no fibre breaking at extension e should be found at first.
文摘There exists an Ehresmann connection on the fibred constrained sub-manifold defined by Pfaffian differential constraints. It is proved that curvature of the connection is closely related to the d-delta commutation relation in the classical nonholonomic mechanics. It is also proved that conditions of complete integrability for Pfaffian systems in Frobenius sense are equivalent to the three requirements upon the conditional variations in the classical calculus of variations: (1) the variations belong to the constrained manifold, (2) variational operators commute with differential operators, (3) variations satisfy the Chetaev's conditions. Thus this theory verifies the conjecture or experience of researchers of mechanics on the integrability conditions in terms of variation calculus.
文摘The definition of nonlinear control sysms on fibre bundles proposed by Brockett and Willems is incomplete from the mathematical view geometric framework is proposed and a minimal realization theory is developed for nonlinear control systems on fibre bundles which is elaborated as a natural generalization of Sussmann's theory and differs essentially from Van der Schaft's approach. Limitations of realization theory given by Van der Schaft are also discussed.
基金Project supported by the National Natural Science Foundation of China.
文摘Ⅰ. INTRODUCTION Classifying all the possible smooth involutions on a given smooth dosed n-manifold, up to equivariant cobordism, is an interesting problem in the study of manifolds with involutions. But, very few contributions have been seen in this subject except Ref. [1], just because there were hardly any effective methods to solve this problem. With a kind
基金Project supported by the National Natural Science Foundation of China.
文摘Given a smooth unfree involution (M^n, T), where M^n is a smooth closed n-manifold, weshall associate (M^n, T) with a number sequence I(T), called the involution number sequenceassociated with (M^n, T). We shall prove that I(T)is precisely the strictly increasing arrange-ment of all the possible integers n-k in which F^k is nonempty, F^k being the disjointunion of all the k-dimensional components in the fixed point set F of the involution (M^n,T). For application, we shall give a proof for the well-known fact that the fixed point set ofa smooth unfree involution on S^n must be a constant-dimensional smooth closed submanifoldof S^n.
