This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. The...This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. Then, two theorems are given for constructing biorthogonal （orthogonal） two-direction refinable functions in L^2（R^s） and their biorthogonal （orthogonal） two-direction wavelets, respectively. From the constructed biorthogonal （orthogonal） two-direction wavelets, symmetric biorthogonal （orthogonal） multiwaveles in L^2（R^s） can be obtained easily. Applying the projection method to biorthogonal （orthogonal） two-direction wavelets in L^2（R^s）, we can get dual （tight） two-direction wavelet frames in L^2（R^m）, where m ≤ s. From the projected dual （tight） two-direction wavelet frames in L^2（R^m）, symmetric dual （tight） frames in L^2（R^m） can be obtained easily. In the end, an example is given to illustrate theoretical results.展开更多
Based on the discussion about working mechanism of horizontal reinforcement and that of vertical reinforcement,respectively,the working mechanism of two-direction reinforced composite foundation was studied.The enhanc...Based on the discussion about working mechanism of horizontal reinforcement and that of vertical reinforcement,respectively,the working mechanism of two-direction reinforced composite foundation was studied.The enhancing effect of horizontal reinforcement on vertical reinforced composite foundation was analyzed.A simplified calculation method for such two-direction reinforced working system was presented.A model experiment was carried out to validate the proposed method.In the experiment,geocell reinforcement worked as the horizontal reinforcement,while gravel pile composite foundation worked as the vertical reinforcement.The results show that the calculated curve is close to the measured one.The installation of geosynthetic reinforcement can increase the bearing capacity of composite foundation by nearly 68% at normal foundation settlement,which suggests that the enhancing effect by geosynthetic reinforcement should be taken into account in current design/analysis methods.展开更多
Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using ...Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical nu- merical method is with great advantage in the computational efficiency. Moreover, study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.展开更多
Based on Evans’spatial smoothing preprocessing scheme,a new approach calledtwo-direction spatial smoothing preprocessing method is presented.It is proved that the decorre-lation,the effective aperture and the maximum...Based on Evans’spatial smoothing preprocessing scheme,a new approach calledtwo-direction spatial smoothing preprocessing method is presented.It is proved that the decorre-lation,the effective aperture and the maximum number of distinguishable coherent signals(whenarray size is given)of the new method are better than those of the Evans’method.Simulationresults give a comparison between the eigenvector spectrums produced by the two methods.展开更多
Many experiment researches have been developed before. But most of them were carried out with the condition that the tunnel’s ratio of length and diameter (x/D) is under 1000. Recently, the process that compression w...Many experiment researches have been developed before. But most of them were carried out with the condition that the tunnel’s ratio of length and diameter (x/D) is under 1000. Recently, the process that compression wave convents into shock wave in the overlong tunnel has also been paid attention. In this paper, features of shock wave as it propagates through a overlong tunnel is investigated, rupturing thin films at the entrance to obtain three kinds of shock wave with different intensities. Then study their features respectively during they propagates through a overlong tunnel with x/D over 6000 at most. Comprehend shock wave more deeply by comparing the results of experiments.展开更多
基金supported by the Natural Science Foundation China(11126343)Guangxi Natural Science Foundation(2013GXNSFBA019010)+1 种基金supported by Natural Science Foundation China(11071152)Natural Science Foundation of Guangdong Province(10151503101000025,S2011010004511)
文摘This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. Then, two theorems are given for constructing biorthogonal （orthogonal） two-direction refinable functions in L^2（R^s） and their biorthogonal （orthogonal） two-direction wavelets, respectively. From the constructed biorthogonal （orthogonal） two-direction wavelets, symmetric biorthogonal （orthogonal） multiwaveles in L^2（R^s） can be obtained easily. Applying the projection method to biorthogonal （orthogonal） two-direction wavelets in L^2（R^s）, we can get dual （tight） two-direction wavelet frames in L^2（R^m）, where m ≤ s. From the projected dual （tight） two-direction wavelet frames in L^2（R^m）, symmetric dual （tight） frames in L^2（R^m） can be obtained easily. In the end, an example is given to illustrate theoretical results.
基金Project (2006AA11Z104) supported by the National High-Tech Research and Development Program("863" Program)
文摘Based on the discussion about working mechanism of horizontal reinforcement and that of vertical reinforcement,respectively,the working mechanism of two-direction reinforced composite foundation was studied.The enhancing effect of horizontal reinforcement on vertical reinforced composite foundation was analyzed.A simplified calculation method for such two-direction reinforced working system was presented.A model experiment was carried out to validate the proposed method.In the experiment,geocell reinforcement worked as the horizontal reinforcement,while gravel pile composite foundation worked as the vertical reinforcement.The results show that the calculated curve is close to the measured one.The installation of geosynthetic reinforcement can increase the bearing capacity of composite foundation by nearly 68% at normal foundation settlement,which suggests that the enhancing effect by geosynthetic reinforcement should be taken into account in current design/analysis methods.
基金Project supported by the National Natural Science Foundation of China (No.10432030).
文摘Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical nu- merical method is with great advantage in the computational efficiency. Moreover, study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.
文摘Based on Evans’spatial smoothing preprocessing scheme,a new approach calledtwo-direction spatial smoothing preprocessing method is presented.It is proved that the decorre-lation,the effective aperture and the maximum number of distinguishable coherent signals(whenarray size is given)of the new method are better than those of the Evans’method.Simulationresults give a comparison between the eigenvector spectrums produced by the two methods.
文摘Many experiment researches have been developed before. But most of them were carried out with the condition that the tunnel’s ratio of length and diameter (x/D) is under 1000. Recently, the process that compression wave convents into shock wave in the overlong tunnel has also been paid attention. In this paper, features of shock wave as it propagates through a overlong tunnel is investigated, rupturing thin films at the entrance to obtain three kinds of shock wave with different intensities. Then study their features respectively during they propagates through a overlong tunnel with x/D over 6000 at most. Comprehend shock wave more deeply by comparing the results of experiments.
