The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for t...The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.展开更多
Intact rock is typically described according to its uniaxial compressive strength （UCS）. The UCS is needed in the design of geotechnical engineering problems including stability of rock slopes and design of shallow ...Intact rock is typically described according to its uniaxial compressive strength （UCS）. The UCS is needed in the design of geotechnical engineering problems including stability of rock slopes and design of shallow and deep foundations resting on and/or in rocks. Accordingly, a correct measure-ment/evaluation of the UCS is essential to a safe and economic design. Typically, the UCS is measured using the unconfined compression tests performed on cylindrical intact specimens with a minimum length to width ratio of 2. In several cases, especially for weak and very weak rocks, it is not possible to extract intact specimens with the needed minimum dimensions. Thus, alternative tests （e.g. point load test, Schmidt hammer） are used to measure rock strength. The UCS is computed based on the results of these tests through empirical correlations. The literature includes a plethora of these correlations that vary widely in estimating rock strength. Thus, it is paramount to validate these correlations to check their suitability for estimating rock strength for a specific location and geology. A review of the available correlations used to estimate the UCS from the point load test results is performed and summarized herein. Results of UCS, point load strength index and Young＇s modulus are gathered for calcareous sandstone specimens extracted from the Dubai area. A correlation for estimating the UCS from the point load strength index is proposed. Furthermore, the Young＇s modulus is correlated to the UCS.展开更多
This paper studies transverse vibration of rectangular plates with two opposite edges simply supperted other two edges arbitrarily supported and free edges elaslically supported at points,A highly accurate solution is...This paper studies transverse vibration of rectangular plates with two opposite edges simply supperted other two edges arbitrarily supported and free edges elaslically supported at points,A highly accurate solution is presented for calculating inherent frequencies and mode shape of rectangular platen elaslically supported at points. The number and location of these points on free edges may be completely arbitrary. This paper uses impulse function to represent reaction and moment at points. Fourter series is used to expand the impulse function along the edges. Characteristic equations satisfying all boundary conditions are given.Inherent frequencies and mode shape with any accutacy can be gained.展开更多
This paper presents a new method for solving the vibration of arbitrarily shaped membranes with ela.stical supports at points. The reaction forces of elastical supports at points are regarded as unknown external force...This paper presents a new method for solving the vibration of arbitrarily shaped membranes with ela.stical supports at points. The reaction forces of elastical supports at points are regarded as unknown external forces acting on the membranes. The exact solution of the equation of motion is given which includes terms representing the unknown reaction forces. The frequency equation is derived by the use of the linear relationship of the displacements with the reaction forces of elastical supports at points. Finally the calculating formulae of the frequency equation of circular membranes are analytically performed as examples and the inherent frequencies of circular membranes with symmetric elastical supports at two points are numerically calculated.展开更多
The classical elastic impedance （EI） inversion method, however, is based on the L2-norm misfit function and considerably sensitive to outliers, assuming the noise of the seismic data to be the Guassian-distribution....The classical elastic impedance （EI） inversion method, however, is based on the L2-norm misfit function and considerably sensitive to outliers, assuming the noise of the seismic data to be the Guassian-distribution. So we have developed a more robust elastic impedance inversion based on the Ll-norm misfit function, and the noise is assumed to be non-Gaussian. Meanwhile, some regularization methods including the sparse constraint regularization and elastic impedance point constraint regularization are incorporated to improve the ill-posed characteristics of the seismic inversion problem. Firstly, we create the Ll-norm misfit objective function of pre-stack inversion problem based on the Bayesian scheme within the sparse constraint regularization and elastic impedance point constraint regularization. And then, we obtain more robust elastic impedances of different angles which are less sensitive to outliers in seismic data by using the IRLS strategy. Finally, we extract the P-wave and S-wave velocity and density by using the more stable parameter extraction method. Tests on synthetic data show that the P-wave and S-wave velocity and density parameters are still estimated reasonable with moderate noise. A test on the real data set shows that compared to the results of the classical elastic impedance inversion method, the estimated results using the proposed method can get better lateral continuity and more distinct show of the gas, verifying the feasibility and stability of the method.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.10872163)the Natural Science Foundation of Education Department of Shaanxi Province (Grant No.08JK394)
文摘The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.
文摘Intact rock is typically described according to its uniaxial compressive strength （UCS）. The UCS is needed in the design of geotechnical engineering problems including stability of rock slopes and design of shallow and deep foundations resting on and/or in rocks. Accordingly, a correct measure-ment/evaluation of the UCS is essential to a safe and economic design. Typically, the UCS is measured using the unconfined compression tests performed on cylindrical intact specimens with a minimum length to width ratio of 2. In several cases, especially for weak and very weak rocks, it is not possible to extract intact specimens with the needed minimum dimensions. Thus, alternative tests （e.g. point load test, Schmidt hammer） are used to measure rock strength. The UCS is computed based on the results of these tests through empirical correlations. The literature includes a plethora of these correlations that vary widely in estimating rock strength. Thus, it is paramount to validate these correlations to check their suitability for estimating rock strength for a specific location and geology. A review of the available correlations used to estimate the UCS from the point load test results is performed and summarized herein. Results of UCS, point load strength index and Young＇s modulus are gathered for calcareous sandstone specimens extracted from the Dubai area. A correlation for estimating the UCS from the point load strength index is proposed. Furthermore, the Young＇s modulus is correlated to the UCS.
文摘This paper studies transverse vibration of rectangular plates with two opposite edges simply supperted other two edges arbitrarily supported and free edges elaslically supported at points,A highly accurate solution is presented for calculating inherent frequencies and mode shape of rectangular platen elaslically supported at points. The number and location of these points on free edges may be completely arbitrary. This paper uses impulse function to represent reaction and moment at points. Fourter series is used to expand the impulse function along the edges. Characteristic equations satisfying all boundary conditions are given.Inherent frequencies and mode shape with any accutacy can be gained.
文摘This paper presents a new method for solving the vibration of arbitrarily shaped membranes with ela.stical supports at points. The reaction forces of elastical supports at points are regarded as unknown external forces acting on the membranes. The exact solution of the equation of motion is given which includes terms representing the unknown reaction forces. The frequency equation is derived by the use of the linear relationship of the displacements with the reaction forces of elastical supports at points. Finally the calculating formulae of the frequency equation of circular membranes are analytically performed as examples and the inherent frequencies of circular membranes with symmetric elastical supports at two points are numerically calculated.
基金Projects(U1562215,41674130,41404088)supported by the National Natural Science Foundation of ChinaProjects(2013CB228604,2014CB239201)supported by the National Basic Research Program of China+1 种基金Projects(2016ZX05027004-001,2016ZX05002006-009)supported by the National Oil and Gas Major Projects of ChinaProject(15CX08002A)supported by the Fundamental Research Funds for the Central Universities,China
文摘The classical elastic impedance （EI） inversion method, however, is based on the L2-norm misfit function and considerably sensitive to outliers, assuming the noise of the seismic data to be the Guassian-distribution. So we have developed a more robust elastic impedance inversion based on the Ll-norm misfit function, and the noise is assumed to be non-Gaussian. Meanwhile, some regularization methods including the sparse constraint regularization and elastic impedance point constraint regularization are incorporated to improve the ill-posed characteristics of the seismic inversion problem. Firstly, we create the Ll-norm misfit objective function of pre-stack inversion problem based on the Bayesian scheme within the sparse constraint regularization and elastic impedance point constraint regularization. And then, we obtain more robust elastic impedances of different angles which are less sensitive to outliers in seismic data by using the IRLS strategy. Finally, we extract the P-wave and S-wave velocity and density by using the more stable parameter extraction method. Tests on synthetic data show that the P-wave and S-wave velocity and density parameters are still estimated reasonable with moderate noise. A test on the real data set shows that compared to the results of the classical elastic impedance inversion method, the estimated results using the proposed method can get better lateral continuity and more distinct show of the gas, verifying the feasibility and stability of the method.
