An eigen-function expansion method based on a new orthogonal inner product is proposed by Sahoo et al. (2000) for the study of the hydroelastic response of mat-type VLFS in head seas. However, their main emphasis is o...An eigen-function expansion method based on a new orthogonal inner product is proposed by Sahoo et al. (2000) for the study of the hydroelastic response of mat-type VLFS in head seas. However, their main emphasis is on the effect of edge conditions and they assume that the plate is of a semi-infinite length. In reality, the plate is of finite length. For consideration of the finite length effect, the reflection and transmission from the other end must be considered. The effect of this reflection and transmission on the hydroelastic response of VLFS is of interest for practical application. Furthermore, the physical meaning of the new inner product was not given in their paper. In this paper, it is shown that the new inner product can he derived from the governing equation and the bottom boundary conditions. Then the same eigen-function expansion method is adopted for the study of the hydroelastic response of an elastic plate of finite length in surface waves. Detailed comparisons are made between the present finite length model and the semi-infinite model and between the present model predictions and the experimental results. It is found that that the finite length effect is significant and the accuracy of present model is higher than the semi-infinite model. Furthermore, a new phenomenon, which is not mentioned in Sahoo et al. (2000), is found. Taht is, for larger L/h ratios, the reflection and transmission coefficients will oscillate with the non-dimensional parameter k(0) h. Further study is needed for full understanding of this phenomenon.展开更多
The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an...The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamic stress intensity factor at the crack tip was given. A Green's function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.展开更多
In this paper, mathematical modeling of the propagation of torsional surface waves in a transverse isotropic elastic medium with varying rigidity and density under a rigid layer has been considered. The equation of mo...In this paper, mathematical modeling of the propagation of torsional surface waves in a transverse isotropic elastic medium with varying rigidity and density under a rigid layer has been considered. The equation of motion has been formulated in the elastic medium using suitable boundary conditions. The frequency equation containing Whittaker’s function for phase velocity due to torsional surface waves has been derived. The effect of rigid layer in the propagation of torsional surface waves in a transverse isotropic elastic medium with varying rigidity and density has been discussed. The numerical results have been shown graphically. It is observed that the influence of transverse and longitudinal rigidity and density of the medium have a remarkable effect on the propagation of the torsional surface waves. Frequency equations have also been derived for some particular cases, which are in perfect agreement with some standard results.展开更多
基金The project was supported by the national Natural Science Foundation of China(Grant No.50039010)the Science and Technology Development Foundation of Shanghai Municipal Government(00XD14015)
文摘An eigen-function expansion method based on a new orthogonal inner product is proposed by Sahoo et al. (2000) for the study of the hydroelastic response of mat-type VLFS in head seas. However, their main emphasis is on the effect of edge conditions and they assume that the plate is of a semi-infinite length. In reality, the plate is of finite length. For consideration of the finite length effect, the reflection and transmission from the other end must be considered. The effect of this reflection and transmission on the hydroelastic response of VLFS is of interest for practical application. Furthermore, the physical meaning of the new inner product was not given in their paper. In this paper, it is shown that the new inner product can he derived from the governing equation and the bottom boundary conditions. Then the same eigen-function expansion method is adopted for the study of the hydroelastic response of an elastic plate of finite length in surface waves. Detailed comparisons are made between the present finite length model and the semi-infinite model and between the present model predictions and the experimental results. It is found that that the finite length effect is significant and the accuracy of present model is higher than the semi-infinite model. Furthermore, a new phenomenon, which is not mentioned in Sahoo et al. (2000), is found. Taht is, for larger L/h ratios, the reflection and transmission coefficients will oscillate with the non-dimensional parameter k(0) h. Further study is needed for full understanding of this phenomenon.
文摘The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamic stress intensity factor at the crack tip was given. A Green's function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.
文摘In this paper, mathematical modeling of the propagation of torsional surface waves in a transverse isotropic elastic medium with varying rigidity and density under a rigid layer has been considered. The equation of motion has been formulated in the elastic medium using suitable boundary conditions. The frequency equation containing Whittaker’s function for phase velocity due to torsional surface waves has been derived. The effect of rigid layer in the propagation of torsional surface waves in a transverse isotropic elastic medium with varying rigidity and density has been discussed. The numerical results have been shown graphically. It is observed that the influence of transverse and longitudinal rigidity and density of the medium have a remarkable effect on the propagation of the torsional surface waves. Frequency equations have also been derived for some particular cases, which are in perfect agreement with some standard results.
