Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was...Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Results and Conclusion The known results of oscillation of solutions for a class of boundary value problem of hyperbolic partial functional differential equations with discrete deviating arguments are generalized, and the oscillatory criteria of solutions for such equation with two kinds of boundary value conditions are obtained.展开更多
In this paper, a boundary element formulation in the wave-number space domain for solving the wave equation for a borehole with arbitrary shape in acoustic logging problems is presented. The problem is treated as a tw...In this paper, a boundary element formulation in the wave-number space domain for solving the wave equation for a borehole with arbitrary shape in acoustic logging problems is presented. The problem is treated as a two-dimensional medium with the discrete wave- number method in the vertical direction. The method is validated by comparing the results obtained by this method with those obtained by the finite-difference method. The method is used to study the effect on wave propagation in a vertical borehole of a vertical fracture. For a monopole source, the dispersion curves for Stoneley waves yield three branches. For dipole and quadrupole sources, different orientations of the source yield different results. When the dipole source is orthogonal to the fracture, the dispersion curve is similar to that of the open hole, while the curves are quite different when the source is parallel to the fracture. These characteristics enable us to determine the orientation of the vertical fracture.展开更多
This paper discusses the application of the boundary contour method fo r resolving plate bending problems. The exploitation of the integrand divergence free property of the plate bending boundary integral equation bas...This paper discusses the application of the boundary contour method fo r resolving plate bending problems. The exploitation of the integrand divergence free property of the plate bending boundary integral equation based on the Kirc hhoff hypothesis and a very useful application of Stokes' Theorem are presented to convert surface integrals on boundary elements to the computation of bending potential functions on the discretized boundary points,even for curved surface elements of arbitrary shape. Singularity and treatment of the discontinued corne r point are not needed at all. The evaluation of the physics variant at internal points is also shown in this article. Numerical results are presented for some plate bending problems and compared against analytical and previous solutions.展开更多
文摘Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Results and Conclusion The known results of oscillation of solutions for a class of boundary value problem of hyperbolic partial functional differential equations with discrete deviating arguments are generalized, and the oscillatory criteria of solutions for such equation with two kinds of boundary value conditions are obtained.
基金Acknowledgements We thank the thoughtful comments from two anonymous reviewers. This work is partly supported by a contract with Schlumberger-Doll Research, Schlumberger and partly by the National Science Foundation of China under D40521002.
文摘In this paper, a boundary element formulation in the wave-number space domain for solving the wave equation for a borehole with arbitrary shape in acoustic logging problems is presented. The problem is treated as a two-dimensional medium with the discrete wave- number method in the vertical direction. The method is validated by comparing the results obtained by this method with those obtained by the finite-difference method. The method is used to study the effect on wave propagation in a vertical borehole of a vertical fracture. For a monopole source, the dispersion curves for Stoneley waves yield three branches. For dipole and quadrupole sources, different orientations of the source yield different results. When the dipole source is orthogonal to the fracture, the dispersion curve is similar to that of the open hole, while the curves are quite different when the source is parallel to the fracture. These characteristics enable us to determine the orientation of the vertical fracture.
文摘This paper discusses the application of the boundary contour method fo r resolving plate bending problems. The exploitation of the integrand divergence free property of the plate bending boundary integral equation based on the Kirc hhoff hypothesis and a very useful application of Stokes' Theorem are presented to convert surface integrals on boundary elements to the computation of bending potential functions on the discretized boundary points,even for curved surface elements of arbitrary shape. Singularity and treatment of the discontinued corne r point are not needed at all. The evaluation of the physics variant at internal points is also shown in this article. Numerical results are presented for some plate bending problems and compared against analytical and previous solutions.
