The solutions of Green’s function are significant for simplification of problem on a two-phase saturated medium.Using transformation of axisymmetric cylindrical coordinate and Sommerfeld’s integral,superposition of ...The solutions of Green’s function are significant for simplification of problem on a two-phase saturated medium.Using transformation of axisymmetric cylindrical coordinate and Sommerfeld’s integral,superposition of the influence field on a free surface,authors obtained the solutions of a two-phase saturated medium subjected to a concentrated force on the semi-space.展开更多
By the analysis for the vectors of a wave field in the cylindrical coordinate and Sommerfeld＇s identity as well as Green＇s functions of Stokes＇ solution pertaining the conventional elastic dynamic equation, the res...By the analysis for the vectors of a wave field in the cylindrical coordinate and Sommerfeld＇s identity as well as Green＇s functions of Stokes＇ solution pertaining the conventional elastic dynamic equation, the results of Green＇s function in an infinite space of an axisymmetric coordinate are shown in this paper. After employing a supplementary influence field and the boundary conditions in the free surface of a senti-space, the authors obtain the solutions of Green＇s function for Lamb＇s dynamic problem. Besides, the vertical displacement uzz and the radial displacement urz can match Lamb＇s previous results, and the solutions of the linear expansion source u^r and the linear torsional source uee are also given in the paper. The authors reveal that Green＇s function of Stokes＇ solution in the semi-space is a comprehensive form of solution expressing the dynamic Lamb＇s problem for various situations. It may benefit the investigation of deepening and development of Lamb＇s problems and solution for pertinent dynamic problems conveniently.展开更多
By applying the integral transform method and the inverse transformation technique based upon the two types of integration, the present paper has successfully obtained an exact algebraic solution for a two-dimensional...By applying the integral transform method and the inverse transformation technique based upon the two types of integration, the present paper has successfully obtained an exact algebraic solution for a two-dimensional Lamb＇s problem due to a strip impulse loading for the first time. With the algebraic result, the excitation and propagation processes of stress waves, including the longitudinal wave, the transverse wave, and Rayleigh-wave, are discussed in detail. A few new conclusions have been drawn from currently available integral results or computational results.展开更多
Based on Biots theory on fluid-saturated porous media, the displacement functions are adopted to convert the 3-D Biots wave equations in the cylindrical coordinate for transversely isotropic saturated poroelastic medi...Based on Biots theory on fluid-saturated porous media, the displacement functions are adopted to convert the 3-D Biots wave equations in the cylindrical coordinate for transversely isotropic saturated poroelastic media into two棗one 6-order and one 2-order棗uncoupling differential governing equations. Then, the differential equations are solved by the Fourier expanding and Hankel integral transform method. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media are obtained. Furthermore, the systematic study on Lambs problems for the transversely isotropic saturated poroelastic media is performed. Integral solutions for surface radial, vertical and circumferential displacements are obtained in both cases of drained surface and undrained surface under the vertical and horizontal harmonic excitation force. In the end of this paper, the numerical examples are presented. The calculation results indicate that the difference between the model of isotropic saturated poroelastic media and that of transversely isotropic saturated poroelastic media is obvious.展开更多
基金supported by the National Natural Science Foundation of China (10572129)
文摘The solutions of Green’s function are significant for simplification of problem on a two-phase saturated medium.Using transformation of axisymmetric cylindrical coordinate and Sommerfeld’s integral,superposition of the influence field on a free surface,authors obtained the solutions of a two-phase saturated medium subjected to a concentrated force on the semi-space.
基金supported by the National Natural Science Foundation of China(No.11172268)
文摘By the analysis for the vectors of a wave field in the cylindrical coordinate and Sommerfeld＇s identity as well as Green＇s functions of Stokes＇ solution pertaining the conventional elastic dynamic equation, the results of Green＇s function in an infinite space of an axisymmetric coordinate are shown in this paper. After employing a supplementary influence field and the boundary conditions in the free surface of a senti-space, the authors obtain the solutions of Green＇s function for Lamb＇s dynamic problem. Besides, the vertical displacement uzz and the radial displacement urz can match Lamb＇s previous results, and the solutions of the linear expansion source u^r and the linear torsional source uee are also given in the paper. The authors reveal that Green＇s function of Stokes＇ solution in the semi-space is a comprehensive form of solution expressing the dynamic Lamb＇s problem for various situations. It may benefit the investigation of deepening and development of Lamb＇s problems and solution for pertinent dynamic problems conveniently.
基金Project supported by the National Natural Science Foundation of China(No.10572002).
文摘By applying the integral transform method and the inverse transformation technique based upon the two types of integration, the present paper has successfully obtained an exact algebraic solution for a two-dimensional Lamb＇s problem due to a strip impulse loading for the first time. With the algebraic result, the excitation and propagation processes of stress waves, including the longitudinal wave, the transverse wave, and Rayleigh-wave, are discussed in detail. A few new conclusions have been drawn from currently available integral results or computational results.
基金the National Natural Science Foundation of China (Grant No.56978003).
文摘Based on Biots theory on fluid-saturated porous media, the displacement functions are adopted to convert the 3-D Biots wave equations in the cylindrical coordinate for transversely isotropic saturated poroelastic media into two棗one 6-order and one 2-order棗uncoupling differential governing equations. Then, the differential equations are solved by the Fourier expanding and Hankel integral transform method. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media are obtained. Furthermore, the systematic study on Lambs problems for the transversely isotropic saturated poroelastic media is performed. Integral solutions for surface radial, vertical and circumferential displacements are obtained in both cases of drained surface and undrained surface under the vertical and horizontal harmonic excitation force. In the end of this paper, the numerical examples are presented. The calculation results indicate that the difference between the model of isotropic saturated poroelastic media and that of transversely isotropic saturated poroelastic media is obvious.
