A study of the dynamic interaction between foundation and the underlying soil has been presented in a recent paper based on the assumption of saturated ground and elastic circular plate excited by the axisymmetrical h...A study of the dynamic interaction between foundation and the underlying soil has been presented in a recent paper based on the assumption of saturated ground and elastic circular plate excited by the axisymmetrical harmonic source. However, the assumption may not always be valid. The work is extended to the case of a circular plate resting on transversely isotropic saturated soil and subjected to a non-axisymmetrical harmonic force. The analysis is based on the theory of elastic wave in transversely isotropic saturated poroelastic media established. By the technique of Fourier expansion and Hankel transform, the governing difference equations for transversely isotropic saturated soil are easily solved and the cooresponding Hankel transformed stress and displacement solutions are obtained. Then, under the contact conditions, the problem leads to a pair of dual integral equations which describe the mixed boundary-value problem. Furthermore, the dual integral equations can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure. At the end, a numerical result is presented which indicates that on a certain frequency range, the displacement amplitude of the surface of the foundation increases with the increase of the frequency of the exciting force, and decreases in vibration form with the increase of the distance.展开更多
文摘A study of the dynamic interaction between foundation and the underlying soil has been presented in a recent paper based on the assumption of saturated ground and elastic circular plate excited by the axisymmetrical harmonic source. However, the assumption may not always be valid. The work is extended to the case of a circular plate resting on transversely isotropic saturated soil and subjected to a non-axisymmetrical harmonic force. The analysis is based on the theory of elastic wave in transversely isotropic saturated poroelastic media established. By the technique of Fourier expansion and Hankel transform, the governing difference equations for transversely isotropic saturated soil are easily solved and the cooresponding Hankel transformed stress and displacement solutions are obtained. Then, under the contact conditions, the problem leads to a pair of dual integral equations which describe the mixed boundary-value problem. Furthermore, the dual integral equations can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure. At the end, a numerical result is presented which indicates that on a certain frequency range, the displacement amplitude of the surface of the foundation increases with the increase of the frequency of the exciting force, and decreases in vibration form with the increase of the distance.
