The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential t...The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters,a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study.The transforms of wave functions in cylindrical coordinates can be classifi ed into two basic types: interior transform and exterior transform,and the existing Graf’s addition theorem is only suitable for the former.By performing a new replacement between the two coordinates,the exterior transform formula is fi rst deduced.It is then combined with Graf’s addition theorem to establish a whole-space transform formula.By using the whole-space transform formula,the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application.The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method.The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space.In addition,its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems.展开更多
This paper proposes an analytical model for evaluating the dynamic response of an underground railway tunnel in layered foundation soil with different saturations.The soil is modeled as layered media,and the circular ...This paper proposes an analytical model for evaluating the dynamic response of an underground railway tunnel in layered foundation soil with different saturations.The soil is modeled as layered media,and the circular tunnel lining is modeled as an infinite Flügge cylindrical shell.The separation of variables method is used to solve the motion equation of the shell,and the wave equation of the soil is solved using the Helmholtz decomposition theorem.A dynamic matrix reflecting the wave vectors of soil layers is established using the transfer matrix method.Based on boundary conditions,the tunnel-soil model is coupled using the transformation method of plane wave functions and cylindrical wave functions.The proposed model is validated by comparison with existing tunnel models,and the effects of saturation and the layered properties of soil on the dynamic response of a layered tunnel-soil system is demonstrated via case studies.展开更多
基金the National Natural Science Foundation of China under Grand No.549974011
文摘The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters,a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study.The transforms of wave functions in cylindrical coordinates can be classifi ed into two basic types: interior transform and exterior transform,and the existing Graf’s addition theorem is only suitable for the former.By performing a new replacement between the two coordinates,the exterior transform formula is fi rst deduced.It is then combined with Graf’s addition theorem to establish a whole-space transform formula.By using the whole-space transform formula,the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application.The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method.The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space.In addition,its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems.
基金Supported by:National Natural Science Foundation of China under Grant No.51808405。
文摘This paper proposes an analytical model for evaluating the dynamic response of an underground railway tunnel in layered foundation soil with different saturations.The soil is modeled as layered media,and the circular tunnel lining is modeled as an infinite Flügge cylindrical shell.The separation of variables method is used to solve the motion equation of the shell,and the wave equation of the soil is solved using the Helmholtz decomposition theorem.A dynamic matrix reflecting the wave vectors of soil layers is established using the transfer matrix method.Based on boundary conditions,the tunnel-soil model is coupled using the transformation method of plane wave functions and cylindrical wave functions.The proposed model is validated by comparison with existing tunnel models,and the effects of saturation and the layered properties of soil on the dynamic response of a layered tunnel-soil system is demonstrated via case studies.
