A fluid-structure interaction system subject to Sommerfeld＇s condition is defined as a Sommerfeld system which is divided into three categories： Fluid Sommerfeld （FS） System, Solid Sommerfeld （SS） System and Flu...A fluid-structure interaction system subject to Sommerfeld＇s condition is defined as a Sommerfeld system which is divided into three categories： Fluid Sommerfeld （FS） System, Solid Sommerfeld （SS） System and Fluid Solid Sommerfeld （FSS） System of which Sommerfeld conditions are imposed on a fluid boundary only, a solid boundary only and both fluid and solid boundaries, respectively. This paper follows the previous initial results claimed by simple examples to further mathematically investigate the natural vibrations of generalized Sommerfeld systems. A new parameter representing the speed of radiation wave for generalized 3-D problems with more complicated boundary conditions is introduced into the Sommerfeld condition which allows investigation of the natural vibrations of a Sommerfeld system involving both free surface and compressible waves. The mathematical demonstrations and selected examples confirm and reveal the natural behaviour of generalized Sommerfeld systems defined above. These generalized conclusions can be used in theoretical or engineering analysis of the vibrations of various Sommerfeld systems in engineering.展开更多
A trigonometric series expansion method and two similar modified methods for the Orr-Sommerfeld equation are presented. These methods use the trigonometric series expansion with an auxiliary function added to the high...A trigonometric series expansion method and two similar modified methods for the Orr-Sommerfeld equation are presented. These methods use the trigonometric series expansion with an auxiliary function added to the highest order derivative of the unknown function and generate the lower order derivatives through successive integra- tions. The proposed methods are easy to implement because of the simplicity of the chosen basis functions. By solving the plane Poiseuille flow (PPF), plane Couette flow (PCF), and Blasius boundary layer flow with several homogeneous boundary conditions, it is shown that these methods yield results with the same accuracy as that given by the conventional Chebyshev collocation method but with better robustness, and that ob- tained by the finite difference method but with fewer modal number.展开更多
文摘A fluid-structure interaction system subject to Sommerfeld＇s condition is defined as a Sommerfeld system which is divided into three categories： Fluid Sommerfeld （FS） System, Solid Sommerfeld （SS） System and Fluid Solid Sommerfeld （FSS） System of which Sommerfeld conditions are imposed on a fluid boundary only, a solid boundary only and both fluid and solid boundaries, respectively. This paper follows the previous initial results claimed by simple examples to further mathematically investigate the natural vibrations of generalized Sommerfeld systems. A new parameter representing the speed of radiation wave for generalized 3-D problems with more complicated boundary conditions is introduced into the Sommerfeld condition which allows investigation of the natural vibrations of a Sommerfeld system involving both free surface and compressible waves. The mathematical demonstrations and selected examples confirm and reveal the natural behaviour of generalized Sommerfeld systems defined above. These generalized conclusions can be used in theoretical or engineering analysis of the vibrations of various Sommerfeld systems in engineering.
基金supported by the National Natural Science Foundation of China(Nos.11221062,11521091,and 91752203)
文摘A trigonometric series expansion method and two similar modified methods for the Orr-Sommerfeld equation are presented. These methods use the trigonometric series expansion with an auxiliary function added to the highest order derivative of the unknown function and generate the lower order derivatives through successive integra- tions. The proposed methods are easy to implement because of the simplicity of the chosen basis functions. By solving the plane Poiseuille flow (PPF), plane Couette flow (PCF), and Blasius boundary layer flow with several homogeneous boundary conditions, it is shown that these methods yield results with the same accuracy as that given by the conventional Chebyshev collocation method but with better robustness, and that ob- tained by the finite difference method but with fewer modal number.
