An investigation into natural vibrations of fluid–structure interaction systems subject to Sommerfeld radiation condition

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 problemswithmore 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. Themathematical 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.