THE NATURAL VIBRATION OF FLUID-STRUCTURE INTERACTION SYSTEMS SUBJECT TO THE SOMMERFELD RADIATION CONDITION

摘要

A fluid-structure interaction system subject to a Sommerfeld condition is defined as a Sommerfeld system in this paper. It is well known that the natural vibration of a dynamic system is defined by the eigenvalue problem of the corresponding idealized system with no material damping assumed and external forces. From the defined eigenvalue problem, the real natural frequencies and the corresponding natural modes of the system can be derived. What are the characteristics of natural vibrations of a Sommerfeld system? This paper intends to address this problem by investigating three selected fluid-structure interaction systems. The systems chosen involve the solid structures with one, two and infinite degrees of freedom coupling to an infinite fluid domain subject to a Sommerfeld condition, respectively. The governing equations describing these coupled systems are presented using the theory of continuum mechanics. The theoretical solution for each problem is derived and discussed. The analysis demonstrates that a Sommerfeld system undergoing a natural vibration behaves energy dissipative characteristics although there is no material damping in solid and fluid of the system. The natural vibrations of a Sommerfeld system are governed by a complex eigenvalue problem which has only pairs of complex conjugate natural frequencies. The number of the complex conjugate natural frequencies and corresponding natural modes of this Sommerfeld system equals to the number of the degrees of freedom of the dry solid structure in the system and it is independent of the infinite fluid domain. The natural vibration forms of the solid structure in natural vibrations do not satisfy the orthogonal relationship. The findings in this research reveal some common dynamic characteristics of Sommerfeld systems. An approach for the dynamic response analysis of a Sommerfeld system is proposed based on the orthogonal natural modes of the dry structure in the system which is more efficient for engineering analysis.