Study On New Methods For Solving Fluid-Solid Coupling Vibration And Their Applications

In this dissertation, new theories and applications on solving fluid-solid coupling vibration are studied, concerning some popular numerical approaches -- finite element method (FEM), boundary element method (BEM) and mixed FE-BE method, semi-analytical and semi-numerical method,and numerical manifold method (NMM) which is new developed. The major achievements obtained are summarized as follows:(1) Ordinary BEM has been improved by modifying or reconstructing the fundamental solution of Laplace equation. A novel approach for solving added mass of structure embedded in semi-infinite liquid field is presented. Using mirror method and superposition method to modify the ordinary Green function, free surfaces of fluid do not need to divide into the boundary elements and then computation time is saved. A mixed FE-BE method is also used to analyze coupling vibration of three dimensional structure in a liquid with constant depth. Tetrahedral meshes of the structure are formed by automatic subdivision, and the corresponding coupling equations are derived. Based on the Green function corresponding to a wave in a liquid with constant depth issuing from any source, only surfaces of the structure need to divide into the boundary elements, and the number of freedoms decreases greatly. Besides, interface of general FEM software is also adopted to improve the efficiency of programming and computation.(2) A localized variational principle is presented for analyzing fluid-structure interaction problems in two-dimensional infinite liquid field. The infinite liquid field is divided into two parts by an auxiliary circle, inside which the structure and its neighboring liquid are computed by FEM and outside which an analytical solution is used. By means of this variational principle, all governing equations and boundary conditions are satisfied automatically, and the numerical solutions are incorporated with the analytical solution via hybrid element equations derived. Given examples for incompressible liquid case demonstrate validity and high efficiency of the approach.(3) Based on the general governing equations of revolution thin shells, the 1-order ordinary differential matrix about state parameter vector of revolution shells is firstly derived in this dissertation. This matrix is the important basis for solving interaction problems about revolution shells using the transfer matrix method. By means of the extended homogeneous capacity high precision integration method, static and dynamic solutions are given conveniently, and harmonic responses of revolution shells in a liquid with constant depth are computed. This approach extends the applications of the transfer matrix method, and lays the foundation of semi-analytical and semi-numerical researches on structural vibration and acoustics for revolution shells.(4) High-order NMM and its applications in fluid-solid interaction harmonic analysis are also studied. A simple method is presented for automatically producing the expressions and writing subroutine codes based on simplex integration. Two and three dimensional programs of high-order NMM are further developed respectively for static analysis. Some examples are given to analyze the precision and the adaptability of NMM. This dissertation also presents two dimensional high-order NMM equations of fluid-solid interaction harmonic analysis based on rectangular mathematical meshes. The given results of computing frequencies and harmonic response prove the validity of the approach, and indicate that high-order NMM has high precision and convenient preprocessing. The approach of using covers of analytical solution to simulate special infinite fluid field is also proposed, and the given example suggests that NMM should be very suitable for combination of numerical solutions and analytical solutions, and more convenient than other approaches.(5) NMM with fixed mathematical meshes is proposed in this dissertation, which has more advantages than other methods in solving fluid-solid coupling problems considering large deformation of structure and large disturbance of fluid, because it may be convenient to solve the nonlinear coupling problems when treating both fluid field and solid structure in the same background meshes. As the fundamental research, an attempt is made to compute large displacements of structures using fixed rectangular mathematical meshes and 1-order polynomial cover functions, and it is implemented that material particle moves in fixed meshes. The results of large deflection of a cantilever beam show the feasibility of NMM with fixed meshes, and indicate that more research should be further done on the approach of precisely computing initial stresses in the structures.