Study On Dynamic Re-analysis Of Complex Structures

This thesis focuses on structural dynamic modification, which is a very active research branch globally. The author studied the current research status in dynamic structural dynamic reanalysis, and made major breakthroughs in improvement of accuracy, computational speed and convergence scope.With the increasingly stringent performance and quality requirements of engineering structures, many complex factors become inavoidable at the design phase. When those factors come into the picture, sticking to normal methods would cost enormous, sometimes inafforadable amount of time and resource. This thesis proposes effective methods to cater for some key complex factors in modern engineering applications. The author has applied traditional dynamic substructure technology to structural dynamic modification to address the phenomenal growth of the number of degrees of freedom (DOF) of structural dynamic model. She also proposed innovative methods targeting at repeated eigenvalues or close eigenvalues as a result of the symmetry of structures, the inherent characteristics change caused by the coupling of different mediums and large modifications of structural design parameters.With six chapters, this thesis introduces the author's work on structural dynamic reanalysis based on eigen-sensitivity analysis on design parameters with many complex factors. A series of feasible methods on structural dynamic reanalysis are established. The major research and findings are as follows: 1. Dynamic substructure mode synthesis is applied to substructure sensitivity synthesis for first-order sensitivity of structures with repeated eigenvalues, as well as high-order sensitivity of single eigen-pairs. By using the technology of model reduction, both the number of DOF and cost of computation are significantly reduced. This lays the foundation for large-scale structural dynamic reanalysis problems.2. For repeated eigenvalues, the corresponding eigenvectors are degenerate. With substructure mode synthesis technology, the first-order sensitivity of repeated eigenvalues and corresponding derivable eigenvectors are derived. This solves the key issues for dynamic reanalysis of large complex structures with repeated eigenvalues based on eigen-sensitivity. Computational complexity analysis gives quantitative conclusions on the contributions of substructure sensitivity synthesis on reducing computational cost.3. For fluid-solid coupled problems of structure vibration in fluid medium, the impact of fluid is considered as added mass to the structure. A method of eigen-sensitivity analysis for the fluid-solid coupled system including the flexible plane vibration and fluid flow with respect to the design parameter is developed. With solar arrays of spacecrafts as application background, this provides an effective way of dynamic reanalysis for structures in fluid medium.4. Three-dimensional flow field of ideal fluid induced by vibration of shell structure is analyzed using dipole configuration method, and then the added mass formula of the fluid is provided. According to the potential function expression of the dipole, a set of related functions are constructed, so that the curved surface integral for flux calculation can be convert to the curvilinear integral on the edge of the surface. In this way, both the computational efficiency and accuracy are improved greatly.5. The controlling equations of substructure high-order sensitivity synthesis are derived, generalized expressions of n^th order eigen-derivatives with substructure sensitivity synthesis are also proposed. This method does not need full mode information of substructures and can be applied to large structures with high precision.6. With application of the vector valued rational approximation to structural dynamic reanalysis based substructure high-order sensitivity synthesis, the convergence scope of truncated Taylor Expansion is expanded. It can also be used to efficiently handle reanalysis of structures with large modifications.