Mathematics Theories And Methods On Structure Dynamics Model Updating

The structural dynamics models updating have become increasingly important in the structural dynamics field. This dissertation was to study the mathematical theories and methods for structural dynamical model updating. It gave the solutions and the numerical methods of a special structure model updating. It is composed of five parts:1. The centrosymmetric structural dynamical models updating were studied in the paper. The necessary and sufficient condition for centrosymmetric solution of matrix equation was presented and general solutions were obtained. The optimal approximation solution to a given matrix was provided in the solution set. The results were then applied to solve the centrosymmetric structural dynamical model updating problems. The optimal solution was entreated for the given pencil of matrices.2. Considering pencil of matrices with centrosymmetric could not satisfy characteristic equations in practice, it was necessary to study the centrosymmetric solution of the matrix equation least square problems, and to give pencil of matrices with centrosymmetric of the least squares problems in model updating. 3. The Centrosymmetric structural dynamical systems with damping were studied. The nearest triple matrix of the Centrosymmetric with satisfying characteristic equations was found to a given triple matrix(mass,stiffness and damping matrices). Finally, numerical examples were given.4. A new method for updating linear structural dynamic model was proposed in the paper. The modified parameters were determined by sensitivity analysis. Based upon the orthogonal condition and the characteristic equation of the modal analysis theory, updating equations about the mass and stiffness matrices of the structure were constructed at first. A pretreatment matrix was given and then a stable iterative method was introduced to solve the modified structural parameters. This method was also utilized to update the model of damped dynamic structures.