Matrix Homotopy Perturbation Analysis Of Structural Dynamics

Structural reanalysis has gotten lots of attention from engineering. In the design of products, we always have to modify the structure repeatedly to get better performance, and this process is called reanalysis. Of course, we can re-compute all the structure of new design to get the results. But it means that all the results we have computed in former design are no use to the new structure. So it's important for us to find a method that just consumes a little to get new results from the former results. The homotopy perturbation analysis method in the thesis is the right one.In this thesis, by constructing a homotopy function, we bring homotopy to matrix perturbation for building an eigenpairs curve from the origin structure to the modified. So it's easy to calculate the dynamics' property of modified structure. To be continue, this method can be used in degrade systems, defective systems, and has got good performance also. Besides, we used the method of "divided and conquered" in homotopy perturbation analysis to deal with the reanalysis problems which the structural parameters are changed large. At last, we present a method to predict the step of iteration to keep the reanalysis self-adaption.Comparing to other reanalysis algorithm, the homotopy perturbation algorithm's feature as follow:1. Parallel2. Prepared for large changed of structural parameters3. Integrate algorithm for all forms of vibration systems 4. No need to get all the eigenpairs of systems...