Procedures for approximate eigenproblem reanalysis of structures

In vibration mode superposition analysis, the main computational effort is spent in the solution of the eigenproblem. In reanalysis procedures this solution must be repeated for each change in the design. It is shown in this study how the combined approximations method can be used to improve the efficiency of some common iterative procedures. These procedures can then be used for efficient eigenproblem reanalysis. Solution of the reduced eigenproblem by the combined approximations method is first demonstrated. Procedures based on inverse iteration, inverse iteration with shifts, and subspace iteration are then considered. Some numerical examples show that high accuracy is achieved for very large changes in the design. In cases where higher accuracy is required, additional terms of the approximations may be considered