Vibration reanalysis based on block combined approximations with shifting

• An efficient method is proposed for vibration reanalysis.
• Block combined approximations with shifting is used to simultaneously calculate some eigenpairs.
• The proposed method is based on matrix–matrix operations with Level-3 BLAS.
• The triangular factorizations of shifted matrices generated in original vibration analysis are utilized.
• No factorization of the modified stiffness matrix is needed.

This paper presents an efficient method for vibration reanalysis. The procedure uses block combined approximations with shifting to simultaneously calculate some eigenpairs of modified structures. The triangular factorizations of shifted stiffness matrices generated in initial vibration analysis are utilized to calculate the higher modes. The proposed method is based on matrix–matrix operations with Level-3 BLAS and can provide very fast development of approximate solutions of high quality for frequencies and associated modal shapes of the modified structure. Numerical examples are given to demonstrate the efficiency of the vibration reanalysis algorithm and the accuracy of the approximate solutions.