Free vibration reanalysis of structures with added degrees of freedom

•A modified initial analysis system is constructed to include the newly added degrees of freedom.•Block combined approximations with shifting is then used to simultaneously calculate eigenpairs of the modified structure.•The proposed method consists of matrix–matrix operations with Level-3 BLAS.•The triangular factorizations of shifted stiffness matrices generated in original free vibration analysis are reused.•Only decomposition of shifted sub-stiffness matrix corresponding to the newly added degrees of freedom is needed. This paper deals with free vibration reanalysis for structural topological modifications with added degrees of freedom. A modified initial analysis system (MIAS) is first constructed to include the newly added degrees of freedom. The MIAS is then used to analyze the modified structure, keeping the number of degrees of freedom unchanged. The block combined approximation method with shifting is finally utilized to calculate multiple eigensolutions of the modified structure. The implementation of the approach involves only LDLT factorizations of shifted sub-stiffness matrices corresponding to the newly added degrees of freedom. The proposed method consists of matrix–matrix operations. These operations can be implemented by using Level-3 Basic Linear Algebra Subprograms, the execution efficiency is thus enhanced. Numerical examples are given to demonstrate the effectiveness of the proposed method and the accuracy of the approximate solutions.