Study On Modal Sensitivity Analysis For Damped Structures With Repeated Eigenvalues

Modal-sensitivity analysis of structures was widely used in structural optimization,structural damage identification,structural control and dynamic inversion problems.The modal sensitivity analysis of damped structures,especially those with repeated eigenvalues,had always been a difficult and hot topic of concern to the researchers.This paper researched on the following two aspects:1)Aiming at the problem of calculating the modal sensitivity analysis for symmetrically damped structures with repeated eigenvalues,we proposed a new extended Nelson's method.We selected the non-singular submatrix from the set of eigenvectors corresponding to the repeated eigenvalues to obtain the control equation for the special solution of the modal sensitivity by modifying the original singular matrix to a non-singular matrix which was proved to be non-singular.The method kept the advantages of the traditional Nelson's method and only used the mode shape corresponding to the repeated eigenvalues to solve the equation,there was no need to extend the order of solving the equation and rearrange the matrix.Numerical examples show the effectiveness of the new method.2)Aiming at the problem of calculating the modal sensitivity analysis for asymmetrically damped structures with repeated eigenvalues,we proposed a new construction method for solving special solutions.Without changing the matrix sparsity and without increasing the order of solving the matrix,this method construct a nonsingular coefficient matrix in the n-dimensional original quadratic eigenvalue solution space by using non-singular submatrix properties of left and right eigenmodes in the modification of the singular coefficient matrix of the special solution.This new method did not require additional matrix's rows or columns operations and "fill in",the numerical results show the validity of the new method.