  In this paper, we study the partial pole assignment problem in symmetric
quadratic pencil with time delay. A novel multi-step method is proposed to
solve this problem, resulting in the undesired eigenvalues being moved to
desired values, and the remaining eigenvalues unchanged. By establishing a new
matrix equality relation and using a multi-step method, the problem is
transformed into solving linear systems with low order. Specifically, assuming
that there are $p$ undesired eigenvalues requiring reassigned, the size of the
linear system we finally solved is $p^2$. Notably, the method demonstrates high
efficiency for large systems with only a few poles requiring reassigned.
Numerical examples are provided to illustrate the effectiveness of the proposed
method
