Structure preserving eigenvalue embedding for undamped gyroscopic systems

This paper concerns the eigenvalue embedding problem of undamped gyroscopic systems. Based on a low-rank correction form, the approach moves the unwanted eigenvalues to desired values and the remaining large number eigenvalues and eigenvectors of the original system do not change. In addition, the symmetric structure of mass and stiffness matrices and the skew-symmetric structure of gyroscopic matrix are all preserved. By utilizing the freedom of the eigenvectors, an expression of parameterized solutions to the eigenvalue embedding problem is derived. Finally, a minimum modification algorithm is proposed to solve the eigenvalue embedding problem. Numerical examples are given to show the application of the proposed method.