Partial quadratic eigenvalue assignment in vibrating structures using receptances and system matrices

In this paper, we consider the partial quadratic eigenvalue assignment problem (PQEAP) in vibration by active feedback control. Based on the receptance measurements and system matrices, we propose a constructive method for solving PQEAP, where we only need to solve a small linear system and only a few undesired open-loop eigenvalues with associated eigenvectors are needed. Our method is designed for both single-input and multiple-input vibration controls of vibrating structures. The real form of our method is also presented. Numerical tests show that our method is effective for constructing a solution to PQEAP with both single-input and multiple-input vibration controls.