Estimation of modal masses of a structure with a mass-type damping device

• A method for estimating modal masses of higher modes is presented.
• This method was applied to a 39 story building structure with an active mass damper.
• The good agreement between the analytical and experimental resonance responses.

In this paper, a method for estimating modal masses is presented by extending the procedure proposed by a previous study for estimating the first modal mass to a procedure which allows the estimation of modal masses of higher order modes. System matrices are first obtained by using a general system identification technique, and then the natural frequency and damping ratio of each mode are extracted from the obtained system matrices. Controllability and observability matrices are constructed by using both the identified system matrices and the modal space system matrices in which the modal masses are considered as unknown variables. The modal masses can be obtained based on the fact that the multiplication of the controllability and observability matrices does not change with the type of the system matrices, including the modal space ones. The advantage of the proposed method is that an accurate estimation of the modal mass of a higher mode is possible without the information on the modal vector which is difficult to experimentally identify. The proposed method was applied to a real-world 39 story building structure with an active mass damper and higher order modal masses of the building were identified. The dynamic responses analytically obtained by using the identified modal masses were found very close to the measured responses.