A NEW DESIGN METHOD BASED ON MODAL DAMPING RATIO MATRIX MDOF SYSTEM

摘要

The modal damping ratio matrix gives us the damping statues of a NDOF system. If the stiffness matrix and the damping matrix commute, the diagonal elements of the model damping ratio matrix represent the modal damping ratio at each mode of the system. Otherwise, the measured damping ratios and the damping ratio matrix will be numerically different but will have the same definiteness when compared with the identify matrix. Thus, they yield the same prediction about the qualitative behavior of a system. In this work, a new design method of the damping matrix (or damping) of the system based on the modal damping ratio matrix is presented, for a given mass matrix, stiffness matrix and desired modal damping ratio at each mode, the damping matrix can be recovered, so each damping attached to the masses can be chosen.