Alternatives to Standard Mode Superposition for Analysis of Non-Classically Damped Systems

摘要

The dynamic response of systems with nonclassical damping may be solved exactly by mode superposition. To reduce the computational effort, an approximate procedure that avoids the complex mode solution often is preferred, in which the undamped mode shapes based on the system mass and stiffness matrices are applied as generalized coordinates, and the resulting coupling terms in the generalized damping matrix are ignored. Two other approximate procedures that parallel this are described here: (1) the mass matrix is transformed using eigenvectors based on the stiffness and damping matrices, and (2) the stiffness matrix is transformed using eigenvectors based on the damping and mass matrices; the transformed equation sets are then uncoupled by ignoring the coupling coefficients of the generalized mass and stiffness matrices, respectively. A third procedure is presented that involves the use of corrected diagonal terms in the transformed property matrices, taking into account contributions based on the off-diagonal terms.