| Abstract: | The equations of motion of a structure in undamped modal coordinates may have non-zero off-diagonal terms in the damping matrix. Although these terms are commonly neglected, studies have shown that they may have a significant influence on the response to dynamic loads. In this paper, two independent criteria are developed to determine when these damping terms will affect the structure's modal properties and response. It is found that even small off-diagonal damping values can be significant if the structure has closely spaced natural frequencies. To quantify and understand the influence of these damping terms, closed-form analytical expressions are derived for the modal properties and harmonic and stochastic response of structures with closely spaced natural frequencies. One conclusion is that off-diagonal damping terms will decrease a modal damping ratio for each pair of closely spaced modes. This is significant, since a response analysis performed by neglecting these off-diagonal terms will underestimate the true response. |
