Simplified Analysis of Asymmetric Structures with Supplemental Damping

DAMPING Rakesh K. Goel SUMMARY This study investigated the effects of neglecting off-diagonal terms of the transformed damping matrix on the seismic response of non-proportionally damped asymmetric-plan systems with the specific aim of identifying the range of system parameters for which this simplification can be used without introducing significant errors in the response. For this purpose, a procedure is presented in which modal damping ratios computed by neglecting off-diagonal terms of the transformed damping matrix are used in the traditional modal analysis. The effects of the simplification are evaluated first by comparing the aforementioned modal damping ratios with the apparent damping ratios obtained from the complex-valued eigen analysis. The variation of a parameter that was defined by Warburton and Soni as an indicator of the errors introduced by the simplification is examined next. Finally, edge deformations obtained from the simplified procedure are compared with those obtained from the direct integration of the equations of motion. It is found that the simplified procedure may be used without introducing significant errors in response for most practical values of the system parameters. Furthermore, the estimates of the edge deformations in general tend to be on the conservative side.