A COMPLEX MODAL SUPERPOSITION METHOD FOR THE SEISMIC ANALYSIS OF STRUCTURES WITH SUPPLEMENTAL DAMPERS

摘要

A response spectrum method for the seismic analysis of structures with added dampers is herein introduced.The method is based on a modal decomposition of the equations of motion and the derivation of relationships between spectral accelerations, velocities, and displacements valid for high damping ratios. It involves the calculation of the complex natural frequencies, mode shapes, and participation factors of the system and the use of an acceleration response spectrum. It differs from similar methods proposed in the past in that it properly accounts for the high damping ratios observed in structures with added dampers and employs unique formulations to determine the peak relative velocities and absolute accelerations of the system. A numerical example is provided to illustrate the application of the procedure and compare the results attained with it and a time-history analysis. Through this example, it is shown that the proposed method is simple to use and leads to results that are close to the results from a time-history analysis.