Modal Analysis of Generally Damped Linear Structures Subjected to Seismic Excitations

Keywords: Modal analyses.  Seismic excitations.  Linear structures.  Supplemental damping.  Structural response.  Seismic performance.  Over-damped modes.  Peak responses.  Response spectrum method.

Abstract: A general modal analysis method, in which over-damped modes are taken into account, is developed and described in this report.  This general modal analysis deals with a unified formulation used to evaluate most structural response quantities of interest, such as displacements, velocity, interstory drifts, story shear, damping forces and absolute accelerations.  The primary objectives for this research are: (1) to explore the modal properties of the non-classically damped systems with over-damped modes and to further expand/complement current linear structural modal analysis theory, (2) to improve the present modal analysis procedures to accurately evaluate the peak seismic responses of damped linear structures with over-damped modes, (3) to extend the present response spectrum method to be applicable to the non-classically damped systems with over-damped modes and to establish a solid foundation for structural damping design, and (4) to propose an easy and reasonable criterion to determine the number of modes required to be included in the modal analysis of non-classically damped systems with over-damped modes to achieve an acceptable level of accuracy.