Modal Analysis of Arbitrarily Damped Three-Dimensional Linear Structures Subjected to Seismic Excitations

Keywords: Three-dimensional (3D) modal analyses. Seismic performance. Multi-directional excitations. Complex geometric shaped structures. Seismic damping devices. Ground motion. Vibration modes.

Abstract: This report presents a theoretical framework for the seismic analysis of arbitrarily damped three-dimensional (3D) linear structures. A complex 3-D modal analysis-based approach is developed to estimate the seismic responses to multi-directional excitations, accounting for effects of out-of-plane coupled motions and over-damped vibration modes. The procedures developed are suitable for the seismic analysis of structures with complex geometric shapes enhanced with damping devices introducing non-classical damping. A new modal combination rule, based on the theory of stationary random vibration and the existence of principal axes of ground motions, is developed to calculate the peak responses of structures subjected to seismic inputs given in terms of response spectra. The proposed modal combination considers correlations among perpendicular excitation components and between vibration modes. Finally, an over-damped mode response spectrum that accounts for the peak modal response resulting from the over-damped modes is proposed.