“Dangerous Directions of Seismic Excitation” and Combination of the Close Modal Responses in Linear Spectral Analysis

Authors:  
Rubric:     Theoretical and experimental studies   
Key words: seismic response, linear spectral method, modal analysis in the time domain, dangerous directions of seismic excitation
Annotation:
This paper continues the discussion on the linear spectral analysis using “dangerous directions of seismic excitation” concept. It is shown that in case all components of seismic excitation have similar response spectra, this “directional” approach, though non-physical, gives similar results to the conventional more physical approach, accounting for the statistical independence of diffrent components. This statement, previously proved for the modal responses with separated frequencies, here is extended for the case of close modal frequencies. If the excitation is diffrent, the “directional” approach leads to the systematic errors. The author once again considers the inertial load vectors in the nodes and studies which of them rotate along with the rotation of the “seismic excitation direction” set up by the analyst, and which of them keep their direction and change only module. Besides, the author notes certain limitation of the implementation of the D’Alambert principle to the quasi-static analysis of the damped systems. It turns out, that this approach, treating inertial loads as quasi-static and neglecting damping in the left-hand parts of the equation, gives reasonable results only for the internal forces, but not displacements, and only for systems either with homogeneous damping, or statically-determined.