Absolute Acceleration Transfer Function of Secondary Systems Subjected to Multi- Component Earthquakes

The importance of the equipment and secondary systems in seismic design and performance evaluation is well recognized and has been the subject of many studies. In all of these studies, earthquake is considered as a single component, and in most of them the primary system is considered as shear building. Most attention has been concentrated on the response of secondary system and its response spectrum. In this paper, the transfer function for absolute acceleration of the secondary system is obtained.
The squared modulus of transfer function relates the power spectral density function of the input (excitation) to the output (response), which is useful in the study of the various dynamic parameters of the system. In addition to transfer function, the autocorrelation and power spectral density function of absolute acceleration of the secondary system are obtained. Earthquake is considered as a multi-component system and the necessary formulation is developed for the calculation of these functions as well as the critical angle with and without interaction between the two systems. The damping of the system is considered as proportional in the decoupled analysis, and nonproportional in the coupled analysis. The formulation developed has been illustrated by considering a ten-story torsional builing. Various parameters such as eccentricity, correlation between components, tuning interaction and nonproportional damping are studied. Results show that eliminating the effect of multicomponentness of earthquake can cause large errors especially at large eccentricities.

Keywords: transfer function, Random vibration, secondary systems, critical angle, interaction, nonproportional damping