Chapter Nine - Critical Excitation for Earthquake Energy Input in MDOF System

Abstract

This chapter explores the critical excitation method for earthquake energy input in a multi-degree-of-freedom system. It is a new complex modal analysis-based method in the frequency domain for computation of earthquake input energy to highly damped linear elastic passive control structures. The formulation of the earthquake input energy in the frequency domain is essential for deriving a bound on the earthquake input energy for a class of ground motions. This is because the formulation in the frequency domain only requires the computation of the Fourier amplitude spectrum of the input motion acceleration. Importance of over-damped modes in the energy computation of specific nonproportionally damped models is demonstrated. This is reflected by comparing the energy transfer functions and the displacement transfer functions. It demonstrates numerical examinations for four recorded ground motions. It is demonstrated that the modal analysis-based method in the frequency domain is very efficient in the computation of earthquake input energy. Furthermore, it is shown that the formulation of earthquake input energy in the frequency domain is essential for understanding the robustness of passively controlled structures to disturbances with various frequency contents. This chapter treats a structure with high-level damping to demonstrate the importance of over-damped modes in the computation of earthquake input energy.