Chapter 8 - Critical Excitation for Earthquake Energy Input in SDOF System

Abstract

This chapter explores a new general critical excitation method for a damped linear elastic single-degree-of-freedom (SDOF) system. It introduces the input energy to the SDOF system during an earthquake as a new measure of criticality. It is shown that the formulation of the earthquake input energy in the frequency domain is essential for solving the critical excitation problem. It is also essential for deriving a bound on the earthquake input energy for a class of ground motions. The criticality is expressed in terms of degree of concentration of input motion components on the maximum portion of the characteristic function defining the earthquake input energy. It is remarkable that no mathematical programming technique is required in the solution procedure. The constancy of earthquake input energy for various natural periods and damping ratios is discussed from a new point of view based on an original sophisticated mathematical treatment. It is shown that the constancy of earthquake input energy is directly related to the uniformity of “the Fourier amplitude spectrum” of ground motion acceleration. It is not directly related to the uniformity of the velocity response spectrum. The bounds under acceleration and velocity constraints are clarified through numerical examinations for recorded ground motions.