Chapter Two - Critical Excitation for Stationary and Nonstationary Random Inputs

Abstract

This chapter discusses the methods of critical excitation for stationary and nonstationary random inputs. It is natural to assume that earthquake ground motions are samples or realizations of a nonstationary random process. Therefore, critical excitation methods for nonstationary random inputs may be desirable for constructing and developing realistic earthquake-resistant design methods. However, it may also be relevant to develop the critical excitation methods for stationary random inputs as the basis for development for nonstationary random inputs. First, critical excitation methods for stationary random inputs are discussed in this chapter. Some fundamental and important results are derived through the discussion of these methods. These results play a significant role in the critical excitation methods explained in this book. Second, critical excitation methods for nonstationary random inputs are developed. These methods are based on the theory for stationary random inputs. A sample of a stationary random process is outlined. The mean value and the standard deviation of this process are constant every time. The phase of this process is assumed to be uniformly random. The key idea for stationary random inputs can be used in single-degree-of-freedom models under nonstationary random inputs that can be described by a uniformly modulated excitation model.