Reliability Analysis of Dynamic Systems

Chapter 3

Theoretical Fundamentals of the Perturbation Approach

This chapter presents the technical fundamentals of the core of the proposed combined approach, i.e. a perturbation approach, including the definition of the newly defined parameters and new safety margin, and the derivation of the first two moments of the new parameters.

3.1 Definition of the New Parameters and Safety Margin

As explained in Appendix III, the response amplitude vector can be expressed in terms of the modal properties (equation AIII.26), i.e.

(3.1)

Extracting one element from the response vector, denoted as , gives

(3.2)

Equation (3.2) represents the response at ...