This chapter analyzes the statistical response of a linear-elastic structure subjected to unknown excitations modeled by a stationary stochastic process. It is a probabilistic version of Chap. 3. Both stationary and transient response statistics are analyzed. For stationary statistics, a modal superposition approach in the frequency domain is adopted. For transient statistics, a state-space approach in the time domain is adopted. Although transient statistics are of less relevance in operational modal analysis, they are discussed for better appreciation of the meaning of stationary statistics. Their large time limits are the stationary statistics.
[1]
Yu-Kweng Michael Lin.
Probabilistic Theory of Structural Dynamics
,
1976
.
[2]
M. Grigoriu.
Stochastic Calculus: Applications in Science and Engineering
,
2002
.
[3]
S. Hammarling.
Numerical Solution of the Stable, Non-negative Definite Lyapunov Equation
,
1982
.
[4]
P. Kloeden,et al.
Numerical Solution of Stochastic Differential Equations
,
1992
.
[5]
T. T. Soong,et al.
Random Vibration of Mechanical and Structural Systems
,
1992
.
[6]
S. Sarkani,et al.
Stochastic analysis of structural and mechanical vibrations
,
1996
.