Random Vibration Analysis of Nonstationary Response

Consider a linear dynamical system with degrees of freedom (DOFs) and its equation of motion is given by  

If the matrix M C can be diagonalized by the same set of eigenvectors as the matrix M K, the damping model is said to be classical. Caughey and O Kelly (1965) showed the following necessary and sufficient condition [41]  

The modal forcing f is a linear combination of the components of g so it is also a zero-mean Gaussian vector process. It is stationary with the spectral density matrix function  

Sfico) = (M l )- ToSg(ft )Tj(M )- and the auto-correlation matrix function  

It is well known that the model response x is a zero-mean Gaussian random process with a correlation function between jc andx// [161]  

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