The paper describes an algebraic method for the second-order statistics of the response of multi-degree-of-freedom linear time-invariant dynamical systems to (zero mean) white noise or stationary filtered white noise excitation. The method is based on the observation that the steady-state covariance matrix Y of the response is the solution of the matrix equation AY + YA' = C, where A" is the transpose of A. A simple algorithm, which takes advantage of the special form of A, is given for the solution of the matrix equation. The algorithm is particularly suitable for machine computation. The correlation matrix is simply the product of the impulse response matrix and the covariance matrix.
The above general method is applied to study the flapping response of a flexible lifting rotor blade in hovering or vertical flight to stationary random excitation. The results of this study show that the conventional rigid blade analysis does not in general give an adequate approximate description of the mean square response of the blade. They also suggest that an adequate approximate solution may be obtained by an uncoupled twomodes analysis if the Lock number of the blade is not too large.
An alternate method for the solution of the matrix equation is also given for systems with a large number of degrees of freedom. This alternate method is computationally less efficient but does allow us to keep the calculations strictly in-core for systems with up to 100 degrees of freedom.