Abstract: Considering the randomness of structural physical parameters, after the random factor abstracted from the stiffness matrix and the mass matrix, the random factor is introduced into the vibration control equation and the randomness of parameters in the vibration control equation is represented by the random factors. By using the algebra synthesis method, the mean value and the standard variance of the eigenvalues of the vibration control equation are developed. The closed-loop stability of the vibration control equation of random structures is discussed and the stability criterion is obtained with the 3σ criterion. Finally, an example of the cantilever beam is used to illustrate the feasibility of the method given, which shows that the effect of the elastic Young’s modulus on the eigenvalues is greater than that of the mass density.

Key words: stochastic parameters, vibration control, random factor method, eigenvalues analysis, stability