Transfer matrix method;  random parameters;  eigenvalues;  mean;  Variance

According to the Taylor expansion of structural eigenvalues with indefinite parameters, the statistical characteristics (mean, variance) calculation formula of random change of eigenvalues is derived. Taking the simple supported beam with random parameters as an example, the statistical characteristics of the structural eigenvalues of the simple supported beam when the mass density of the structure changes randomly by using the perturbation Riccati transfer matrix method are used to calculate the applicability of the method, and the mean and variance of the random eigenvalues when the flexural stiffness and length of the cross-section of the simple supported beam are randomly changed by using the method, and the statistical characteristics of the structural eigenvalues of the simple supported beam with random parameters are quantitatively described.