Abstract: The extended transfer matrix of the structural vibration analysis is derived by using the expansion to the transfer matrix to solve structural dynamic characteristic analysis. The algebra equation for calculating the natural frequency is estabilished by using the extended matrix and the structural boundary condition. The natural frequency can be calculated using the numerical value method for the equation and a facility method to solve the natural frequency of chain structures is obtained. Considering the randomness of the structural parameters, the model of the structural dynamic characteristic analysis is founded and the digit characteristics of the natural frequency is obtained using the Monte Carlo random simulation methods. The correctness and facility of the theory and method presented in this paper are checked by two examples. The mean value and the mean square value of the structural natural frequency are calculated, and the effect of the stochastic parameters on structural dynamic characteristic is analyzed.

Key words: stochastic chain mechanical system, extended transfer matrix, random variables, dynamic characteristics analysis