Discrete analysis method for random vibration

Abstract A discrete analysis method which uses recurrent formulas to calculate the stationary and non-stationary random vibration responses for multi-degree of freedom (MDOF) dynamic systems is proposed in this paper. The unconditional stability of the recurrent formulas and their property of being able to calculate the accurate stationary mean and mean square responses are proved. An optimum time step is suggested with which the recurrent formulas can quickly carry out accurate stationary random responses. As an example, these recurrent formulas are applied to MDOF structures. Their practical calculation forms are derived which use the banded shape and symmetric properties of structural dynamic matrices to effectively calculate structural stationary or non-stationary mean and mean square responses. Some numerical examples are given to show the application of the method.