Frequency Reliability Sensitivity for Dynamic Structural Systems#

Parameter uncertainty of structural systems is inherent in most engineering problems. Therefore, reliability analysis of uncertain structural systems is of great significance, and frequency reliability analysis is important to uncertain vibration structure systems. Based on the frequency reliability theory, this article introduces an approach to calculate the reliability of a mechanical structure under dynamic excitation. With the criterion that the absolute value of the difference between the natural frequency and forcing frequency, the reliability mode and the safety probability of random systems are defined, and then the frequency reliability sensitivity analysis method is presented. The structure is supposed to fail if the frequency of the external force is within a predefined distance of structural resonant frequencies. The frequency reliability sensitivity analysis method for resonant problem of dynamic structural systems reliability is proposed by using the random perturbation technique, the reliability theory, and sensitivity approach. The formulas of quasi-failure probability sensitivity are derived when random variables are normally distributed. The reliability is evaluated, and its sensitivity to mean values, variances, and covariances is mathematically expressed, then the efficiency and accuracy of the proposed method are demonstrated by a numerical example.