Uncertainty Quantification in Free Vibration Analysis of Cracked Moderately Thick Plates Using the Non-intrusive Chaotic Radial Basis Function

Purpose In the present study, vibration analyses of cracked plates having uncertain input parameters are investigated by developing a probabilistic methodology. The crack length, crack location, the module of elasticity and material density of the plate are considered as random variables. Methods In this paper, a non-intrusive Chaotic radial basis function computational scheme is developed, and it is combined with an enriched element-free Galerkin approach to obtain the statistics of the natural frequencies of the cracked plates. Results Two types of moderately thick cracked plates, including the internally cracked and side-cracked plates are considered and the results of the developed computational scheme for obtaining the statistics of natural frequencies of the system are compared with those of the Monte Carlo simulation. Also, through various numerical results, the effects of uncertain parameters are investigated on the vibration behavior of cracked plates. Conclusion It is shown that the developed method produces accurate results with significantly less computing time compared with the Monte Carlo simulation. Besides, it is indicated that the statistics of the fundamental natural frequency of the internally cracked plate is reduced by increasing the mean value of the crack length and it is increased by increasing the coefficients of variation of the crack position. It is shown that increasing the uncertainty in the crack length has a small influence on the mean value of the fundamental frequency, while it has an important impact on the variance of the vibration. In addition, it is demonstrated that the uncertainty parameters can importantly change the shape of the probability distribution of the plate natural frequencies. Furthermore, it is seen that, the mean value and the variance of the fundamental natural frequency of side-cracked plates are slightly affected by increasing the coefficient of variation of the side crack position.

Automated summary

This study develops a non-intrusive probabilistic method to analyze the vibration characteristics of cracked plates with uncertain parameters. Numerical simulations show that the uncertain parameters have a significant impact on the natural frequencies of the cracked plates.