Stochastic analysis of the natural frequencies of rectangular plates under random temperature distributions

Abstract

© Proceedings of ISMA 2018 - International Conference on Noise and Vibration Engineering and USD 2018 - International Conference on Uncertainty in Structural Dynamics. All rights reserved.It has been shown in the literature that temperature variations can induce modifications of the static and dynamic characteristics of beam-like and plate-like structures, due to the so-called stress-stiffening effect. In most cases of practical interest, temperature variations associated to environmental and operational conditions are very difficult to control and can be rationally considered as random quantities. In this context, the present paper addresses the propagation of uncertainties affecting the temperature on the natural frequencies of thin rectangular plates. A Rayleigh-Ritz-based dynamic model is first derived for the bending vibrations of plates, accounting for the presence of thermal stresses. This model is combined with a Karhunen-Loève expansion (KL), used to discretize the temperature distribution, which is modeled as a Gaussian random field. The results enable to quantify the influence of temperature randomness on the thermal stresses, and evaluate the sensitivities of the natural frequencies with respect to such randomness.