Stochastic free vibration of composite plates with temperature-dependent properties under spatially varying stochastic high thermal gradient

Abstract

The uncertainty of natural frequencies of composite plates due to the uncertainty of high-temperature distribution on the plate is investigated. Mechanical properties are assumed to be uncertain linear functions of temperature with assuming a stochastic linear dependency function (SLDF). The temperature gradient is assumed to be a Gaussian stochastic field with an exponential kernel. Assuming first-order shear deformation theory, the displacement field is defined. The stochastic assumed modes (SAM) method is proposed and discretized stochastic equations of motion are derived. The probability space is studied using an intrusive polynomial chaos approach. Stochastic simulations are verified using the stochastic finite element method (SFEM) based on the Monte Carlo approach. Results show the proposed semi-analytical method is an efficient alternative to time-consuming SFEM with resulting accurate statistical moments. Uncertainty in natural frequencies is quantified for symmetric and anti-symmetric composite plates with different side to thickness ratios. The applicability of linear dependency of composite material properties to the temperature is evaluated by uncertainty propagation in SLDF. Uncertainties in SLDF and temperature distribution have significant effects on predicted natural frequencies. Based on the results, the application of linear dependency of material properties to the temperature can lead to significant errors in predicted natural frequencies.

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