Affiliations: Department of Advanced Materials and Structures,
Centre de Recherche Public Henri Tudor, Luxembourg-Kirchberg, Luxembourg | Department of Aeronautic and Space Engineering,
Politecnico di Torino, Turin, Italy
Note: [] Corresponding author: G. Giunta, Department of Advanced
Materials and Structures, Centre de Recherche Public Henri Tudor, 29, av. J. F.
Kennedy, L-1855 Luxembourg-Kirchberg, Luxembourg. Tel.: +352 42 59 91 1; Fax:
+352 42 59 91 555; E-mail: gaetano.giunta@tudor.lu
Abstract: The free vibration analysis of composite thin and relatively thick
plates accounting for uncertainty is addressed in this work. Classical and
refined two-dimensional models derived via Carrera's Unified Formulation (CUF)
are considered. Material properties and geometrical parameters are supposed to
be random. The fundamental frequency related to the first bending eigenmode is
stochastically described in terms of the mean value, the standard deviation,
the related confidence intervals and the cumulative distribution function. The
Monte Carlo Method is employed to account for uncertainty. Cross-ply, simply
supported, orthotropic plates are accounted for. Symmetric and anti-symmetric
lay-ups are investigated. Displacements based and mixed two-dimensional
theories are adopted. Equivalent single layer and layer wise approaches are
considered. A Navier type solution is assumed. The conducted analyses have
shown that for the considered cases, the fundamental natural frequency is not
very sensitive to the uncertainty in the material parameters, while uncertainty
in the geometrical parameters should be accounted for. In the case of thin
plates, all the considered models yield statistically matching results. For
relatively thick plates, the difference in the mean value of the natural
frequency is due to the different number of degrees of freedom in the model.
Keywords: Free vibration, uncertainty, Monte Carlo Method, refined two-dimensional models, composite plates
