The present paper may be divided into three parts. In the first part, attention is focussed on the frequency analysis of the vibrations of laminated composite plates. For any lamination sequence, the eigenproperties of the system are obtained by means of the Rayleigh-Ritz method. The second part extends the formulation to the case of laminates supported by inhomogeneous Winkler foundations. Abrupt discontinuities which are introduced by means of piecewise continuous properties of the foundation are shown to be well captured by the Rayleigh-Ritz method, despite the relevant trial functions be extremely regular. In the last part, a novel method, i.e. the stochastic Rayleigh-Ritz method (SRRM), is introduced for the probabilistic analysis of uncertain structures, i.e. those the structural properties of which are modelled as random fields. The theoretical framework is then applied to the composite plates under investigation, the eigenproperties of which are this way described from a probabilistic point of view. Finally, numerical examples are worked out to validate the theoretical considerations previously introduced.

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