FREE VIBRATIONS OF MULTILAYERED PLATES BASED ON A MIXED VARIATIONAL APPROACH IN CONJUNCTION WITH GLOBAL PIECEWISE-SMOOTH FUNCTIONS

This paper presents a two-dimensional model for the analysis of freely vibrating laminated plates. The governing differential equations, associated boundary conditions and constitutive equations are derived from Reissnerʹs mixed variational theorem. Both the governing differential equations and the related boundary conditions are presented in terms of resultant stresses and displacements. The model is able to provide the results for the corresponding three-dimensional theory. Such a performance is guaranteed from an appropriate expansion of relevant kinetic and stress quantities through the thickness of the multilayered plate. The expansion is realized by using a novel selection of global piecewise-smooth functions (GPSFs). The number of GPSFs can be arbitrarily increased to achieve a two-dimensional plate theory which is, at least, as accurate as that of a full layerwise theory. It is also shown that GPSFs permit to deal a multilayered plate as if it was virtually made of a single layer. Indeed, the theory need not explicitly introduce continuity conditions for both displacements and relevant stresses. The performance of the present two-dimensional model in conjunction with the global piecewise-smooth functions is tested and discussed by comparing its resulting eigen-parameters, for a class of simply supported plates, with those of other two-dimensional models and with those existing of the exact three-dimensional theory.