Analyses of freely vibrating cross-ply laminated plates in conjunction with adaptive global piecewise-smooth functions (A-GPSFs)

• An adaptive expansion series is introduced within the frame of multilayer freely vibrating plates.
• Such an adaptive base is singled out from a mother set of global piecewise-smooth functions (GPSFs).
• The base (A-GPSFs) is able to treat the multilayered plate as if it were made up of a single layer.
• Comparisons with the exact three-dimensional theory show accuracy of both base and proposed model.

In this paper freely vibrating multilayered plates are analyzed through a suitable adaptive set of global piecewise-smooth functions (or A-GPSFs). Such a subset of functions is herein singled out from a mother set (GPSFs) formerly introduced by Messina [Messina A. Free vibrations of multilayered plates based on a mixed variational approach in conjunction with global piecewise-smooth functions. J. Sound Vib. 2002, 256(1): 103–129.] in 2002; the interesting novelty of this subset consists in the possibility to select the number of functional components for each single layer of the plate by preserving, or checking in a self-contained way, both the accuracy of the 3D-results and the global characteristics of the GPSFs. The governing differential equations and associated boundary conditions are consistently derived from the classical theorem of virtual displacements and are able to treat the multilayered plate as if it were made up of a single layer. The relevant model is essentially two-dimensional along with an expansion through the thickness aimed at modeling a three-dimensional dynamical behavior. The generalization, the simplicity and the accuracy of the present model, based on adaptive global piecewise-smooth functions, result from the comparison of the associated eigen-parameters with those of other models and with those of the exact three-dimensional theory.