Dynamic properties predictions for laminated plates by high order theories

Abstract

The main aim of this study is to predict the elastic and damping properties of composite laminated plates. Some approximate methods for the stress state predictions for laminated plates are presented. For simple uniform bending and transverse loading conditions, this problem has an exact elasticity solution. This paper presents a new stress analysis method for the accurate determination of the detailed stress distributions in laminated plates subjected to cylindrical bending. The present method is adaptive and does not rely on strong assumptions about the model of the plate. The theoretical model described here incorporates deformations of each sheet of the lamina, which account for the effects of transverse shear deformation, transverse normal strain-stress and nonlinear variation of displacements with respect to the thickness coordinate. Dynamic and damping predictions of laminated plates for various geometrical, mechanical and fastening properties are defined. The comparison with the Timoshenko beam theory is systematically done for analytical and approximation variants. The values of damping are got at a bend in three- and five-layered plates. For the threelayered plates the equivalent beam of Timoshenko exactly approximates a “sandwich” (with a soft damping kernel) dynamic properties of sandwich in a wide frequency range. For a plate with soft external layers the equivalent beam needs to be found in every frequency range separately. A hard bounded layer multiplies damping in a plate with soft external layers, however only at higher frequency of vibrations. For the high-frequency vibrations of plates the anomalous areas of diminishing of damping (for sandwiches) and increase are got for plates with soft covers. At the moderate amount of approximations the exact divisions of tensions are got in the layers of plates, thus the stresses continuity and surface terms are approximated exactly enough. Unlike the widespread theories of plates with the terms set a priori on surfaces (as a rule levels to the zero tensions) the offered equations allow to satisfy and complicated boundary conditions, instead of only free fastened plates. It allowed to explore the row of important examples for plates fastened in a hard holder and to explore influence of not only plates but also construction of holder on damping.