Free oscillations of three-layered plates

Abstract

The paper is devoted to improving the theory of bending and vibrations of three-layer plates with transverse compressible filler and thin outer bearing layers. For the outer layers, the Kirchhoff-Love hypothesis is accepted and the motion of their points is described by the equations of the theory of thin plates relative to forces and moments. Unlike bearing layers, a filler is considered as a three-dimensional body that does not obey any simplifying hypotheses. The equations of the bimoment theory of thick plates with respect to forces, moments and bimoments, created in the framework of the three-dimensional theory of elasticity, taking into account the nonlinearity of the distribution law of displacements and stresses over the thickness, are taken as the equations of motion of the filler. Expressions of forces, moments, and bimoments in the layers, as well as boundary conditions at the edges of a three-layer plate with respect to force factors, are given. In the conjugate zones of the layers, the complete contact conditions for the continuity of displacements and stresses are set. An example is considered and numerical results are obtained.