Investigation of three-layer rectangular panel bending by variation method

The task of transverse bending of a rectangular three-layer panel with the lightweight filler is considered. The differential equation system of transverse bending of the panel is generated within the scope of Lagrange variational principle. An explicit solution of the differential equation system in double trigonometric Fourier series is obtained. It is shown that the maximum deflection of the three-layer panel can be compared with the three-layer beam deflection, with a multiple panel width excess over its length.