Low frequency antiplane shear vibrations of a three-layered elastic plate

Antiplane shear vibrations of three-layered strongly vertically inhomogeneous laminates are considered. Polynomial long wave low frequency approximations of the exact dispersion relation are derived and further simplified for the two setups of material and geometric problem parameters corresponding, particularly, to laminated glass plates as well as photovoltaic panels. The associated 1D shortened equations of motion are also established using the conventional asymptotic procedure earlier developed for thin homogeneous structures.