Finite-Element Harmonic Analysis of Sandwich Plates with Periodically Modulated Faces and a Viscoelastic Core

Constrained-layer damping in sandwich floors and wall panels is usually analysed with uniform faces and a uniform core, while phononic treatments of periodicity address stop bands rather than the first few forced resonances of a finite plate. A seven-degree-of-freedom rectangular finite element is formulated here for a three-layer sandwich plate whose face thicknesses and core shear moduli vary in the plane as separable cosines. The kinematics follow Mead–Markus: Kirchhoff faces, first-order shear in a soft Kelvin–Voigt core, and a single transverse deflection. Membrane interpolation is bilinear; bending uses the Adini–Clough–Melosh incomplete quartic. A Navier–Galerkin sine series on two single-mass plates verifies the element to within one frequency step. On the modulated plate the Galerkin first peak is f1=8.93Hz, and the finite-element first peak is f1=9.57Hz; on the uniform plate, both methods give f1=7.66Hz. These three frequencies belong to the materials and planform of those two plates. Three archives then isolate core periodicity, face periodicity, and the layout of a fixed total attached mass. The first resonance of the core-campaign reference stays near 12Hz; its height follows the area-averaged storage modulus. The two mean face thicknesses, c1m and c3m, dominate the higher peaks; at fixed sum an unequal split is stiffer than two equal faces. Relocating the attached masses onto midlines or a diagonal rearranges the centre-point frequency-response function more than reweighting the 3×3 lattice. The spectra contain no phononic stop band.