Analysis of thick sandwich plates with a viscoelastic core by polyharmonic-spline RBF-FD and a layerwise theory

A strong-form meshless method is presented for static bending, free vibration and harmonic response of sandwich plates with a viscoelastic core. Established first-order layerwise kinematics with nine generalized displacements are combined with local polyharmonic-spline radial basis function-generated finite differences and polynomial augmentation. The contribution is the sparse differential-operator implementation and its documented accuracy and limitations for strongly contrasting face and core stiffnesses. A constant complex core modulus provides a frequency-domain damping approximation. Verification against the same layerwise Navier theory includes grid, polynomial-degree and stencil-size studies, perturbed and graded nodes, and unequal face thicknesses. A conventional nine-node finite-element implementation supplies additional cost and response comparisons. A seven-variable Murakami zig-zag model is compared under identical material and inertia assumptions. The material loss-factor bound is derived as a necessary admissibility condition, rather than a sufficient spurious-mode test. In particular, a corner-supported, free-edge diagnostic reveals inaccurate retained modes and a lack of demonstrated collocation convergence. Transient comparisons use an explicitly stated equivalent-viscous modal model. The results establish an accuracy envelope for the tested simply supported plates while identifying boundary treatment and realistic frequency/temperature-dependent constitutive laws as priorities for further development.