Multi-parametric dynamic analysis of lightweight elastic laminates

Multi-parametric asymptotic analysis of dynamic phenomena in lightweight three-layered structures is performed. The presence of high contrast in densities of skin and core layers may lead to the small value of the lowest shear thickness resonance frequency, allowing a two-mode long wave low-frequency approximation of the exact dispersion relation. The range of uniform asymptotic validity of the two-mode approximation with respect to relative thickness and density are established. The theoretical predictions are illustrated numerically.