Spectral and Evolution Analysis of Composite Elastic Plates with High Contrast

Abstract We analyse the behaviour of thin composite plates whose material properties vary periodically in-plane and possess a high degree contrast between individual components. Starting from equations three-dimensional linear elasticity that describe soft inclusions embedded in relatively stiff thin-plate matrix, we derive corresponding asymptotically equivalent two-dimensional plate equations. Our approach is based on recent results concerning decomposition deformations with bounded scaled symmetrised gradients. Using an operator-theoretic approach, calculate limit resolvent associated spectrum effective evolution obtain our under various asymptotic relations size (equivalently, period) thickness as well scaling combinations contrast, spectrum, time. In particular, demonstrate significant qualitative differences models obtained different regimes.