Antiplane shear of an asymmetric sandwich plate

Abstract An asymmetric three-layered laminate with prescribed stresses along the faces is considered. The outer layers are assumed to be much stiffer than inner one. focus on long-wave low-frequency anti-plane shear. Asymptotic analysis of original dispersion relation reveals a harmonic supporting slow quasi-static (or static at limit) decay near cut-off wave propagation. In spite asymmetry problem, leading order shortened polynomial factorises into two simpler ones corresponding fundamental mode and aforementioned harmonic. associated 1D equations motion derived in paper also split second-order operators line factorisation relation. Asymptotically justified boundary conditions established using Saint-Venant’s principle modified by taking account high-contrast properties laminate.