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

考虑沿面具有规定应力的不对称三层层压板。假定外层比内层硬得多。重点是长波低频反平面剪切。原始色散关系的渐近分析显示，低频谐波支持缓慢的准静态（或极限静态）衰减以及近截止波传播。尽管存在问题的不对称性，但缩短的前导多项式色散关系分解为对应于基本模式和上述谐波的两个更简单的多项式。根据缩短的色散关系的因式分解，本文中得出的相关一维运动方程也分为两个二阶算子。