We consider a body, homogeneous or periodic, equipped with a structure composed of dynamic inhomogeneities uniformly distributed along a line, and study free and forced sinusoidal waves (Floquet - Bloch waves for the discrete system) in such a system. With no assumption concerning the wave nature, we show that if the structure reduces the phase velocity, the wave localizes exponentially at the structure line, and the latter can expand the transmission range in the region of long waves. Based on a general solution presented in terms of non-specified Green’s functions, we consider the wave localization in some continuous elastic bodies and a regular lattice. We determine the localization-related frequency ranges and the localization degree in dependence on the frequency. While 2D-models are considered throughout the text, the axisymmetric localization phenomenon in the 3D-space is also mentioned. The dynamic field created in such a structured system by an external harmonic force is obtained consisting of three different parts: the localized wave, a diverging wave, and non-spreading oscillations. Expressions for the wave amplitudes and the energy fluxes in the waves are presented.

我们考虑一个体的，均匀的或周期性的，配备有结构动态不均匀组成沿着一条线均匀地分布，研究自由和强迫正弦波-以这样的（弗洛凯布洛赫波的离散系统）系统。在没有关于波的性质的假设的情况下，我们表明如果结构降低相速度，则波将以指数形式定位在结构线上，而结构线可以扩大长波区域中的传输范围。基于以非特定格林函数表示的一般解，我们考虑了一些连续弹性体和规则晶格中的波局部化。我们根据频率确定与定位相关的频率范围和定位程度。尽管全文中都考虑了2D模型，但同时也提到了3D空间中的轴对称定位现象。在这样的结构化系统中，由外部谐波力产生的动态场由三个不同部分组成：局部波，发散波和非扩展振荡。