  In the present work, we experimentally implement, numerically compute with
and theoretically analyze a configuration in the form of a single column
woodpile periodic structure. Our main finding is that a Hertzian,
locally-resonant, woodpile lattice offers a test bed for the formation of
genuinely traveling waves composed of a strongly-localized solitary wave on top
of a small amplitude oscillatory tail. This type of wave, called a nanopteron,
is not only motivated theoretically and numerically, but are also visualized
experimentally by means of a laser Doppler vibrometer. This system can also be
useful for manipulating stress waves at will, for example, to achieve strong
attenuation and modulation of high-amplitude impacts without relying on damping
in the system.
