The paper by M. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani presents the first full band-structure calculations for periodic elastic composites. The authors focus on transverse polarization of vibrations, obtaining a "phononic" band gap that extends throughout the Brillouin zone. This complete acoustic gap has significant implications for suppressing zero-point motion and phonon localization, which could lead to improvements in transducers and the creation of vibrationless environments. The study is inspired by recent developments in photonic crystals, where complete band gaps have been observed. The authors motivate their work by three main reasons: the potential for a vibrationless environment, the possibility of enhancing transducer performance, and the exploration of Anderson localization in classical waves. The calculations are performed for a system composed of an array of infinite cylinders made of an isotropic solid embedded in an elastic background, using a two-dimensional Bloch vector approach. The results show a vibrational band gap between the first two bands, indicating that wave propagation in the transverse plane is forbidden for vibrations parallel to the cylinders. The study highlights the complexity and richness of elastic composites compared to dielectric composites, and the potential for achieving a complete phononic gap in periodic systems of liquids and gases.The paper by M. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani presents the first full band-structure calculations for periodic elastic composites. The authors focus on transverse polarization of vibrations, obtaining a "phononic" band gap that extends throughout the Brillouin zone. This complete acoustic gap has significant implications for suppressing zero-point motion and phonon localization, which could lead to improvements in transducers and the creation of vibrationless environments. The study is inspired by recent developments in photonic crystals, where complete band gaps have been observed. The authors motivate their work by three main reasons: the potential for a vibrationless environment, the possibility of enhancing transducer performance, and the exploration of Anderson localization in classical waves. The calculations are performed for a system composed of an array of infinite cylinders made of an isotropic solid embedded in an elastic background, using a two-dimensional Bloch vector approach. The results show a vibrational band gap between the first two bands, indicating that wave propagation in the transverse plane is forbidden for vibrations parallel to the cylinders. The study highlights the complexity and richness of elastic composites compared to dielectric composites, and the potential for achieving a complete phononic gap in periodic systems of liquids and gases.