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We have studied the compression (P) wave band structures at a low frequency in two-dimensional solid–solid phononic crystals. The plane-wave expansion method based on the decomposition of elastic waves was used. The pressure field distribution of P-wave localized modes at Γ points in the lowest bands, including multiple flat bands of systems comprising different configurations, were analyzed. The results show that a lower symmetry of the scatterer are an effective method to enhance the localization of vibration modes. The property has potential applications in the design of waveguides.

This paper discusses material named Polyurethane bonding which can be used in the stabilization of railroad ballast layer. An experimentation of the static and dynamic response of this material is important in designing appropriate solutions for railroad ballast layer, especially for the transition zone. A comprehensive study on the SHPB testing of Polyurethane bonding is presented in the strain rate range of 1000s${}^{-1}$–4000s${}^{-1}$. Variable power law was used to predict the material response at elevated strain rates as high as 10,000s${}^{-1}$. These results are compared with the material’s quasi-static response. The effects of strain rate on material parameters like Young’s Modulus and Yield Strength were investigated under various high strain rate dynamic experiments. It was found that the yield strength as well as Young’s modulus increased with the strain rate and the trend was more evident at higher strain rates. Quasi-Static Uniaxial Compression tests gave the typical stress–strain relationship of the material. A close investigation of the material response indicates that the behavior of this class of Polyurethane has a close resemblance with PMMA at the quasi-static as well as at various high strain rates.