In this manuscript, acoustic wave propagation in a novel three-dimensional porous phononic crystal-Kagome lattice, is studied by using finite element method. Firstly, a Kagome-sphere structure is established based on Kagome truss. For lattice with fixed rods (sphere radius varied) or fixed spheres (rod radius varied), the band structures are calculated in order to clarify the influence of geometrical parameters (sphere and rod sizes) on the bandgap characteristics in Kagome-sphere lattice. The vibration modes at the band edges of the lowest bandgaps are investigated with the aim to understand the mechanism of the bandgap generation. It is found that the emergence of the bandgap is due to the local resonant vibration of the unit cell at the adjacent bands. The width and position of this bandgap can be tuned by adjusting the geometrical parameters. An equivalent mass-spring model is proposed and the equivalent system resonance frequency can be evaluated which predicts well the upper and lower edges of the complete bandgaps. Moreover, the critical geometrical parameter is formulated which gives the critical geometrical condition for the opening of the complete bandgaps. The results in this paper are relevant to the bandgap structure design of three-dimensional porous phononic crystals (PPCs).
The objective of this paper is to study the large deflection of a fully clamped sandwich beam under high-velocity impact by considering the time in-homogeneity of the core deformation. Firstly, a unified dynamic yielding criterion for metallic sandwich beams considering the mass redistribution along with the core compression is proposed. Different from the traditional yielding surface, when the core is partially densified, the yield surface is asymmetric. The well-known yielding criterion for the solid monolithic beam is a special case of our model. Moreover, a membrane factor is proposed and an analytical solution for the large deflection of the beam under blasting loading is given. Comparison of the analytical solutions with numerical ones reveals that the present analytical model improves the prediction accuracy of the high-velocity impact response of fully clamped sandwich beams. Moreover, the present analytical method can also be degenerated to predict the low velocity/energy impact response of sandwich beams.
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