AdditiveManufacturing (AM) is widely used to fabricate phononic crystals (PnCs) in recent years. Friction Stir AdditiveManufacturing (FSAM) is a new-type solid state fabrication technologywhich is fusion free with low distortions. FSAMwas selected to fabricate the designed PnCs. Themanufactured specimenwas distorted due to the temperature rise in themanufacturing process and the band gaps (BGs)were changedwith the distortions. Results indicate that the band gap of the PnCsmoves to be in higher frequency domain due to the residual distortions of themanufactured PnCs. The residual distortion of FSAMPnCs is 2.77 times smaller in comparisonwith the Tungsten Inert Gas (TIG) welding. So, the differences of the band gap between the designed PnCs and the FSAM specimen are only in the range of 0.15%–0.55%due to the lower temperature rise in FSAM.The further analysis shows that the change of the BGs is caused by the growth of the inertiamoment for the FSAMPnCs. With the increase of the rotating speed in FSAM, the residual distortion of the FSAMPnCs is increased due to the increase of thewelding temperature. This can lead to the increase of the inertiamoment, which is the key reason for the increase of the BG characteristics of the FSAMPnCs.

Band gap characteristics of friction stir additive manufactured phononic crystals

Abstract Additive Manufacturing (AM) is widely used to fabricate phononic crystals (PnCs) in recent years. Friction Stir Additive Manufacturing (FSAM) is a new-type solid state fabrication technology which is fusion free with low distortions. FSAM was selected to fabricate the designed PnCs. The manufactured specimen was distorted due to the temperature rise in the manufacturing process and the band gaps (BGs) were changed with the distortions. Results indicate that the band gap of the PnCs moves to be in higher frequency domain due to the residual distortions of the manufactured PnCs. The residual distortion of FSAM PnCs is 2.77 times smaller in comparison with the Tungsten Inert Gas (TIG) welding. So, the differences of the band gap between the designed PnCs and the FSAM specimen are only in the range of 0.15%–0.55% due to the lower temperature rise in FSAM. The further analysis shows that the change of the BGs is caused by the growth of the inertia moment for the FSAM PnCs. With the increase of the rotating speed in FSAM, the residual distortion of the FSAM PnCs is increased due to the increase of the welding temperature. This can lead to the increase of the inertia moment, which is the key reason for the increase of the BG characteristics of the FSAM PnCs. 

A boundary element method (BEM) is implemented and applied to compute the band structures of phononic crystals taking account of three different kinds of imperfect interface layers. By using the Bloch theorem and the interface conditions the eigenvalue equations related to the wave vector are derived. The influences of the spring-interface model, mass-interface model and spring-mass-interface model on the dispersion curves and the band-gaps are investigated by comparing with that of the perfect interfaces. For different interface models, the effects of various interface parameters and mass density ratios on the lower edge, upper edge and width of the first complete band-gap are analyzed and discussed. It will be shown that a weak interface imperfection would not affect the dispersion curves, but a relatively strong interface imperfection may significantly affect the band structures of phononic crystals and it cannot be ignored. Moreover, the three interface models have different influences on the wave propagation and band-gap characteristics of the phononic crystals.

Band structure analysis of phononic crystals with imperfect interface layers by the BEM

Band structure calculation of 2D fluid/solid and solid/fluid phononic crystal using a modified smoothed finite element method with fluid-solid interaction.

Jianghao Xu

Papers

Band structure calculation of 2D fluid/solid and solid/fluid phononic crystal using a modified smoothed finite element method with fluid-solid interaction.