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Schematic view of a unit-cell of the four investigated structures. (a) One-side stubbed plate with simple silicone rubber stub. (b) Double-side stubbed plate with simple silicone rubber stub. (c) One-side stubbed plate with composite stub. (d) Double-side stubbed plate with composite stub. For the whole study, the thickness of the plate is equal to e = 0.05a = 0.5 mm, while the diameter of the different stubs is fixed to d = 2r = 0.6 cm.
Band structures of the four studied structures. The blue region indicates the complete local resonance band gap, and the red dashed one the out-of-plane modes BG.
Absolute value of the displacement field of the modes indicated by A–F in the band structures of Figure 2. The modes denoted by A and B show an in-plane motion of the stubbed plate. The modes C and D show a stronger in-plane motion of the stubbed plate under the double-side and in-phase effects of the stubs deposited on each side. The modes E and F show the out-of-plane motion of the plate under the single and double stub effects. The stronger effect of the double-side configuration compared to the one-side can be clearly seen by the larger lateral and vertical displacements of the plate as well as by its colour intensity.
Band structure of a double-side stubbed plate with two different stub heights. Two expected band gaps related to each stub resonant eigenmodes are opened. No constructive coupling between both stubs can be occurred in this case.
Physical properties of silicone rubber, lead, and aluminum.
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