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The complete flexural vibration is studied in the honeycomb plates with a new chiral-truss core structure.The design of the chiral-truss with the add-on elastic metamaterial in each repeated cell will be proposed to generate the new band gaps for the vibration suppression of the plates.Numerical simulations show that the low-frequency gaps exist in the composite plates.The frequency response of the finite plates is simulated by the finite element analysis.The work will be significant in the application of aerospace engineering.