Fig. 3: Dependence of fundamental physical parameters of acoustic and optic branches on the angle θ.
From: Origin and tuning of bandgap in chiral phononic crystals
a, b Influence of \({{{\boldsymbol{\theta }}}}\) on the inertial amplification coefficient \({{{\boldsymbol{p}}}}\), bending stiffness \({{{{\boldsymbol{k}}}}}_{{{{\boldsymbol{b}}}}}\), and stretch stiffness \({{{{\boldsymbol{k}}}}}_{{{{\boldsymbol{s}}}}}\) of the conventional chiral PnCs. The method of the normalized stiffness is \({{{\boldsymbol{k}}}}{{{\boldsymbol{/}}}}{{{{\boldsymbol{k}}}}}_{{{{\boldsymbol{r}}}}}\) where \({{{{\boldsymbol{k}}}}}_{{{{\boldsymbol{r}}}}} = {{{\boldsymbol{1}}}}{{{\boldsymbol{e}}}}{{{\boldsymbol{5}}}}\) \({{{\bf{N}}}}\,{{{{\bf{m}}}}}^{{{{\boldsymbol{-}}}}{{{\bf{1}}}}}\) (see Fig. S1 in Supplementary Note 3 for more details of \({{{\boldsymbol{\theta }}}}\), and see Supplementary Eqs. (47) and (48) for the governing equation about \({{{{\boldsymbol{k}}}}}_{{{{\boldsymbol{b}}}}}\) and \({{{{\boldsymbol{k}}}}}_{{{{\boldsymbol{s}}}}}\), respectively). c Bandgap variation with the different \({{{\boldsymbol{\theta }}}}{{{\boldsymbol{.}}}}\,\)Therein, the gray shaded area is the bandgap ranges.
