(color online) Phonon transmission function of 8-ZGNR: (a) without cavity; (b) with a cavity; (c) with two cavities; (d) with three cavities, respectively. Different curves corresponding to the total transmission rate (blue solid line), transmission rate of IPMs (red dashed line), and transmission rate of FPMs (black dotted line), respectively. (e), (f) Phonon local density of state of the (e) FPMs and the (f) IPMs at ω=25 cm⁻¹. Reprinted with permission from Ref. [100]. Copyright (2014) by Elsevier Publishing.