The band structure and transmission coefficient of the two-dimensional ternary locally resonant phononic crystal are computed by the finite element method with the calculated frequency up to 120 kHz.The band gap in the high frequency range is found and considered as the Bragg band gap in the locally resonant phononic crystal which has the locally resonant band gap in the low frequency range normally.Then,a composite phononic crystal by hybridizing the Bragg scattering phononic crystal and the locally resonant phononic crystal is proposed.Simultaneous Bragg and locally resonant band gaps are displayed and discussed for the composite phononic crystal.The results show that the simultaneous Bragg band gap and locally resonant band gap can be tuned.
An alternate yet general form of the classical effective thermal conductivity model （Maxwell model） for two-phase porous materials is presented, serving an explicit thermo-physicM basis. It is demonstrated that the reduced effective thermal conductivity of the porous media due to non-conducting pore inclusions is caused by the mechanism of thermal stretching, which is a combi- nation of reduced effective heat flow area and elongated heat transfer distance （thermal tortuosity）.
