Effects of thermo-order-mechanical coupling on band structures in liquid crystal nematic elastomer porous phononic crystals

Liquid crystal nematic elastomers are one kind of smart anisotropic and viscoelastic solids simultaneously combing the properties of rubber and liquid crystals, which is thermal sensitivity. In this paper, the wave dispersion in a liquid crystal nematic elastomer porous phononic crystal subjected to an external thermal stimulus is theoretically investigated. Firstly, an energy function is proposed to determine thermo-induced deformation in NE periodic structures. Based on this function, thermo-induced band variation in liquid crystal nematic elastomer porous phononic crystals is investigated in detail. The results show that when liquid crystal elastomer changes from nematic state to isotropic state due to the variation of the temperature, the absolute band gaps at different bands are opened or closed. There exists a threshold temperature above which the absolute band gaps are opened or closed. Larger porosity benefits the opening of the absolute band gaps. The deviation of director from the structural symmetry axis is advantageous for the absolute band gap opening in nematic state whist constrains the absolute band gap opening in isotropic state. The combination effect of temperature and director orientation provides an added degree of freedom in the intelligent tuning of the absolute band gaps in phononic crystals.