Localization of elastic waves in one-dimensional detuned phononic crystals with flexoelectric effect

ABSTRACT Although forbidden band effect in perfectly periodic phononic crystals (PC) is very attractive, random disordered (i.e. detuning) phenomenon is inevitable in engineering processing, thus exploring the effect of detuning on the wave characteristics of PC becomes a necessity. In this study, fundamental governing equations and boundary conditions are derived from the principle of virtual work. Wave characteristics and localization factor of one-dimensional (1D) detuned nano-PC are investigated based on the transfer matrix method, with flexoelectric effect duly accounted for. Subsequently, with nano-PC taken for illustration, forbidden band properties and localization factor of 1D elastic waves in harmonic and detuned states are systematically characterized. It is demonstrated that localization factor can characterize the energy band structure of 1D PC perfectly. Flexoelectric effect tends to widen the width of forbidden band with increasing detuning, and detuning is linearly related to the bandwidth. The forbidden band is more sensitive to flexoelectric coefficient detuning than thickness detuning. The research results provide useful theoretical guidance for designing high-frequency nanoscaled devices with the function of filtering based on band gap effect of nano-PC. Graphical abstract