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 $\mathrm{B}\mathrm{a}\mathrm{T}\mathrm{i}{\mathrm{O}}_3-\mathrm{S}\mathrm{r}\mathrm{T}\mathrm{i}{\mathrm{O}}_3$ 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

KEYWORDS:

• Flexoelectric effect
• phononic crystal
• detuning
• localization factor
• forbidden band

Acknowledgments

This work is supported by the National Natural Science Foundation of China (11502110, 11972185, and 12002156), the Open Fund of the State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University (No. SV2018-KF-01, No. SV2018-KF-22), and the Open Project of Space Structure and Mechanism Technology Laboratory of China Aerospace Science and Technology Group Co., Ltd.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [11972185,11502110].