Free vibration of circular and annular nanoplates with surface and flexoelectric effects

Abstract

Free vibration of circular/annular piezoelectric nanoplates with flexoelectric and surface effects is studied. Using Hamilton’s principle, the governing equation and boundary conditions of circular/annular nanoplates are derived. Exact characteristic equations of clamped and simply-supported circular nanoplates are obtained. The static/dynamic flexoelectric and surface effects on the natural frequencies are analyzed. The results show that the flexoelectric and surface effects have obvious size effects. Positive surface stress increases the natural frequencies as if the nanoplate is tightened, and vice versa. There is a competitive mechanism between the influence of the flexoelectric and surface effects on the natural frequencies.

Keywords:

• Flexoelectric effect
• surface effect
• circular nanoplate
• free vibration
• natural frequencies

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 12072374).