Analyses of natural frequency and electromechanical behavior of flexoelectric cylindrical nanoshells under modified couple stress theory

Different from piezoelectric effect, the flexoelectric effect is size dependent and becomes more significant at nanoscale. A nonlinear dynamic model of nanoscale flexoelectric shells is developed based on modified couples stress theory. The governing equations for nonlinear vibration of a flexoelectric cylindrical nanoshell are obtained. The natural frequency and generated voltage of the flexoelectric cylindrical nanoshell is achieved. Effects of geometric dimension, character material length, and vibration amplitude on the natural frequency and the generated voltage are discussed in detail. Results demonstrate that modified couple stress theory and large deformation theory are coupled together and interact with each other in the analyses of natural frequency and electromechanical behavior. Simultaneously taking nonlinearity and couple stress theory into account is necessary.