A quadrilateral non-classical microplate element considering the voltage effect

A quadrilateral non-classical Mindlin element that incorporates voltage effects was introduced for examining the bending and free vibration of piezoelectric multilayer plates. The model was developed to examine multilayer plates in the presence of voltage effects. Hamilton’s principle was initially employed to formulate the equation of motion for a multilayer Mindlin plate, considering both size and voltage effects. The equations of motion were resolved through the Galerkin’s method. The suggested element is a rectangular element featuring four-nodes, each possessing 15 degrees of freedom, accounting for both bending and stretching deformations. This element meets the requirements for C0 continuity and C1 weak continuity, and incorporates size and voltage effects. The results were examined with both experimental and analytical data. Upon investigating the voltage effect, it was found that the stiffness matrix depends on both the magnitude and sign of the voltage. Furthermore, it has been demonstrated that the natural frequencies of higher modes are less affected by voltage variations compared to lower modes. In the end, the model was compared to experimental results obtained from a multilayer microcantilever.