Modeling the coupled flexoelectric-piezoelectric effects on bending and free vibration in nano-laminated plates: a variational decomposition approach
摘要
Piezoelectric nano-laminated plates have been widely used in micro–nano sensors, energy harvesters, and other micro-intelligent devices, owing to their excellent mechanical properties and unique force-electric coupling characteristics. At the micro–nanoscale, surface and flexoelectric effects become significant and cannot be neglected. To date, most studies on piezoelectric nanoplate structures have not accounted for the combination of surface and flexoelectric effects, and research on piezoelectric nano-laminated plates remains relatively limited. In this paper, a novel model for rectangular piezoelectric nano-bilayer plates was established based on Kirchhoff plate theory, integrating contributions from both surface piezoelectric and flexoelectric effects. This model incorporates both surface and flexoelectric effects, and further accounts for the distinct material properties of the upper and lower surfaces, as well as those of individual layers. The displacement variational method was utilized to obtain analytical solutions for the bending deflection and natural frequency of piezoelectric laminated plates subject to complex boundary conditions. The influences of the piezoelectric layer thickness, residual surface stresses, and the flexoelectric coefficient of the piezoelectric layer on both the bending deflection and natural frequency were systematically investigated. The methodologies and results presented in this study offer a theoretical foundation and analytical tools for the microstructural design, multi-physics characterization, and bending deformation analysis of rectangular piezoelectric nano-laminated intelligent components.