Flexoelectric Effect on Bending and Free Vibration Behaviors of Piezoelectric Sandwich FGP Nanoplates Via Nonlocal Strain Gradient Theconory

Purpose: Flexoelectricity refers to the phenomenon of the link between electrical polarization and strain gradient fields in piezoelectric materials, particularly at the nanoscale. The goal of this study is to look into the bending and vibration properties of piezoelectric sandwich nanoplates in more detail, focusing on the flexoelectric effect and nonlocal strain gradient. Method: The plate consists of three distinct layers, including two outside skin layers formed of piezoelectric smart material exhibiting the flexoelectric effect and an inner core layer consisting of functionally graded porous (FGP) material. The general equations of motion with improved accuracy are derived using Hamilton’s principle and the revised higher order shear deformation plate theory (RPT). The use of the Galerkin–Vlasov method allows for the determination of the static bending characteristics and particular vibration frequencies of plates with various boundary conditions. A computational program is implemented using the Matlab software platform. Then, the program’s correctness is assessed by doing a comparative analysis using previously published, dependable findings in specific instances of the model described in the article. Moreover, it is crucial to carry out a comprehensive analysis to evaluate the influence of various attributes on a system’s static bending response and free vibration. The parameters include the flexoelectric effect, nonlocal and strain gradient parameters, elastic foundation stiffness coefficient, porosity coefficient, and geometric conditions. Results: The results of this research have practical consequences for the effective planning and management of similar systems, such as micro-electro-mechanical and nano-electromechanical devices. The results of this work are an important premise for developing more complex problems shortly, such as buckling analysis and dynamics problems. In addition, this is also a valuable reference for engineers designing models in engineering practice. Conclusion: The article presents a set of numerical experiments that provide significant findings. The stiffness of the plate is increased by the parameter f14, and therefore, the maximum deflection decreases as f14 rises. Nonlocal and strain gradient coefficients have contrary effects on the structure, so modulating these two coefficients is crucial for regulating the structure’s stiffness. The ratio between the thicknesses of the piezoelectric layer and the FGP core layer plays a crucial role in the study of increasing or decreasing the overall structure’s stiffness. An augmentation in the grading index will lead to a decrease in the overall stiffness of the structure, while an augmentation in the elastic base stiffness would result in an increase in the overall stiffness. Furthermore, the porosity coefficient, contingent upon the characteristics of the object, will induce either an augmentation or diminution in the magnitude of the inherent vibration frequency. However, it is quite probable that the displacement value of the plate will be augmented. Some new points in the article: The plate is composed of three layers with two skin layers made of piezoelectric smart material with flexoelectric effect and a core layer made of functionally graded porous material. The nonlocal and strain gradient coefficients change along the thickness direction and the porosity. Navier and Galerkin–Vlasov analytical methods are applied with many different boundary conditions. © Springer Nature Singapore Pte Ltd. 2024.