Wave-Based Approach of Multi-Field Interactions in Piezoelectric Cylindrical Shells with Elastic Foundation: Prediction Modeling & Parametric Study

This study delves into the vibration characteristics of a piezoelectric cylindrical shell situated on an elastic foundation under various physical fields and boundary conditions. The investigation stems from the necessity to comprehend the behavior of nanobuilding blocks on foundations in the realm of nanoelectromechanical systems, which cater to applications in intricate environments. Employing a semi-analytical approach, we combine wave-based methods with Kirchhoff–Love shell theory and nonlocal theory. By applying the Hamilton principle, we derive kinematic relationships and governing equations for the cylindrical shell. Our methodology adopts a wave function approach to establish displacement solutions, integrating scaling parameters to formulate control equations for the piezoelectric shell’s vibration model. This model enables the extraction of natural characteristics and determination of steady-state responses to diverse external loads. The accuracy of our model is verified through numerical examples, comparative analyses, and experimental results. Furthermore, a parametric study is conducted to evaluate the influence of non-local parameters, elastic support stiffness, and external physical fields on the characteristics and response of the cylindrical shell. Ultimately, a prediction model for the piezoelectric cylindrical shell under multi-field conditions is developed, offering a theoretical foundation and references for the advancement of nanoelectromechanical systems.