Modal signal analysis of parabolic shell structures with flexoelectric sensors

The flexoelectric effect, garnering extensive attention in recent years, is an electro-mechanical coupled gradient effect that widely exists in dielectric materials and holds great potential for applications in structural sensing and actuation. The parabolic shell structure, characterized by line focusing, finds widespread use in key structural components such as solar trough collectors and communication antennas. Distributed sensing of the structural states of these parabolic shells is critical for vibration control, health monitoring, and shape control of precision structural systems. Therefore, flexoelectric sensing research based on parabolic shell structure has become an important topic. This study establishes a mathematical model for flexoelectric sensing in a parabolic shell with four-sided simply supported boundary conditions. The model is based on the direct flexoelectric effect, and thin shell assumption, and incorporates specific Lamé parameters and curvature radius. The electro-mechanical strain gradient/signal generation characteristics and distributed modal flexoelectric signals on the parabolic shell are investigated. The sensing signal under the open-circuit conditions is deduced, and the flexoelectric sensing signal and sensing characteristics of different modes are analyzed. The formulation of the flexoelectric neural sensing signal for the parabolic shell structure is provided and divided into two components: a circumferential bending component and a longitudinal bending component. In the case studies, the effects of design parameters such as flexoelectric sensor thickness, size, and aspect ratios are evaluated and compared. The analysis and results of this study offer a theoretical foundation and reference for refining the design parameters of the flexoelectric sensor and determining its optimal sensing position, and potentially paving the way for new applications of flexoelectric sensing technology.